{"id":1959,"date":"2023-11-22T22:25:30","date_gmt":"2023-11-22T21:25:30","guid":{"rendered":"http:\/\/localhost:8080\/maxblog\/?p=1959"},"modified":"2023-11-22T22:28:19","modified_gmt":"2023-11-22T21:28:19","slug":"utiliser-linformation-chiffree-et-statistique-descriptive","status":"publish","type":"post","link":"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/","title":{"rendered":"Utiliser l\u2019information chiffr\u00e9e et statistique descriptive"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1959\" class=\"elementor elementor-1959\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7d71a4a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d71a4a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-389cd7d\" data-id=\"389cd7d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a8169f1 elementor-widget elementor-widget-spacer\" data-id=\"a8169f1\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7643655 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7643655\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f297427\" data-id=\"f297427\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-361d80f elementor-widget elementor-widget-heading\" data-id=\"361d80f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-xl\">Utiliser l\u2019information chiffr\u00e9e et statistique descriptive<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-de06178 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de06178\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-c8b729b\" data-id=\"c8b729b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-1f07f28\" data-id=\"1f07f28\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b7c611b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7c611b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9a7e2c2\" data-id=\"9a7e2c2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fffe349 nc-justify-text elementor-widget elementor-widget-text-editor\" data-id=\"fffe349\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#Introduction\" >Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#Cours\" >Cours<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#1_Proportion_et_pourcentage_dune_sous-population_dans_une_population\" >1. Proportion et pourcentage d&rsquo;une\nsous-population dans une population<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#2_Ensembles_de_reference_inclus_les_uns_dans_les_autres_pourcentage_de_pourcentage\" >2. Ensembles de r\u00e9f\u00e9rence inclus les uns\ndans les autres : pourcentage de pourcentage<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#3_Evolution_variation_absolue_et_variation_relative\" >3. \u00c9volution : variation absolue et\nvariation relative<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#4_Evolutions_successives_evolution_reciproque\" >4. \u00c9volutions successives, \u00e9volution\nr\u00e9ciproque<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#5_Indicateurs_de_tendance_centrale_moyenne_ponderee\" >5. Indicateurs de tendance centrale :\nmoyenne pond\u00e9r\u00e9e<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#6_Linearite_de_la_moyenne\" >6. Lin\u00e9arit\u00e9 de la moyenne<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#7_Indicateurs_de_dispersion_ecart_interquartile_ecart_type\" >7. Indicateurs de dispersion : \u00e9cart\ninterquartile, \u00e9cart type<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#Methodes\" >M\u00e9thodes<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#1_Exploiter_la_relation_entre_effectifs_proportions_et_pourcentages\" >1. Exploiter la relation entre effectifs,\nproportions et pourcentages<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#2_Traiter_des_situations_simples_mettant_en_jeu_des_pourcentages_de_pourcentages\" >2. Traiter des situations simples mettant en\njeu des pourcentages de pourcentages<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#3_Exploiter_la_relation_entre_deux_valeurs_successives_et_leur_taux_devolution\" >3. Exploiter la relation entre deux valeurs\nsuccessives et leur taux d&rsquo;\u00e9volution<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#4_Calculer_le_taux_devolution_global_et_le_taux_devolution_reciproque\" >4. Calculer le taux d&rsquo;\u00e9volution global et le\ntaux d&rsquo;\u00e9volution r\u00e9ciproque<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.maxdecours.com\/maxblog\/utiliser-linformation-chiffree-et-statistique-descriptive\/#5_Decrire_verbalement_les_differences_entre_deux_series_statistiques\" >5. D\u00e9crire verbalement les diff\u00e9rences entre\ndeux s\u00e9ries statistiques<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction <span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Comprendre et utiliser l&rsquo;information chiffr\u00e9e et la\nstatistique descriptive permet d&rsquo;analyser et d&rsquo;interpr\u00e9ter des donn\u00e9es de\nmani\u00e8re efficace et significative. Ces outils et concepts sont fondamentaux\ndans divers domaines tels que la recherche, l&rsquo;\u00e9conomie, la science, et bien\nplus encore.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Cours\"><\/span>Cours<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Proportion_et_pourcentage_dune_sous-population_dans_une_population\"><\/span><span style=\"font-size:14.0pt\">1. Proportion et pourcentage d&rsquo;une\nsous-population dans une population<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">La <b>proportion<\/b> exprime une partie par rapport \u00e0 un\ntout, et le <b>pourcentage<\/b> est la proportion multipli\u00e9e par 100. <\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Proportion =\n\\frac{Taille\\:de\\:la\\:sous-population}{Taille\\:de\\:la\\:population\\:totale} <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Pourcentage = Proportion \\times 100 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Consid\u00e9rons une classe de 30 \u00e9l\u00e8ves\ncomprenant 15 filles.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Proportion\\:de\\:filles = \\frac{15}{30} = 0,5 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Pourcentage\\:de\\:filles = 0,5 \\times 100 = 50\\% <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Ensembles_de_reference_inclus_les_uns_dans_les_autres_pourcentage_de_pourcentage\"><\/span><span style=\"font-size:14.0pt\">2. Ensembles de r\u00e9f\u00e9rence inclus les uns\ndans les autres : pourcentage de pourcentage<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Il est possible de calculer un pourcentage d&rsquo;une\nsous-population, puis de prendre un pourcentage de ce r\u00e9sultat.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Parmi les 15 filles, 9 aiment lire.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Pourcentage\\:des\\:filles\\:qui\\:aiment\\:lire =\n\\frac{9}{15} \\times 100 = 60\\% <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\">\nPourcentage\\:total\\:d&#039;\u00e9l\u00e8ves\\:qui\\:sont\\:des\\:filles\\:aimant\\:lire = 50\\%\n\\times 60\\% = 30\\% <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"3_Evolution_variation_absolue_et_variation_relative\"><\/span><span style=\"font-size:14.0pt\">3. \u00c9volution : variation absolue et\nvariation relative<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Variation absolue<\/b> : C&rsquo;est la diff\u00e9rence entre la\nvaleur finale et la valeur initiale.<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Variation\\:Absolue = Valeur\\:Finale &#8211;\nValeur\\:Initiale <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Variation relative<\/b> : C&rsquo;est la variation absolue\nexprim\u00e9e en pourcentage de la valeur initiale.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Variation\\:Relative =\n\\frac{Variation\\:Absolue}{Valeur\\:Initiale} \\times 100 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Si le prix d&rsquo;un livre passe de 10\u20ac \u00e0 12\u20ac,<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Variation\\:Absolue = 12\u20ac &#8211; 10\u20ac = 2\u20ac <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Variation\\:Relative = \\frac{2\u20ac}{10\u20ac} \\times 100 =\n20\\% <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"4_Evolutions_successives_evolution_reciproque\"><\/span><span style=\"font-size:14.0pt\">4. \u00c9volutions successives, \u00e9volution\nr\u00e9ciproque<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>\u00c9volutions successives<\/b> : Les coefficients\nmultiplicateurs se multiplient entre eux lorsqu&rsquo;une valeur subit plusieurs\n\u00e9volutions.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Coefficient\\:Total = Coefficient_1 \\times\nCoefficient_2 \\times \\ldots \\times Coefficient_n <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>\u00c9volution r\u00e9ciproque<\/b> : On utilise l&rsquo;inverse du\ncoefficient multiplicateur.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Coefficient\\:R\u00e9ciproque =\n\\frac{1}{Coefficient\\:Original} <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Un investissement de 100\u20ac augmente de 10%\npuis diminue de 10%.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Coefficient\\:total = 1,1 \\times 0,9 = 0,99 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u00c9volution\\:R\u00e9ciproque = \\frac{1}{0,99} \u2248 1,0101 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"5_Indicateurs_de_tendance_centrale_moyenne_ponderee\"><\/span><span style=\"font-size:14.0pt\">5. Indicateurs de tendance centrale :\nmoyenne pond\u00e9r\u00e9e<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">La <b>moyenne pond\u00e9r\u00e9e<\/b> est une moyenne qui prend en\ncompte l&rsquo;importance relative de chaque valeur.<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Moyenne\\:Pond\u00e9r\u00e9e = \\frac{\\sum (Valeur_i \\times\nPoids_i)}{\\sum Poids_i} <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Deux \u00e9tudiants obtiennent des notes en\nMaths (Poids=3) et Histoire (Poids=1). L&rsquo;\u00e9tudiant A a 15 en Maths et 10 en\nHistoire, l&rsquo;\u00e9tudiant B a 10 en Maths et 14 en Histoire.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Moyenne\\:Pond\u00e9r\u00e9e_A = \\frac{(15 \\times 3) + (10\n\\times 1)}{3 + 1} = 13,75 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Moyenne\\:Pond\u00e9r\u00e9e_B = \\frac{(10 \\times 3) + (14\n\\times 1)}{3 + 1} = 11 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"6_Linearite_de_la_moyenne\"><\/span><span style=\"font-size:14.0pt\">6. Lin\u00e9arit\u00e9 de la moyenne<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">La moyenne a une propri\u00e9t\u00e9 de lin\u00e9arit\u00e9.<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Moyenne(aX + b) = a \\times Moyenne(X) + b <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Un ensemble [2, 4, 6] a une moyenne de 4.\nSi chaque \u00e9l\u00e9ment est multipli\u00e9 par 2 et augment\u00e9 de 1, l&rsquo;ensemble devient [5,\n9, 13] et la moyenne est 9, soit 2 \u00d7 4 + 1.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"7_Indicateurs_de_dispersion_ecart_interquartile_ecart_type\"><\/span><span style=\"font-size:14.0pt\">7. Indicateurs de dispersion : \u00e9cart\ninterquartile, \u00e9cart type<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Quartiles<\/b> : Les quartiles divisent un ensemble de\ndonn\u00e9es ordonn\u00e9es en quatre parties \u00e9gales.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp; <\/span>&#8211; <b>Q1<\/b> est la plus\npetite valeur de l\u2019ensemble telles qu\u2019au moins 25% des donn\u00e9es soient\ninf\u00e9rieures ou \u00e9gales \u00e0 cette valeur.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp; <\/span>&#8211; <b>Q2<\/b> est la\nm\u00e9diane de l\u2019ensemble.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp; <\/span>&#8211; <b>Q3<\/b> est la\nplus petite valeur de l\u2019ensemble telles qu\u2019au moins 75% des donn\u00e9es soient\ninf\u00e9rieures ou \u00e9gales \u00e0 cette valeur.<\/p>\n\n<p class=\"MsoNormal\"><span style=\"mso-spacerun:yes\">&nbsp; <\/span>&#8211; <b>Q4<\/b> est la\nvaleur maximale de l\u2019ensemble.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Par exemple, pour d\u00e9terminer la position de Q1, on calcule <span class=\"katex-eq\" data-katex-display=\"false\">25\\%\n\\times \\text{nombre de donn\u00e9es}<\/span>. Si ce produit n&rsquo;est pas un nombre\nentier, on arrondit \u00e0 l&rsquo;entier sup\u00e9rieur pour s&rsquo;assurer d&rsquo;avoir au moins 25%\ndes donn\u00e9es en-dessous de Q1.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Pour l&rsquo;ensemble [10, 20, 30, 40, 50],<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Position\\:de\\:Q1 = 25\\% \\times 5 = 1,25 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">On arrondit \u00e0 2 pour s&rsquo;assurer que 25% des donn\u00e9es (au moins\n1 valeur) sont en-dessous de Q1. Donc, Q1 = 20.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>\u00c9cart interquartile (Q3-Q1) <\/b>: Il mesure la\ndispersion autour de la m\u00e9diane.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u00c9cart\\:Interquartile = Q3 &#8211; Q1 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>\u00c9cart type<\/b> : Il mesure \u00e0 quel point les donn\u00e9es\nsont proches de la moyenne.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u00c9cart\\:Type = \\sqrt{\\frac{\\sum (Valeur_i &#8211;\nMoyenne)^2}{Nombre\\:de\\:Valeurs}} <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Pour l&rsquo;ensemble [10, 20, 30, 40, 50],<\/p>\n\n<p class=\"MsoNormal\">&#8211; Q1 = 20, Q3 = 40<\/p>\n\n<p class=\"MsoNormal\">&#8211; \u00c9cart interquartile = 40 &#8211; 20 = 20.<\/p>\n\n<p class=\"MsoNormal\">&#8211; \u00c9cart type \u2248 14,14.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Methodes\"><\/span>M\u00e9thodes<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Exploiter_la_relation_entre_effectifs_proportions_et_pourcentages\"><\/span><span style=\"font-size:14.0pt\">1. Exploiter la relation entre effectifs,\nproportions et pourcentages<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Effectif <\/b>: C&rsquo;est le nombre total d&rsquo;\u00e9l\u00e9ments dans\nune cat\u00e9gorie.<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Proportion<\/b> : C&rsquo;est le rapport de l&rsquo;effectif d&rsquo;une\ncat\u00e9gorie \u00e0 l&rsquo;effectif total.<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Pourcentage<\/b> : C&rsquo;est la proportion multipli\u00e9e par\n100.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Proportion =\n\\frac{Effectif\\:de\\:la\\:cat\u00e9gorie}{Effectif\\:total} <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Pourcentage = Proportion \\times 100 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Traiter_des_situations_simples_mettant_en_jeu_des_pourcentages_de_pourcentages\"><\/span><span style=\"font-size:14.0pt\">2. Traiter des situations simples mettant en\njeu des pourcentages de pourcentages<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">On peut calculer un pourcentage d&rsquo;une sous-population, puis\nun autre pourcentage sur ce r\u00e9sultat. <\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Si 60% des \u00e9l\u00e8ves sont des filles et que\n70% de ces filles pratiquent un sport, alors 42% des \u00e9l\u00e8ves sont des filles\npratiquant un sport (60% \u00d7 70%).<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"3_Exploiter_la_relation_entre_deux_valeurs_successives_et_leur_taux_devolution\"><\/span><span style=\"font-size:14.0pt\">3. Exploiter la relation entre deux valeurs\nsuccessives et leur taux d&rsquo;\u00e9volution<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Le <b>taux d&rsquo;\u00e9volution<\/b> entre deux valeurs <span class=\"katex-eq\" data-katex-display=\"false\">V_1<\/span>\net <span class=\"katex-eq\" data-katex-display=\"false\">V_2<\/span> est donn\u00e9 par :<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Taux\\:d&#039;\u00e9volution = \\frac{V_2 &#8211; V_1}{V_1} \\times 100\n<\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Si le prix d&rsquo;une marchandise passe de 100\u20ac\n\u00e0 120\u20ac, le taux d&rsquo;\u00e9volution est <span class=\"katex-eq\" data-katex-display=\"false\"> \\frac{120 &#8211; 100}{100} \\times 100 = 20\\%\n<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"4_Calculer_le_taux_devolution_global_et_le_taux_devolution_reciproque\"><\/span><span style=\"font-size:14.0pt\">4. Calculer le taux d&rsquo;\u00e9volution global et le\ntaux d&rsquo;\u00e9volution r\u00e9ciproque<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Taux d&rsquo;\u00e9volution global<\/b> \u00e0 partir de taux\nd&rsquo;\u00e9volution successifs :<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> Taux\\:d&#039;\u00e9volution\\:global = (1 + \\frac{T_1}{100})\n\\times (1 + \\frac{T_2}{100}) \\times \\ldots \\times (1 + \\frac{T_n}{100}) &#8211; 1 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Taux d&rsquo;\u00e9volution r\u00e9ciproque<\/b> : Si une valeur\naugmente de <span class=\"katex-eq\" data-katex-display=\"false\">T\\%<\/span>, alors le taux d&rsquo;\u00e9volution r\u00e9ciproque est <span class=\"katex-eq\" data-katex-display=\"false\">\n\\frac{100}{100 + T} \\times 100 &#8211; 100\\% <\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Si un investissement augmente de 10% puis\ndiminue de 10%, le taux d&rsquo;\u00e9volution global est <span class=\"katex-eq\" data-katex-display=\"false\"> (1 + \\frac{10}{100})\n\\times (1 &#8211; \\frac{10}{100}) &#8211; 1 = -1\\% <\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"5_Decrire_verbalement_les_differences_entre_deux_series_statistiques\"><\/span><span style=\"font-size:14.0pt\">5. D\u00e9crire verbalement les diff\u00e9rences entre\ndeux s\u00e9ries statistiques<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Pour comparer deux s\u00e9ries statistiques, on peut :<\/p>\n\n<p class=\"MsoNormal\">&#8211; Examiner les <b>indicateurs de tendance centrale<\/b>\n(moyenne, m\u00e9diane) pour identifier o\u00f9 se situe le centre de chaque s\u00e9rie.<\/p>\n\n<p class=\"MsoNormal\">&#8211; Analyser les <b>indicateurs de dispersion<\/b> (\u00e9cart type,\n\u00e9cart interquartile) pour comprendre l&rsquo;\u00e9tendue et la variabilit\u00e9 des donn\u00e9es.<\/p>\n\n<p class=\"MsoNormal\">&#8211; Utiliser des <b>repr\u00e9sentations graphiques<\/b> (diagrammes\nen barres, bo\u00eetes \u00e0 moustaches) pour visualiser les diff\u00e9rences.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Exemple :<\/b> Deux classes peuvent avoir la m\u00eame moyenne\nen math\u00e9matiques, mais une classe peut avoir un \u00e9cart type plus \u00e9lev\u00e9,\nindiquant une plus grande vari\u00e9t\u00e9 dans les scores.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n\n\n\n\n<style>@font-face\n\t{font-family:\"Cambria Math\";\n\tpanose-1:2 4 5 3 5 4 6 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:roman;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face\n\t{font-family:Calibri;\n\tpanose-1:2 15 5 2 2 2 4 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:swiss;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536859905 -1073732485 9 0 511 0;}@font-face\n\t{font-family:\"Calibri Light\";\n\tpanose-1:2 15 3 2 2 2 4 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:swiss;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-469750017 -1073732485 9 0 511 0;}p.MsoNormal, li.MsoNormal, 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class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8392cf9\" data-id=\"8392cf9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-071e74f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"071e74f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8c43dc4\" data-id=\"8c43dc4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa0c527 elementor-widget elementor-widget-spacer\" data-id=\"aa0c527\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3c0ad71 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3c0ad71\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a39de31\" data-id=\"a39de31\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-342de24 elementor-widget elementor-widget-spacer\" data-id=\"342de24\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Utiliser l\u2019information chiffr\u00e9e et statistique descriptive Introduction &nbsp; Comprendre et utiliser l&rsquo;information chiffr\u00e9e et la statistique descriptive permet d&rsquo;analyser et d&rsquo;interpr\u00e9ter des donn\u00e9es de mani\u00e8re efficace et significative. Ces outils et concepts sont fondamentaux dans divers domaines tels que la recherche, l&rsquo;\u00e9conomie, la science, et bien plus encore. &nbsp; Cours &nbsp; 1. Proportion et pourcentage [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_canvas","format":"standard","meta":{"footnotes":""},"categories":[25,26,5],"tags":[],"_links":{"self":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1959"}],"collection":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/comments?post=1959"}],"version-history":[{"count":8,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1959\/revisions"}],"predecessor-version":[{"id":1968,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1959\/revisions\/1968"}],"wp:attachment":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/media?parent=1959"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/categories?post=1959"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/tags?post=1959"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}