{"id":162,"date":"2008-04-30T18:31:45","date_gmt":"2008-04-30T16:31:45","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/statistiques-a-deux-variables-avec-xcas\/"},"modified":"2023-10-14T20:14:03","modified_gmt":"2023-10-14T18:14:03","slug":"statistiques-a-deux-variables-avec-xcas","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/","title":{"rendered":"Statistiques \u00e0 deux variables avec Xcas"},"content":{"rendered":"

\nVoici comment on peut r\u00e9soudre un exercice classique sur les statistiques \u00e0 deux variables.<\/p>\n

Enonc\u00e9<\/h2>\n
\n

Soit la s\u00e9rie statistique suivante :<\/p>\n\n\n\n\n
$X$<\/td>\n0<\/td>\n5<\/td>\n10<\/td>\n15<\/td>\n20<\/td>\n25<\/td>\n30<\/td>\n<\/tr>\n
$Y$<\/td>\n18<\/td>\n21<\/td>\n25<\/td>\n30<\/td>\n36<\/td>\n42<\/td>\n50<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Donner les principaux param\u00e8tres de cette s\u00e9rie (moyenne, \u00e9cart-type, …)<\/p>\n

R\u00e9solution \u00e0 l’aide de Xcas<\/h2>\n
\n

\n\nX:=[0,5,10,15,20,25,30]\n<\/code>\n<\/font color><\/p>\n

$$[0,5,10,15,20,25,30]$$<\/p>\n

\n\nY:=[18,21,25,30,36,42,50]\n<\/code>\n<\/font color><\/p>\n

$$[18,21,25,30,36,42,50]$$<\/p>\n

Donner les principaux param\u00e8tres de cette s\u00e9rie (moyenne, \u00e9cart-type, …)<\/p>\n

\n\nvar2stat_e(X,Y):=\nlocal x,y,S;\nS:=zip((x,y)->x*y,X,Y);\nprint(\"- N : \"+size(X)+\";\");\nprint(\"------------- premi\u00e8re s\u00e9rie x ------------------\");\nprint(\"- Moyenne des x: \"+normal(moyenne(X))+\";\");\nprint(\"- Variance des x: \"+normal(variance(X))+\";\");\nprint(\"- Ecart-type des x: \"+normal(ecart_type(X))+\";\");\nprint(\"- Somme des x : \"+normal(sum(X))+\";\");\nprint(\"- Somme des x^2 : \"+normal(sum(X^2))+\";\");\nprint(\"- M\u00e9diane des x : \"+normal(median(X))+\";\");\nprint(\"- Q1 des x: \"+normal(quartile1(X))+\";\");\nprint(\"- Q3 des x: \"+normal(quartile3(X))+\";\");\nprint(\"- Min des x: \"+normal(min(X))+\";\");\nprint(\"- Max des x: \"+normal(max(X))+\";\");\nprint(\"------------- Deuxi\u00e8me s\u00e9rie y ------------------\");\nprint(\"- Moyenne des y: \"+normal(moyenne(Y))+\";\");\nprint(\"- Variance des y: \"+normal(variance(Y))+\";\");\nprint(\"- Ecart-type des y: \"+normal(ecart_type(Y))+\";\");\nprint(\"- Somme des y : \"+normal(sum(Y))+\";\");\nprint(\"- Somme des y^2 : \"+normal(sum(Y^2))+\";\");\nprint(\"- M\u00e9diane des y: \"+normal(median(Y))+\";\");\nprint(\"- Q1 des y : \"+normal(quartile1(Y))+\";\");\nprint(\"- Q3 des y: \"+normal(quartile3(Y))+\";\");\nprint(\"- Min des y: \"+normal(min(Y))+\";\");\nprint(\"- Max des y: \"+normal(max(Y))+\";\");\nprint(\"------------- Param\u00e8tres communs ------------------\");\nprint(\"- Somme des xy : \"+normal(sum(S))+\";\");\nprint(\"- Covariance des xy : \"+normal(covariance(X,Y))+\";\");\n<\/em>\n:;\n<\/code>\n<\/font color><\/p>\n

\/\/ Parsing var2stat_e<\/p>\n

\/\/ Success compiling var2stat_e<\/p>\n

\n\nvar2stat_e(X,Y)\n<\/code>\n<\/font color><\/p>\n

\u00ab\u00a0– N : 7;\u00a0\u00bb<\/p>\n

\u00ab\u00a0————- premi\u00e8re s\u00e9rie x ——————\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Moyenne des x: 15;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Variance des x: 100;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Ecart-type des x: 10;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des x : 105;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des x^2 : 2275;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– M\u00e9diane des x : 15.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Q1 des x: 5.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Q3 des x: 20.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Min des x: 0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Max des x: 30;\u00a0\u00bb<\/p>\n

\u00ab\u00a0————- Deuxi\u00e8me s\u00e9rie y ——————\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Moyenne des y: 222\/7;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Variance des y: 5666\/49;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Ecart-type des y: sqrt(5666)\/7;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des y : 222;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des y^2 : 7850;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– M\u00e9diane des y: 30.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Q1 des y : 21.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Q3 des y: 36.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Min des y: 18;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Max des y: 50;\u00a0\u00bb<\/p>\n

\u00ab\u00a0————- Param\u00e8tres communs ——————\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des xy : 4075;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Covariance des xy : 745\/7;\u00a0\u00bb<\/p>\n

Si on veut les valeurs approch\u00e9es :<\/p>\n

\n\nvar2stat_a(X,Y):=\nlocal x,y,S;\nS:=zip((x,y)->x*y,X,Y);\nprint(\"- N : \"+size(X)+\";\");\nprint(\"------------- premi\u00e8re s\u00e9rie x ------------------\");\nprint(\"- Moyenne des x: \"+evalf(moyenne(X))+\";\");\nprint(\"- Variance des x: \"+evalf(variance(X))+\";\");\nprint(\"- Ecart-type des x: \"+evalf(ecart_type(X))+\";\");\nprint(\"- Somme des x : \"+evalf(sum(X))+\";\");\nprint(\"- Somme des x^2 : \"+evalf(sum(X^2))+\";\");\nprint(\"- M\u00e9diane des x : \"+eval(median(X))+\";\");\nprint(\"- Q1 des x: \"+evalf(quartile1(X))+\";\");\nprint(\"- Q3 des x: \"+evalf(quartile3(X))+\";\");\nprint(\"- Min des x: \"+evalf(min(X))+\";\");\nprint(\"- Max des x: \"+evalf(max(X))+\";\");\nprint(\"------------- Deuxi\u00e8me s\u00e9rie y ------------------\");\nprint(\"- Moyenne des y: \"+evalf(moyenne(Y))+\";\");\nprint(\"- Variance des y: \"+evalf(variance(Y))+\";\");\nprint(\"- Ecart-type des y: \"+evalf(ecart_type(Y))+\";\");\nprint(\"- Somme des y : \"+evalf(sum(Y))+\";\");\nprint(\"- Somme des y^2 : \"+evalf(sum(Y^2))+\";\");\nprint(\"- M\u00e9diane des y: \"+eval(median(Y))+\";\");\nprint(\"- Q1 des y : \"+evalf(quartile1(Y))+\";\");\nprint(\"- Q3 des y: \"+evalf(quartile3(Y))+\";\");\nprint(\"- Min des y: \"+evalf(min(Y))+\";\");\nprint(\"- Max des y: \"+evalf(max(Y))+\";\");\nprint(\"------------- Param\u00e8tres communs ------------------\");\nprint(\"- Somme des xy : \"+evalf(sum(S))+\";\");\nprint(\"- Covariance des xy : \"+evalf(covariance(X,Y))+\";\");\n<\/em>\n:;\n<\/code>\n<\/font color><\/p>\n

\/\/ Parsing var2stat_a<\/p>\n

\/\/ Success compiling var2stat_a<\/p>\n

\n\nvar2stat_a(X,Y)\n<\/code>\n<\/font color><\/p>\n

\u00ab\u00a0————- premi\u00e8re s\u00e9rie x ——————\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Moyenne des x: 15.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Variance des x: 100.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Ecart-type des x: 10.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des x : 105.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des x^2 : 2275.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– M\u00e9diane des x : 15.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Q1 des x: 5.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Q3 des x: 20.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Min des x: 0.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Max des x: 30.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0————- Deuxi\u00e8me s\u00e9rie y ——————\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Moyenne des y: 31.7142857143;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Variance des y: 115.632653061;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Ecart-type des y: 10.753262438;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des y : 222.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des y^2 : 7850.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– M\u00e9diane des y: 30.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Q1 des y : 21.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Q3 des y: 36.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Min des y: 18.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Max des y: 50.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0————- Param\u00e8tres communs ——————\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Somme des xy : 4075.0;\u00a0\u00bb<\/p>\n

\u00ab\u00a0– Covariance des xy : 106.428571429;\u00a0\u00bb<\/p>\n

<\/math><\/p>\n","protected":false},"excerpt":{"rendered":"

Voici comment on peut r\u00e9soudre un exercice classique sur les statistiques \u00e0 deux variables. Enonc\u00e9 Soit la s\u00e9rie statistique suivante : $X$ 0 5 10 15 20 25 30 $Y$…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2228,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-162","page","type-page","status-publish","hentry"],"yoast_head":"\nStatistiques \u00e0 deux variables avec Xcas - Maths & Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Statistiques \u00e0 deux variables avec Xcas - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Voici comment on peut r\u00e9soudre un exercice classique sur les statistiques \u00e0 deux variables. Enonc\u00e9 Soit la s\u00e9rie statistique suivante : $X$ 0 5 10 15 20 25 30 $Y$…\" \/>\n<meta property=\"og:url\" content=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/\" \/>\n<meta property=\"og:site_name\" content=\"Maths & Num\u00e9rique\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-14T18:14:03+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/\",\"url\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/\",\"name\":\"Statistiques \u00e0 deux variables avec Xcas - Maths & Num\u00e9rique\",\"isPartOf\":{\"@id\":\"https:\/\/wordpress.callac.online\/#website\"},\"datePublished\":\"2008-04-30T16:31:45+00:00\",\"dateModified\":\"2023-10-14T18:14:03+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/wordpress.callac.online\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Logiciels math\u00e9matiques\",\"item\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Xcas\",\"item\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Statistiques avec Xcas\",\"item\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/\"},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"Statistiques \u00e0 deux variables avec Xcas\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/wordpress.callac.online\/#website\",\"url\":\"https:\/\/wordpress.callac.online\/\",\"name\":\"Maths & Num\u00e9rique\",\"description\":\"Des outils pour les enseignants de math\u00e9matiques et de num\u00e9rique\",\"publisher\":{\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/04061f1ca2c2c42039142a704be95940\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/wordpress.callac.online\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":[\"Person\",\"Organization\"],\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/04061f1ca2c2c42039142a704be95940\",\"name\":\"dlefur\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/4a9e17be136808c6597f28aa2b6c13126dab066fdc2198ff60090972c9b7fafc?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/4a9e17be136808c6597f28aa2b6c13126dab066fdc2198ff60090972c9b7fafc?s=96&d=mm&r=g\",\"caption\":\"dlefur\"},\"logo\":{\"@id\":\"https:\/\/wordpress.callac.online\/#\/schema\/person\/image\/\"},\"description\":\"Enseignant de math\u00e9matiques Lyc\u00e9e Pasteur S\u00e3o Paulo\",\"sameAs\":[\"http:\/\/wordpress.callac.online\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Statistiques \u00e0 deux variables avec Xcas - Maths & Num\u00e9rique","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/statistiques-avec-xcas\/statistiques-a-deux-variables-avec-xcas\/","og_locale":"fr_FR","og_type":"article","og_title":"Statistiques \u00e0 deux variables avec Xcas - Maths & Num\u00e9rique","og_description":"Voici comment on peut r\u00e9soudre un exercice classique sur les statistiques \u00e0 deux variables. 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