cour statiqtique s2 : les indices

<div class="separator" style="clear: both; text-align: center;"> <a href="https://www.blogger.com/blogger.g?blogID=5451411611633370691" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">LES  INDICES<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody> <tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj-2S6BLDEisr4fM_Hlcn_HuMaIk5Q90BrhTRlToa7Y7d-ly6Bx30zZnDwqykqvcstlrVDEX4GH-XDVZO5AK8bQMZqdaW0S3U53JwcJMfC-CaXgBXq4ulRzkhQi45vRcsJ41HxMb1D5DyC/s1600/statistique.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="cour statiqtique s2 : les indices" border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj-2S6BLDEisr4fM_Hlcn_HuMaIk5Q90BrhTRlToa7Y7d-ly6Bx30zZnDwqykqvcstlrVDEX4GH-XDVZO5AK8bQMZqdaW0S3U53JwcJMfC-CaXgBXq4ulRzkhQi45vRcsJ41HxMb1D5DyC/s1600/statistique.jpg" title="cour statiqtique s2 : les indices" width="200" /></a></td></tr> <tr><td class="tr-caption" style="text-align: center;">cour statiqtique s2 : les indices</td></tr> </tbody></table> <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Généralités :<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> Dans le domaine économique on se trouve en présence de grandeurs pour lesquelles on a d'autant plus de difficultés à saisir leur évolution dans le temps ou dans l'espace ou à la fois dans le temps et dans l'espace .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Exemples : <o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 33.0pt;"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-    Qu'est ce qu'un niveau de vie ?<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Comment évolue un pouvoir d'achat ?<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Il faut alors des instruments de mesure qui peuvent donner des renseignements et une image dynamique de ces phénomènes .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Ces instruments sont appelés les indices .<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> Définition :<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Un indice est un nombre sans dimension permettant de suivre l'évolution et de comparer les valeurs d'une même grandeur susceptible de varier dans différentes situations (temps ; espace ; catégorie socioprofessionnelle …).<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les grandeurs peuvent être soit :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Simples alors l'indice est dit simple ou élémentaire .<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Complexes alors l'indice est dit synthétique .<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> </span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les indices simples :   <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Calcul de l'indice simple .  <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L'indice étant sans dimension, la connaissance d'une seule valeur n'a donc pas de signification en soi ; par contre la comparaison de plusieurs valeurs apporte une information .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On fixe une situation de base comme référence 0.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">La valeur de la grandeur X observée dans cette situation de base sera notée X₀ .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">La même grandeur prenant la valeur X_tdans la situation t.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On peut définir l'indice simple (dit élémentaire) de la grandeur X dans la situation t relativement à la situation de référence 0, le rapport :<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 60.2pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 63.8pt;" valign="top" width="85"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">I_t/0 = <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:21pt; height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025" width="28" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1451462833"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Pour des raisons de simple commodité pratique de l'expression de l'indice, le résultat de ce rapport est généralement multiplié par 100, soit :<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 60.2pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">I_t/0 =<span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style='width:21pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1026" width="28" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1451462834"> </o:OLEObject> </xml><![endif]-->.100<o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L'interprétation d'un indice simple doit citer la grandeur étudiée, les situations concernées, la valeur et le sens de variation. <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si I_t/0</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">></span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100 , soit  a = I_t/0- 100 .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On dit que la grandeur X a connu une augmentation de a % entre la situationde référence 0 et la situation t.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si I_t/0 </span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100, soit d = 100 - I_t/0 .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On dit que la grandeur X a connu une diminution de d % entre la situation de référence 0 et la situation t.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Remarque : Dans la définition précédente on a employé le terme général de situations; le plus souvent il s'agit d'époques .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">t sera donc l'époque d'observation ou de calcul de l'indice et <st1:metricconverter productid="0 l" w:st="on">0 l</st1:metricconverter>'époque de base.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Exemple : Supposons qu'à une date donnée 0, le prix d'une certaine marchandise soit P₀= 4 dh l'unité . Supposons qu'à une date ultérieure le prix de cette même marchandise soit P_t = 5,20 dh l'unité .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On cherche l'indice simple du prix de la marchandise étudiée à la date t calculée sur la base 100 à la date de référence 0.<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">          I_t/0 = <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style='width:44.25pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image004.gif" v:shapes="_x0000_i1027" width="59" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1451462835"> </o:OLEObject> </xml><![endif]-->  =  <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1028" type="#_x0000_t75" style='width:81.75pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image005.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1028" width="109" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1451462836"> </o:OLEObject> </xml><![endif]-->.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On remarque que I_t/0</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">></span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">100  donc a = 130 - 100 = 30.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On dit que la marchandise étudiée a connu une augmentation de son prix unitaire de 30 % entre la date de référence 0 et la date d'observation t.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Ainsi on peut dire qu'on dépense 130 dh à la date t pour acquérir la même marchandise qui coûtait 100 dh à la date de base 0.<o:p></o:p></span></div> <div class="MsoNormal"> <b><u><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Propriétés des indices simples</span></u></b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Trois propriétés essentielles caractérisent les indices simples .<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l3 level1 lfo2; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">a)<span style="font-size: 7pt;">     </span></span><!--[endif]--><b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L'identité</span></b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> : Il y a identité lorsque la valeur de l'indice est égale à 100.<o:p></o:p></span></div> <div class="MsoNormal"> <b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">I_t/0 = <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1029" type="#_x0000_t75" style='width:77.25pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image007.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image008.gif" v:shapes="_x0000_i1029" width="103" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1451462837"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></b></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Cela signifie<b> </b>que X_t = X₀c'est à dire que la grandeur X étudiée n'a pas enregistré de variation à la date t par rapport à la date de référence 0.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Exemple : Un journal vendu à 2,50 dh à la date de référence 0 (an 1999) est toujours vendu à 2,50 dh à la date d'observation t (an 2004).<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">I_t/0=<span style="mso-text-raise: -14.0pt; position: relative; top: 14.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1030" type="#_x0000_t75" style='width:83.25pt;height:33pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image009.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="44" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image010.gif" v:shapes="_x0000_i1030" width="111" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1030" DrawAspect="Content" ObjectID="_1451462838"> </o:OLEObject> </xml><![endif]-->.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l3 level1 lfo2; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">b)<span style="font-size: 7pt;">    </span></span><!--[endif]--><b><u><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">La réversibilité</span></u></b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> : Il y a réversibilité lorsque le produit de l'indice d'une grandeur à la date t calculée sur la base 100 à la date de référence 0 par  l'indice de la même grandeur à la date 0 calculée sur la base 100 à la date t est égal à 10⁴.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">                           I_t/0 <span style="mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" style='width:9pt;height:9.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image011.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="13" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image012.gif" v:shapes="_x0000_i1031" width="12" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1031" DrawAspect="Content" ObjectID="_1451462839"> </o:OLEObject> </xml><![endif]--> I_0/t = 10⁴<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">En effet :<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">          I_t/0= <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75" style='width:48pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image013.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image014.gif" v:shapes="_x0000_i1032" width="64" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1032" DrawAspect="Content" ObjectID="_1451462840"> </o:OLEObject> </xml><![endif]-->     et      I_0/t = <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" style='width:48pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image015.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image016.gif" v:shapes="_x0000_i1033" width="64" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1033" DrawAspect="Content" ObjectID="_1451462841"> </o:OLEObject> </xml><![endif]-->   d'où   I_t/0</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">´</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> I_0/t =10000<span style="mso-text-raise: -5.0pt; position: relative; top: 5.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1034" type="#_x0000_t75" style='width:1in;height:17.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image017.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="23" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image018.gif" v:shapes="_x0000_i1034" width="96" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1034" DrawAspect="Content" ObjectID="_1451462842"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Ce qui montre qu'un indice simple est réversible .<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l3 level1 lfo2; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">c)<span style="font-size: 7pt;">     </span></span><!--[endif]--><b><u><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">La transférabilité ou la circularité d'un indice</span></u></b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Considérons les mesures X₀, X_tet X_t' d'une grandeur aux dates  0, t et t'.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Soit les trois indices simples suivants :<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">  I_t/0= <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75" style='width:48pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image013.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image014.gif" v:shapes="_x0000_i1035" width="64" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035" DrawAspect="Content" ObjectID="_1451462843"> </o:OLEObject> </xml><![endif]-->  ;  I_t'/0= <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1036" type="#_x0000_t75" style='width:48pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image019.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.gif" v:shapes="_x0000_i1036" width="64" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036" DrawAspect="Content" ObjectID="_1451462844"> </o:OLEObject> </xml><![endif]-->   ;    I_t'/t  = <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75" style='width:48pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image021.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image022.gif" v:shapes="_x0000_i1037" width="64" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037" DrawAspect="Content" ObjectID="_1451462845"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">  On dit qu'un indice simple est transférable si :   I_t'/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75" style='width:21.75pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image023.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image024.gif" v:shapes="_x0000_i1038" width="29" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1038" DrawAspect="Content" ObjectID="_1451462846"> </o:OLEObject> </xml><![endif]-->I_t'/t<span style="mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75" style='width:9pt;height:9.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image011.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="13" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image012.gif" v:shapes="_x0000_i1039" width="12" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1039" DrawAspect="Content" ObjectID="_1451462847"> </o:OLEObject> </xml><![endif]-->I_t/0 .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Autrement dit  <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75" style='width:78.75pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image025.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image026.gif" v:shapes="_x0000_i1040" width="105" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1040" DrawAspect="Content" ObjectID="_1451462848"> </o:OLEObject> </xml><![endif]-->.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Ce qui montre qu'un indice simple est transférable .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Exemple : Soit le prix du litre du gasoil au Maroc aux dates suivantes :<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Juillet      1996 (date 0)  P₀ =  4 dh.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Octobre   1996 (date t)   P_t =  4,32 dh.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Février    1997 (date t')  P_t' =  5,40 dh.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Calculons les indices simples :<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">I_t/0 = <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1041" type="#_x0000_t75" style='width:135pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image027.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image028.gif" v:shapes="_x0000_i1041" width="180" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1041" DrawAspect="Content" ObjectID="_1451462849"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">I_t'/0= <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1042" type="#_x0000_t75" style='width:135.75pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image029.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image030.gif" v:shapes="_x0000_i1042" width="181" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1042" DrawAspect="Content" ObjectID="_1451462850"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">I_t'/t = <span style="mso-text-raise: -15.0pt; position: relative; top: 15.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1043" type="#_x0000_t75" style='width:135.75pt;height:35.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image031.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="47" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image032.gif" v:shapes="_x0000_i1043" width="181" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1043" DrawAspect="Content" ObjectID="_1451462851"> </o:OLEObject> </xml><![endif]-->.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On vérifie aisément que    I_t'/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75" style='width:21.75pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image023.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image024.gif" v:shapes="_x0000_i1044" width="29" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1044" DrawAspect="Content" ObjectID="_1451462852"> </o:OLEObject> </xml><![endif]-->I_t'/t<span style="mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1045" type="#_x0000_t75" style='width:9pt;height:9.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image011.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="13" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image012.gif" v:shapes="_x0000_i1045" width="12" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1045" DrawAspect="Content" ObjectID="_1451462853"> </o:OLEObject> </xml><![endif]-->I_t/0<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Soit  135 = <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1046" type="#_x0000_t75" style='width:21.75pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image023.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image024.gif" v:shapes="_x0000_i1046" width="29" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1046" DrawAspect="Content" ObjectID="_1451462854"> </o:OLEObject> </xml><![endif]-->(125<span style="mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1047" type="#_x0000_t75" style='width:9pt;height:9.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image011.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="13" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image012.gif" v:shapes="_x0000_i1047" width="12" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1047" DrawAspect="Content" ObjectID="_1451462855"> </o:OLEObject> </xml><![endif]-->108) . <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> <u>Les indices synthétiques</u> :<o:p></o:p></span></b></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Généralités : </span></b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">La recherche d'un indice<b> </b>peut ne pas être<b> </b>limitée à la comparaison des mesures d'une seule grandeur aux époques de référence 0 <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">et d'observation t.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On peut en effet envisager de caractériser avec un indice l'évolution de plusieurs grandeurs et de calculer non plus un indice simple mais un indice synthétique .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On distingue deux types d'indices synthétiques :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les indices synthétiques simples qui représentent une moyenne arithmétique simple d'indices élémentaires.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les indices synthétiques pondérés qui représentent une moyenne pondérée d'indices simples .<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> </span></div> <div class="MsoNormal"> <b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Principe de construction des indices synthétiques</span></b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> .<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Construire un indice synthétique , c'est résumer en une seule valeur un grand nombre d'observations de plusieurs grandeurs.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">La construction d'un indice synthétique nécessite :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">a)<span style="font-size: 7pt;">     </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Le choix du nombre d'éléments à retenir, c'est à dire l'échantillon d'éléments jugé représentatif.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">b)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">La nature des éléments à retenir :<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Il convient de retenir des éléments remplissant les deux conditions suivantes :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Chaque élément retenu devant être en rapport aussi faible que possible avec les autres éléments également retenus.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Chaque élément retenu devant être en rapport aussi fort que possible avec les autres éléments non retenus susceptibles de figurer dans l'échantillon.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">c)<span style="font-size: 7pt;">     </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Mode de calcul :<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Le statisticien doit d'abord justifier le choix entre le calcul de l'indice des moyennes ou la moyenne des indices.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Exemple : A partir d'une enquête statistique, on a obtenu les prix d'un kg de viande, d'un litre d'huile, d'un kg de sucre et d'un kg de beurre au cours des périodes 0 et t .<o:p></o:p></span></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <br /></div> </td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <st1:metricconverter productid="1 kg" w:st="on"><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1 kg</span></st1:metricconverter><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> de viande  <o:p></o:p></span></div> </td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1L d'huile <o:p></o:p></span></div> </td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <st1:metricconverter productid="1 kg" w:st="on"><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1 kg</span></st1:metricconverter><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> de sucre <o:p></o:p></span></div> </td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <st1:metricconverter productid="1 kg" w:st="on"><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1 kg</span></st1:metricconverter><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> de beurre<o:p></o:p></span></div> </td> </tr> <tr> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Prix P₀(dh)<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         50<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         6<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         4<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">        20<o:p></o:p></span></div> </td> </tr> <tr> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Prix P_t(dh)<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         70<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         9<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         5<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">        30<o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">     <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On va calculer l'indice des moyennes arithmétiques des prix et la moyenne arithmétique des indices des prix de chaque produit .<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l5 level1 lfo4; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1)<span style="font-size: 7pt;">    </span></span><!--[endif]--><b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L'indice des moyennes</span></b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> <b>des prix </b>:<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On calcule les moyennes arithmétiques des prix P₀et P_t .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1048" type="#_x0000_t75" style='width:15.75pt;height:17.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image033.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="23" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image034.gif" v:shapes="_x0000_i1048" width="21" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1048" DrawAspect="Content" ObjectID="_1451462856"> </o:OLEObject> </xml><![endif]--> <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1049" type="#_x0000_t75" style='width:135.75pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image035.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image036.gif" v:shapes="_x0000_i1049" width="181" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1049" DrawAspect="Content" ObjectID="_1451462857"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75" style='width:15pt;height:17.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image037.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="23" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image038.gif" v:shapes="_x0000_i1050" width="20" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1050" DrawAspect="Content" ObjectID="_1451462858"> </o:OLEObject> </xml><![endif]--><span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1051" type="#_x0000_t75" style='width:149.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image039.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image040.gif" v:shapes="_x0000_i1051" width="199" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1051" DrawAspect="Content" ObjectID="_1451462859"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L'indice des moyennes des prix est :       I_t/0 = <span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1052" type="#_x0000_t75" style='width:2in;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image041.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image042.gif" v:shapes="_x0000_i1052" width="192" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1052" DrawAspect="Content" ObjectID="_1451462861"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">2) <b>La moyenne des indices </b>:<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Cherchons d'abord pour chaque produit la valeur de l'indice élémentaire des prix à la période t calculée sur la base 100 à la période de référence 0.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> Indice des prix de la viande    (<st1:metricconverter productid="1 kg" w:st="on">1 kg</st1:metricconverter>)      : I_t/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1053" type="#_x0000_t75" style='width:74.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image043.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image044.gif" v:shapes="_x0000_i1053" width="99" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1053" DrawAspect="Content" ObjectID="_1451462862"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice des prix de l'huile         (<st1:metricconverter productid="1 litre" w:st="on">1 litre</st1:metricconverter>)     :  I_t/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1054" type="#_x0000_t75" style='width:68.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image045.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image046.gif" v:shapes="_x0000_i1054" width="91" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1054" DrawAspect="Content" ObjectID="_1451462863"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice des prix du sucre          (<st1:metricconverter productid="1 kg" w:st="on">1 kg</st1:metricconverter>)       :  I_t/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1055" type="#_x0000_t75" style='width:68.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image047.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image048.gif" v:shapes="_x0000_i1055" width="91" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1055" DrawAspect="Content" ObjectID="_1451462864"> </o:OLEObject> </xml><![endif]--> <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice des prix du beurre        (<st1:metricconverter productid="1 kg" w:st="on">1 kg</st1:metricconverter>)       :  I_t/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1056" type="#_x0000_t75" style='width:74.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image049.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image050.gif" v:shapes="_x0000_i1056" width="99" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1056" DrawAspect="Content" ObjectID="_1451462865"> </o:OLEObject> </xml><![endif]--> <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">La moyenne arithmétique des indices des prix entre les  périodes 0 et t est : <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">I_t/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1057" type="#_x0000_t75" style='width:150pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image051.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image052.gif" v:shapes="_x0000_i1057" width="200" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1057" DrawAspect="Content" ObjectID="_1451462866"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On remarque que la moyenne arithmétique des indices des prix (141,25) est différente de l'indice des moyennes arithmétique des prix (142,5).<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Pour justifier le choix on élimine celui qui change avec le changement des unités des produits .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Reprenons le tableau précédent dans lequel remplaçons par exemple  l'unité le litre de l'huile par le mètre cube (<st1:metricconverter productid="1000 litres" w:st="on">1000 litres</st1:metricconverter>) et le kg du sucre par la tonne soit (<st1:metricconverter productid="1000 kg" w:st="on">1000 kg</st1:metricconverter>), on aura le tableau suivant :<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <br /></div> </td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <st1:metricconverter productid="1 kg" w:st="on"><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1 kg</span></st1:metricconverter><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> de viande<o:p></o:p></span></div> </td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1m³ d'huile<o:p></o:p></span></div> </td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1 tonne sucre<o:p></o:p></span></div> </td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <st1:metricconverter productid="1 kg" w:st="on"><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1 kg</span></st1:metricconverter><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> de beurre<o:p></o:p></span></div> </td> </tr> <tr> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Prix   P₀(dh)<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         50<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">      6000<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">      4000<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         20<o:p></o:p></span></div> </td> </tr> <tr> <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Prix   P_t(dh)<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         70<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">      9000<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">      5000<o:p></o:p></span></div> </td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 92.1pt;" valign="top" width="123"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">         30<o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal" style="margin-left: 33.0pt;"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">  <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Reprenons les mêmes calculs que précédemment et calculons l'indice des moyennes arithmétiques des prix :<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On calcule d'abord les nouvelles moyennes arithmétiques des prix P₀ et P_t.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -6.0pt; position: relative; top: 6.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1058" type="#_x0000_t75" style='width:15pt;height:20.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image053.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="27" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image054.gif" v:shapes="_x0000_i1058" width="20" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1058" DrawAspect="Content" ObjectID="_1451462867"> </o:OLEObject> </xml><![endif]--> =<span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1059" type="#_x0000_t75" style='width:200.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image055.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image056.gif" v:shapes="_x0000_i1059" width="267" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1059" DrawAspect="Content" ObjectID="_1451462868"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -6.0pt; position: relative; top: 6.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1060" type="#_x0000_t75" style='width:14.25pt;height:20.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image057.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="27" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image058.gif" v:shapes="_x0000_i1060" width="19" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1060" DrawAspect="Content" ObjectID="_1451462869"> </o:OLEObject> </xml><![endif]--> =<span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1061" type="#_x0000_t75" style='width:189.75pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image059.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image060.gif" v:shapes="_x0000_i1061" width="253" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1061" DrawAspect="Content" ObjectID="_1451462870"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">D'où l'indice des moyennes :  I_t/0= <span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1062" type="#_x0000_t75" style='width:147.75pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image061.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image062.gif" v:shapes="_x0000_i1062" width="197" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1062" DrawAspect="Content" ObjectID="_1451462871"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> On remarque que l'indice des moyennes a changé avec le changement des unités (140 </span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">¹</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">142,5).<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Calculons maintenant la moyenne arithmétique des indices des prix de chacun des quatre produits.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice des prix de la viande           (<st1:metricconverter productid="1 kg" w:st="on">1 kg</st1:metricconverter>)   : I_t/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1063" type="#_x0000_t75" style='width:74.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image043.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image044.gif" v:shapes="_x0000_i1063" width="99" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1063" DrawAspect="Content" ObjectID="_1451462872"> </o:OLEObject> </xml><![endif]--> <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice des prix de l'huile               (1m³)   :  I_t/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1064" type="#_x0000_t75" style='width:86.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image063.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image064.gif" v:shapes="_x0000_i1064" width="115" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1064" DrawAspect="Content" ObjectID="_1451462873"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice des prix du sucre                (1 t)     :  I_t/0 = <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1065" type="#_x0000_t75" style='width:86.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image065.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image066.gif" v:shapes="_x0000_i1065" width="115" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1065" DrawAspect="Content" ObjectID="_1451462874"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice des prix du beurre              (<st1:metricconverter productid="1 kg" w:st="on">1 kg</st1:metricconverter>)  :  I_t/0  = <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1066" type="#_x0000_t75" style='width:74.25pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image049.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image050.gif" v:shapes="_x0000_i1066" width="99" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1066" DrawAspect="Content" ObjectID="_1451462875"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">D'où la moyenne arithmétique des indices des prix est :<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1067" type="#_x0000_t75" style='width:9.75pt;height:15.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image067.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="21" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image068.gif" v:shapes="_x0000_i1067" width="13" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1067" DrawAspect="Content" ObjectID="_1451462876"> </o:OLEObject> </xml><![endif]-->_t/0= <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1068" type="#_x0000_t75" style='width:150pt;height:30.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image069.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image052.gif" v:shapes="_x0000_i1068" width="200" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1068" DrawAspect="Content" ObjectID="_1451462877"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On remarque que la moyenne arithmétique des indices des prix est insensible aux changements des unités .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">En conclusion l'indice des moyennes n'est pratiquement jamais utilisé puisque l'utilisation d'unités différentes (multiples ou sous multiples des unités) conduit à un indice différent, ce qui est tout à fait illogique du point de vue économique.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Conséquence : Le mode de calcul le plus approprié est la moyenne arithmétique des indices.    <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <b><u><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Principaux types d'indices:<o:p></o:p></span></u></b></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les formules d'indices sont nombreuses, cependant dans la pratique, elles se réduisent à un petit nombre de types dont les principaux sont ceux de LASPEYRES et de PAASCHE qui portent essentiellement sur les prix et les quantités .<o:p></o:p></span></div> <div class="MsoNormal"> <b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les indices de LASPEYRES</span></b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">.<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On notera :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">P_i.o et Q_i.orespectivement le prix et la quantité du i^ème produit à l'époque de référence 0.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 51.0pt; mso-list: l1 level1 lfo1; tab-stops: list 51.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">-<span style="font-size: 7pt;">         </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">P_i.tet Q_i.trespectivement le prix et la quantité du i^ème produit à l'époque d'observation t.<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L'indice des prix de LASPEYRES.<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 67.3pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 11.0cm;" valign="top" width="416"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L_p = <span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1069" type="#_x0000_t75" style='width:90pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image070.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image071.gif" v:shapes="_x0000_i1069" width="120" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1069" DrawAspect="Content" ObjectID="_1451462878"> </o:OLEObject> </xml><![endif]--> = <span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1070" type="#_x0000_t75" style='width:159pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image072.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image073.gif" v:shapes="_x0000_i1070" width="212" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1070" DrawAspect="Content" ObjectID="_1451462879"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On dit que le coefficient de pondération de l'indice des prix est : P_i.o<span style="mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1071" type="#_x0000_t75" style='width:9pt;height:9.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image011.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="13" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image012.gif" v:shapes="_x0000_i1071" width="12" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1071" DrawAspect="Content" ObjectID="_1451462880"> </o:OLEObject> </xml><![endif]-->Q_i.o.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Remarques :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 21.75pt; mso-list: l4 level1 lfo5; tab-stops: list 21.75pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si L_p</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">></span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100 : soit a = L_p</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">-</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">100, on dit que les prix ont augmenté de a % entre la période de référence 0 et la période d'observation t.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 21.75pt; mso-list: l4 level1 lfo5; tab-stops: list 21.75pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">2)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si L_p</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100 : soit d = 100 </span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">-</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> L_p , on dit que les prix ont diminué de d % entre la période de référence 0 et la période d'observation t.<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">                    <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">7.5.1.2 L'indice des quantités de LASPEYRES .<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 33.0pt;"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 67.3pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 11.0cm;" valign="top" width="416"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L_q = <span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1072" type="#_x0000_t75" style='width:87pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image074.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image075.gif" v:shapes="_x0000_i1072" width="116" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1072" DrawAspect="Content" ObjectID="_1451462881"> </o:OLEObject> </xml><![endif]-->=<span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1073" type="#_x0000_t75" style='width:162pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image076.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image077.gif" v:shapes="_x0000_i1073" width="216" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1073" DrawAspect="Content" ObjectID="_1451462882"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal" style="margin-left: 33.0pt;"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">On dit de même que le coefficient de pondération de l'indice des quantités est : Q_i.o<span style="mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1074" type="#_x0000_t75" style='width:9pt;height:9.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image011.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="13" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image012.gif" v:shapes="_x0000_i1074" width="12" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1074" DrawAspect="Content" ObjectID="_1451462883"> </o:OLEObject> </xml><![endif]-->P_{i.o<o:p></o:p>}</span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Remarques :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l7 level1 lfo6; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si L_q</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">></span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100 , soit a = L_q</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">-</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100, on dit que les quantités ont augmenté entre la période de référence 0 et la période d'observation t.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l7 level1 lfo6; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">2)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si L_q</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100 , soit d = 100 </span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">-</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> L_q, on dit que les quantités ont diminué de d % entre la période de référence 0 et la période d'observation t.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 33.0pt;"> <br /></div> <div class="MsoNormal" style="margin-left: 33.0pt;"> <b><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les indices de PAASCHE <o:p></o:p></span></b></div> <div class="MsoNormal" style="margin-left: 33.0pt;"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice de LASPEYRES des valeurs globales <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 124.0pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 5.0cm;" valign="top" width="189"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L_vg = <span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1075" type="#_x0000_t75" style='width:90pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image078.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image079.gif" v:shapes="_x0000_i1075" width="120" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1075" DrawAspect="Content" ObjectID="_1451462884"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les indices de PAASCHE<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice de PAASCHE des prix  <o:p></o:p></span></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 124.0pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 5.0cm;" valign="top" width="189"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"><span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1076" type="#_x0000_t75" style='width:114pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image080.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image081.gif" v:shapes="_x0000_i1076" width="152" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1076" DrawAspect="Content" ObjectID="_1451462885"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Remarques :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l0 level1 lfo7; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si P_p</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">></span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100, soit a = P_p</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">-</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100; on dit que les prix ont augmenté de a % entre l'époque de référence 0 et l'époque d'observation t.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l0 level1 lfo7; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">2)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si Pp </span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100, soit d = 100 </span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">-</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> P_p ; on dit que les prix ont diminué de d % entre l'époque de référence 0 et la période d'observation t.<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice de PAASCHE des quantités <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 124.0pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 5.0cm;" valign="top" width="189"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">P_q = <span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1077" type="#_x0000_t75" style='width:89.25pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image082.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image083.gif" v:shapes="_x0000_i1077" width="119" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1077" DrawAspect="Content" ObjectID="_1451462886"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Remarque :<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l6 level1 lfo8; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">1)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si P_q</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">></span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100, soit a = P_q</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">-</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100 ; on dit que les quantités ont augmenté de a % entre l'époque de référence 0 et l'époque d'observation t.<o:p></o:p></span></div> <div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l6 level1 lfo8; tab-stops: list 18.0pt; text-indent: -18.0pt;"> <!--[if !supportLists]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">2)<span style="font-size: 7pt;">    </span></span><!--[endif]--><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Si P_q</span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> 100 , soit d = 100 </span><span style="font-family: Symbol; font-size: 14.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">-</span><span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;"> P_q; on dit que les quantités ont diminué de d % entre l'époque de référence 0 et l'époque d'observation t .<o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice de PAASCHE des valeurs globales <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 124.0pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 5.0cm;" valign="top" width="189"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">P_{vg  =}<span style="mso-text-raise: -16.0pt; position: relative; top: 16.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1078" type="#_x0000_t75" style='width:90pt;height:38.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image078.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="51" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image079.gif" v:shapes="_x0000_i1078" width="120" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1078" DrawAspect="Content" ObjectID="_1451462887"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Les indices de FISHER <o:p></o:p></span></div> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">L'indice de FISHER est la moyenne géométrique des deux indices de LASPEYRES et de PAASCHE . Il compris entre ces deux indices et vient pallier à leurs carences .<o:p></o:p></span></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 145.25pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 70.9pt;" valign="top" width="95"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">F = <span style="mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1079" type="#_x0000_t75" style='width:38.25pt;height:17.25pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image084.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="23" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image085.gif" v:shapes="_x0000_i1079" width="51" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1079" DrawAspect="Content" ObjectID="_1451462888"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice de LASPEYRES des prix <o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 116.9pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">F_p = <span style="mso-text-raise: -8.0pt; position: relative; top: 8.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1080" type="#_x0000_t75" style='width:48.75pt;height:21.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image086.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="29" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image087.gif" v:shapes="_x0000_i1080" width="65" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1080" DrawAspect="Content" ObjectID="_1451462889"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">Indice de FISHER des quantités<o:p></o:p></span></div> <div class="MsoNormal"> <br /></div> <table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 116.9pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 3.5pt 0cm 3.5pt; mso-table-layout-alt: fixed;"> <tbody> <tr style="height: 27.15pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;"> <td style="border: solid windowtext 1.0pt; height: 27.15pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 3.5pt 0cm 3.5pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal"> <span style="font-size: 14.0pt; mso-bidi-font-size: 10.0pt;">F_q = <span style="mso-text-raise: -8.0pt; position: relative; top: 8.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1081" type="#_x0000_t75" style='width:47.25pt;height:21.75pt' o:ole="" fillcolor="window"> <v:imagedata src="file:///C:\DOCUME~1\STAGIA~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image088.wmz" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img height="29" src="file:///C:/DOCUME~1/STAGIA~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image089.gif" v:shapes="_x0000_i1081" width="63" /><!--[endif]--></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1081" DrawAspect="Content" ObjectID="_1451462890"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></div> </td> </tr> </tbody></table> <br /> <div class="MsoNormal"> cours fsjes maroc</div>

cour statiqtique s2 : les indices

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