{"id":109600,"date":"2020-01-29T18:13:57","date_gmt":"2020-01-29T17:13:57","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/estadistica\/ovarianza.html"},"modified":"2024-05-27T17:49:58","modified_gmt":"2024-05-27T15:49:58","slug":"ovarianza","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/estadistica\/ovarianza.html","title":{"rendered":"Covarianza"},"content":{"rendered":"<section style=\"\">\n<div class=\"cContContenido\">\n<p class=\"\">La <strong>covarianza<\/strong> de una variable bidimensional es la media aritm\u00e9tica de los productos de las desviaciones de cada una de las variables respecto a sus medias respectivas.<\/p>\n<p class=\"\">La <strong>covarianza<\/strong> se representa por<strong> s<sub>xy<\/sub><\/strong> o <strong>\u03c3<sub>xy<\/sub><\/strong>.<\/p>\n<p class=\"actividades_2_v_ir\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/covarianza-1.gif\" alt=\"Explicaciones y ejemplos de covarianza - 1\"  ><\/p>\n<p class=\"actividades_2_g_ir\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/covarianza-2.gif\" alt=\"Explicaciones y ejemplos de covarianza - 2\"  ><\/p>\n<\/div>\n<p class=\"\">La <strong>covarianza<\/strong> indica el sentido de la correlaci\u00f3n entre las variables<\/p>\n<p class=\"actividades_2_v\">Si <strong>\u03c3<sub>xy<\/sub> >0<\/strong> la correlaci\u00f3n es directa.<\/p>\n<p class=\"actividades_2_g\">Si <strong>\u03c3<sub>xy<\/sub> &lt;0<\/strong> la correlaci\u00f3n es inversa.\n                      <\/p>\n<p class=\"\">La <strong>covarianza<\/strong> presenta como inconveniente, el hecho de que su valor depende de la escala elegida para los ejes.<\/p>\n<p class=\"\">Es decir, la <strong>covarianza<\/strong> variar\u00e1 si expresamos la altura en metros o en cent\u00edmetros. Tambi\u00e9n variar\u00e1 si el dinero lo expresamos en euros o en d\u00f3lares.<\/p>\n<h2 class=\"t\">Ejemplos<\/h2>\n<p class=\"\">Las notas de 12 alumnos de una clase  en Matem\u00e1ticas y F\u00edsica son las siguientes:<\/p>\n<table class=\"responsive sbc\" data-min=\"8\" data-max=\"12\">\n<th>Matem\u00e1ticas<\/th>\n<th>F\u00edsica<\/th>\n<tbody>\n<tr>\n<td>2<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>9<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"\">Hallar la <strong>covarianza<\/strong> de la distribuci\u00f3n.<\/p>\n<table width=\"30%\" border=\"1\" class=\"t_izq\" cellspacing=\"0\" cellpadding=\"6\" style=\"\">\n<tr>\n<th>x<sub>i<\/sub><\/th>\n<th>y<sub>i<\/sub><\/th>\n<th>x<sub>i<\/sub> \u00b7 y<sub>i<\/sub><\/th>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<td>9<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>2<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>4<\/td>\n<td>16<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>4<\/td>\n<td>20<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>4<\/td>\n<td>24<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>6<\/td>\n<td>36<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>4<\/td>\n<td>28<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>6<\/td>\n<td>42<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>7<\/td>\n<td>56<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>9<\/td>\n<td>90<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>10<\/td>\n<td>100<\/td>\n<\/tr>\n<tr>\n<td style=\"color:#900;\">72<\/td>\n<td style=\"color:#900;\">60<\/td>\n<td style=\"color:#900;\">431<\/td>\n<\/tr>\n<\/table>\n<p class=\"\">Despu\u00e9s de tabular los datos hallamos las <a href=\"https:\/\/www.superprof.es\/apuntes\/escolar\/matematicas\/estadistica\/descriptiva\/media-aritmetica.html\">medias aritm\u00e9ticas<\/a>:<\/p>\n<p class=\"actividades_2_r\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/covarianza-3.gif\" alt=\"Explicaciones y ejemplos de covarianza - 3\"  ><\/p>\n<p class=\"actividades_2_v\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/covarianza-4.gif\" alt=\"Explicaciones y ejemplos de covarianza - 4\"  ><\/p>\n<p class=\"\">Los valores de dos variables X e Y se distribuyen seg\u00fan la tabla siguiente:<\/p>\n<p><\/p>\n<table class=\"responsive sbc\" data-min=\"8\" data-max=\"12\">\n<tr>\n<th>Y\/X<\/th>\n<th>0<\/th>\n<th>2<\/th>\n<th>4<\/th>\n<\/tr>\n<tr>\n<th>1<\/th>\n<td>2<\/td>\n<td>1<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<th>2<\/th>\n<td>1<\/td>\n<td>4<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<th>3<\/th>\n<td>2<\/td>\n<td>5<\/td>\n<td>0<\/td>\n<\/tr>\n<\/table>\n<p class=\"\">Hallar la <strong>covarianza<\/strong> de la distribuci\u00f3n.<\/p>\n<p class=\"\">En primer lugar convertimos la tabla de doble entrada en tabla simple y calculamos las medias aritm\u00e9ticas.<\/p>\n<table class=\"responsive sbc\" data-min=\"8\" data-max=\"12\">\n<tr>\n<th>x<sub>i<\/sub><\/th>\n<th>y<sub>i<\/sub><\/th>\n<th>f<sub>i<\/sub><\/th>\n<th>x<sub>i<\/sub> \u00b7 f<sub>i<\/sub><\/th>\n<th>y<sub>i<\/sub> \u00b7 f<sub>i<\/sub><\/th>\n<th>x<sub>i<\/sub> \u00b7 y<sub>i <\/sub>\u00b7 f<sub>i<\/sub><\/th>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>0<\/td>\n<td>2<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>2<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>2<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>3<\/td>\n<td>2<\/td>\n<td>0<\/td>\n<td>6<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>8<\/td>\n<td>8<\/td>\n<td>16<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>3<\/td>\n<td>5<\/td>\n<td>10<\/td>\n<td>15<\/td>\n<td>30<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>1<\/td>\n<td>3<\/td>\n<td>12<\/td>\n<td>3<\/td>\n<td>12<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>8<\/td>\n<td>4<\/td>\n<td>16<\/td>\n<\/tr>\n<tr>\n<td style=\"color:#900;\"> <\/td>\n<td style=\"color:#900;\"> <\/td>\n<td style=\"color:#900;\">20<\/td>\n<td style=\"color:#900;\">40<\/td>\n<td style=\"color:#900;\">41<\/td>\n<td style=\"color:#900;\">76<\/td>\n<\/tr>\n<\/table>\n<p class=\"actividades_2_r\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/covarianza-5.gif\" alt=\"Explicaciones y ejemplos de covarianza - 5\"  ><\/p>\n<p class=\"actividades_2_v\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/covarianza-6.gif\" alt=\"Explicaciones y ejemplos de covarianza - 6\"  ><\/p>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>La covarianza de una variable bidimensional es la media aritm\u00e9tica de los productos de las desviaciones de cada una de las variables respecto a sus medias respectivas. La covarianza se representa por sxy o \u03c3xy. La covarianza indica el sentido de la correlaci\u00f3n entre las variables Si \u03c3xy >0 la correlaci\u00f3n es directa. Si \u03c3xy [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"categories":[380],"tags":[371],"class_list":["post-109600","post","type-post","status-publish","format-standard","hentry","category-estadistica","tag-o"],"acf":[],"author_meta":{"display_name":"Andra","author_link":"https:\/\/www.superprof.es\/diccionario\/author\/andra"},"featured_img":null,"coauthors":[],"tax_additional":{"categories":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/estadistica\" class=\"advgb-post-tax-term\">Estad\u00edstica<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">Estad\u00edstica<\/span>"]},"tags":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/estadistica\" class=\"advgb-post-tax-term\">o<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">o<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 6 a\u00f1os hace","modified":"Actualizado 2 a\u00f1os hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 27 mayo 2024"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 13 min","modified":"Actualizado el 27 mayo 2024 17 h 49 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/109600","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/comments?post=109600"}],"version-history":[{"count":1,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/109600\/revisions"}],"predecessor-version":[{"id":136163,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/109600\/revisions\/136163"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=109600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=109600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=109600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}