{"id":4015,"date":"2025-02-18T05:24:33","date_gmt":"2025-02-18T05:24:33","guid":{"rendered":"https:\/\/lash.utrng.edu.mx\/?p=4015"},"modified":"2025-03-19T04:20:30","modified_gmt":"2025-03-19T04:20:30","slug":"medidas-de-tendencia-central-localizacion-y-dispersion","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=4015","title":{"rendered":"4. Medidas de tendencia central, localizaci\u00f3n y dispersi\u00f3n"},"content":{"rendered":"\n<p>La Media o la Varianza son ejemplo de indicadores que se representan mediante las letras griegas \u03bc, \u03c3, \u03c1, etc., y se les llama <strong>par\u00e1metros<\/strong>. En el caso de una distribuci\u00f3n de frecuencias tambi\u00e9n se pueden establecer medidas descriptivas y para distinguirlas de los par\u00e1metros, se usan letras latinas como x, s, r, etc.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/med.jpg\" alt=\"\" class=\"wp-image-4024\" style=\"width:469px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/med.jpg 1024w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/med-300x300.jpg 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/med-150x150.jpg 150w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/med-768x768.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<!--more-->\n\n\n\n<p><strong><span class=\"has-inline-color has-luminous-vivid-orange-color\">Medidas de Tendencia Central:<\/span><\/strong><\/p>\n\n\n\n<p><strong>Media<\/strong>(<img loading=\"lazy\" decoding=\"async\" width=\"14\" height=\"20\" class=\"wp-image-3368\" style=\"width: 14px;\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2021\/02\/image-3.png\" alt=\"\">). Se define como el promedio aritm\u00e9tico de los datos de una muestra. Para diferenciarla de la media de la poblaci\u00f3n se representa con <img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"21\" class=\"wp-image-3365\" style=\"width: 150px;\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2021\/02\/image.png\" alt=\"\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2021\/02\/image.png 393w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2021\/02\/image-300x41.png 300w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/>.<\/p>\n\n\n\n<p><strong>Mediana<\/strong>(Me). Es el valor que corresponde a la mitad de los datos ordenados de una muestra<\/p>\n\n\n\n<p><strong>Moda o Modo<\/strong>(Mo). El elemento de la muestra que tiene m\u00e1s frecuencia, es decir, el que m\u00e1s se repite. puede haber mas de una moda(bimodal o multimodal). Cuando todos los elementos son diferentes, la moda no existe o todos son la moda.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong><span class=\"has-inline-color has-luminous-vivid-orange-color\">Medidas de <\/span><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Localizaci\u00f3n<\/mark><\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Cuartiles<\/strong>:<strong>(Q)<\/strong> \u2192 Dividen los datos en <strong>4 partes<\/strong> (25% cada una).<\/li>\n\n\n\n<li><strong>Deciles<\/strong>:<strong>(D)<\/strong> \u2192 Dividen los datos en <strong>10 partes<\/strong> (10% cada una).<\/li>\n\n\n\n<li><strong>Percentiles<\/strong>:<strong>(P)<\/strong> \u2192 Dividen los datos en <strong>100 partes<\/strong> (1% cada una).<\/li>\n<\/ul>\n\n\n\n<p>F\u00f3rmula General para la Posici\u00f3n de un Cuantil:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"121\" height=\"53\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-23.png\" alt=\"\" class=\"wp-image-4016\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"167\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-24.png\" alt=\"\" class=\"wp-image-4017\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-24.png 626w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-24-300x80.png 300w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/figure>\n\n\n\n<p><strong>Ejemplos:<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Cuartiles (Q)<\/strong><\/h3>\n\n\n\n<p>Son tres valores que dividen los datos en <strong>4 grupos de 25%<\/strong> cada uno.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Q1 (Primer cuartil)<\/strong> \u2192 25% de los datos est\u00e1n por debajo.<\/li>\n\n\n\n<li><strong>Q2 (Mediana o Segundo cuartil)<\/strong> \u2192 50% de los datos est\u00e1n por debajo.<\/li>\n\n\n\n<li><strong>Q3 (Tercer cuartil)<\/strong> \u2192 75% de los datos est\u00e1n por debajo.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"422\" height=\"195\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-25.png\" alt=\"\" class=\"wp-image-4018\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-25.png 422w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-25-300x139.png 300w\" sizes=\"auto, (max-width: 422px) 100vw, 422px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Deciles (D)<\/strong><\/h3>\n\n\n\n<p>Son valores que dividen los datos en <strong>10 grupos de 10%<\/strong> cada uno.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>D1<\/strong> \u2192 10% de los datos est\u00e1n por debajo.<\/li>\n\n\n\n<li><strong>D5<\/strong> \u2192 Mediana (50% de los datos por debajo).<\/li>\n\n\n\n<li><strong>D9<\/strong> \u2192 90% de los datos por debajo.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"463\" height=\"162\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-26.png\" alt=\"\" class=\"wp-image-4019\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-26.png 463w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-26-300x105.png 300w\" sizes=\"auto, (max-width: 463px) 100vw, 463px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Percentiles (P)<\/strong><\/h3>\n\n\n\n<p>Dividen los datos en <strong>100 partes de 1% cada una<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>P25<\/strong> = Q1<\/li>\n\n\n\n<li><strong>P50<\/strong> = Q2 (mediana)<\/li>\n\n\n\n<li><strong>P75<\/strong> = Q3<\/li>\n\n\n\n<li><strong>P90<\/strong> \u2192 90% de los datos est\u00e1n por debajo.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"638\" height=\"127\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-27.png\" alt=\"\" class=\"wp-image-4020\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-27.png 638w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/image-27-300x60.png 300w\" sizes=\"auto, (max-width: 638px) 100vw, 638px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong><span class=\"has-inline-color has-luminous-vivid-orange-color\">Medidas de Dispersi\u00f3n<\/span><\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rango<\/strong>. indica la m\u00e1xima separaci\u00f3n entre los datos.<\/li>\n\n\n\n<li><strong>Varianza<\/strong>. nos da una medida de dispersi\u00f3n relativa al tama\u00f1o muestral<\/li>\n\n\n\n<li><strong>Desviaci\u00f3n t\u00edpica o est\u00e1ndar<\/strong>: &nbsp;la ra\u00edz cuadrada de la varianza.<\/li>\n\n\n\n<li><strong>Coeficiente de variaci\u00f3n<\/strong>. El cociente de la Desviaci\u00f3n est\u00e1ndar muestral entre la media muestral:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2021\/02\/image-6.png\"><img loading=\"lazy\" decoding=\"async\" width=\"225\" height=\"105\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2021\/02\/image-6.png\" alt=\"\" class=\"wp-image-3375\"\/><\/a><\/figure><\/div>\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-5468e644-d049-42f8-823a-2af390af5514\" href=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/matriz1.xlsx\">matriz1<\/a><a href=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/matriz1.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-5468e644-d049-42f8-823a-2af390af5514\">Descarga<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-2741c871-585d-4e78-801b-bd08ee45130e\" href=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/matriz_700_datos_aleatorios.xlsx\">matriz_700_datos_aleatorios<\/a><a href=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/matriz_700_datos_aleatorios.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-2741c871-585d-4e78-801b-bd08ee45130e\">Descarga<\/a><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Ejercicio<\/h2>\n\n\n\n<p>Descargar el siguiente archivo y resolver las indicaciones que al interior se proponen:<\/p>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-96febdcb-4e21-4047-b091-bc0de785294c\" href=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/matriz_100_datos_con_estadisticas.xlsx\">matriz_100_datos_con_estadisticas<\/a><a href=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/02\/matriz_100_datos_con_estadisticas.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-96febdcb-4e21-4047-b091-bc0de785294c\">Descarga<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>La Media o la Varianza son ejemplo de indicadores que se representan mediante las letras griegas \u03bc, \u03c3, \u03c1, etc., y se les llama par\u00e1metros. En el caso de una distribuci\u00f3n de frecuencias tambi\u00e9n se pueden establecer medidas descriptivas y para distinguirlas de los par\u00e1metros, se usan letras latinas como x, s, r, etc.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[93],"tags":[],"class_list":["post-4015","post","type-post","status-publish","format-standard","hentry","category-primerparcialprobest-meca"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4015","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4015"}],"version-history":[{"count":6,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4015\/revisions"}],"predecessor-version":[{"id":4078,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4015\/revisions\/4078"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}