[{"data":1,"prerenderedAt":1677},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/medidas-de-concentracion-estadistica:0":3},{"page":4,"book":25,"news":1671,"questionSent":19,"questions":1672,"formData":1673,"attachments":22,"chartData":22,"pending":19,"chartOptions":1674,"afspec":19,"aflink":1676},{"id":5,"book_id":6,"chapter_id":7,"name":8,"slug":9,"html":10,"priority":11,"created_at":12,"updated_at":13,"created_by":14,"updated_by":18,"draft":19,"markdown":20,"revision_count":15,"template":19,"owned_by":21,"editor":20,"trends":22,"raw_html":23,"tags":24},4058,2,0,"Medidas de concentración (estadística)","medidas-de-concentracion-estadistica","\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-la-c\">En estadística, la \u003Cstrong>concentración\u003C/strong> hace referencia a en qué medida el total de una variable se reparte de forma desigual entre los diferentes elementos de una muestra o población; por ejemplo, las medidas de concentración se aplican al estudio de la desigualdad en la distribución de la renta, en estudios sobre concentración industrial o empresarial, en el estudio de la concentración parcelaria y en el análisis del reparto de la facturación entre diferentes establecimientos. Por tanto, debe subrayarse que el estudio de la concentración queda fuera de lugar en aquellos casos en los que la suma de valores de la variable estadística no tenga un significado como totalidad y por tanto no exista un reparto entre diferentes elementos.\u003C/p>\r\n\u003Cp id=\"bkmrk-el-instrumento-b%C3%A1sic\">El instrumento básico más común para el análisis de la concentración es la curva de Lorenz, que proporciona para cada porcentaje \\()p_i\\) de elementos con menor participación su participación porcentual \\(q_i\\) en el total, siendo la línea \\(p_i=q_i\\) la línea de equidistribución, de modo que cuanto más se aleje la curva de Lorenz de dicha línea, mayor será el nivel de concentración. De este modo, una medida básica de concentración viene dada por el índice de Gini, que es una medida entre 0 y 1 del área comprendida entre la línea de equidistribución y la curva del Lorenz, siendo mayor la concentración cuanto mayor sea el índice. Si bien el índice de Gini es una de las medidas de concentración más utilizadas, es cierto también que conlleva una simplificación reduccionista de la realidad de la concentración, al proporcionar una única cifra como resumen de toda una estructura de concentración proporcionada por la curva de Lorenz.\u003C/p>\r\n\u003Cp id=\"bkmrk-otras-medidas-de-con\">Otras medidas de concentración frecuentemente utilizadas son el índice Robin Hood, la mediala, el índice de Theil, que permite descomponer la concentració en concentracion intragrupos y concentración intergrupos; y el índice de Atkinson, que incorpora un parámetro de sensibilidad a la desigualdad. \u003C/p>",329,"2026-03-02T15:23:33.000000Z","2026-03-02T16:54:24.000000Z",{"id":15,"name":16,"slug":17},1,"Admin","admin",{"id":15,"name":16,"slug":17},false,"",{"id":15,"name":16,"slug":17},null,"\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-la-c\">En estadística, la \u003Cstrong>concentración\u003C/strong> hace referencia a en qué medida el total de una variable se reparte de forma desigual entre los diferentes elementos de una muestra o población; por ejemplo, las medidas de concentración se aplican al estudio de la desigualdad en la distribución de la renta, en estudios sobre concentración industrial o empresarial, en el estudio de la concentración parcelaria y en el análisis del reparto de la facturación entre diferentes establecimientos. Por tanto, debe subrayarse que el estudio de la concentración queda fuera de lugar en aquellos casos en los que la suma de valores de la variable estadística no tenga un significado como totalidad y por tanto no exista un reparto entre diferentes elementos.\u003C/p>\r\n\u003Cp id=\"bkmrk-el-instrumento-b%C3%A1sic\">El instrumento básico más común para el análisis de la concentración es la curva de Lorenz, que proporciona para cada porcentaje \\()p_i\\) de elementos con menor participación su participación porcentual \\(q_i\\) en el total, siendo la línea \\(p_i=q_i\\) la línea de equidistribución, de modo que cuanto más se aleje la curva de Lorenz de dicha línea, mayor será el nivel de concentración. De este modo, una medida básica de concentración viene dada por el índice de Gini, que es una medida entre 0 y 1 del área comprendida entre la línea de equidistribución y la curva del Lorenz, siendo mayor la concentración cuanto mayor sea el índice. Si bien el índice de Gini es una de las medidas de concentración más utilizadas, es cierto también que conlleva una simplificación reduccionista de la realidad de la concentración, al proporcionar una única cifra como resumen de toda una estructura de concentración proporcionada por la curva de Lorenz.\u003C/p>\r\n\u003Cp id=\"bkmrk-otras-medidas-de-con\">Otras medidas de concentración frecuentemente utilizadas son el índice Robin Hood, la mediala, el índice de Theil, que permite descomponer la concentració en concentracion intragrupos y concentración intergrupos; y el índice de Atkinson, que incorpora un parámetro de sensibilidad a la desigualdad. \u003C/p>",[],{"id":6,"name":26,"slug":27,"description":20,"created_at":28,"updated_at":29,"created_by":15,"updated_by":15,"owned_by":15,"default_template_id":22,"pages":30,"index":61,"shelves":1664},"Estadística general","estadistica-general","2023-05-06T08:26:42.000000Z","2023-05-16T06:24:05.000000Z",[31,36,41,46,51,56],{"id":32,"name":33,"slug":34,"html":35},275,"Modelo de regresión","modelo-de-regresion","\u003Cp id=\"bkmrk-un-modelo-de-regresi\">Un \u003Cstrong>modelo de regresión\u003C/strong> es un modelo estadístico que establece la relación entre una variable independiente o explicativa o una variable dependiente a partir de los datos obtenidos para las dos variables y estimando los parámetros necesarios para concretar dicha relación, introduciendo generalmente factores de incertidumbre o relativos a la variabilidad de dicha relación. El modelo de regresión más habitual es el modelo de regresión lineal de mínimos cuadrados, que establece una relación lineal entre las dos variables y que estima los parámetros de la recta de regresión minimizando la suma de diferencias cuadradas entre los valores reales y los predichos o estimados para la variable dependiente en función de la variable explicativa.\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-recta-de-regresi%C3%B3n-d\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/recta-de-regresion-de-minimos-cuadrados\">\u003Cstrong>Recta de regresión de mínimos cuadrados\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":37,"name":38,"slug":39,"html":40},3668,"Tabla de doble entrada","tabla-de-doble-entrada","\u003Cp id=\"bkmrk-una-tabla-de-doble-e\">Una \u003Cstrong>tabla de doble entrada\u003C/strong> es una tabla con filas y columnas que se utiliza para relacionar dos variables o criterios de clasificación sobre un fenómeno o conjunto de elementos, de modo que en cada cruce de filas y columna se inserta una información o dato sobre la ocurrencia conjunta de dichas variables. También son tablas de doble entrada aquellas tablas que representan una matriz de datos, en las que las filas representan los elementos o  individuos y las filas las variables que se observan en aquellos. Las tablas de doble entrada se utilizan profusamente en la vida diaria; por ejemplo, para mostrar la planificación de tareas según día de la semana y hora y para construir tablas de contingencia que muestren el número de elementos de una muestra o población que cumplen con las condiciones establecidas en cada fila y columna. \u003Cbr>\u003C/p>",{"id":42,"name":43,"slug":44,"html":45},2073,"Punto de dato","punto-de-dato","\u003Cp id=\"bkmrk-un-punto-de-dato-es-\">Un \u003Cstrong>punto de dato\u003C/strong> es un punto o marca en un gráfico estadístico; por extensión, se refiere también a los datos correspondientes a ese punto. Generalmente, los puntos de datos hacen referencia a los datos, observaciones o mediciones de un elemento o unidad de observación, es decir a series de datos individuales. Por ejemplo, si en una nube de puntos o diagrama de dispersión tenemos en el eje X la edad de los trabajadores y en el eje Y un indicador de productividad, cada punto de dato vendrá conformado por la edad y el indicador de productividad de cada trabajador.  \u003C/p>\r\n\u003Cp id=\"bkmrk-los-puntos-de-datos%2C\">Los puntos de datos, considerados como datos para cada unidad de observación, pueden representarse  y compararse entre sí de diferentes modos:\u003C/p>\r\n\u003Cul id=\"bkmrk-a-trav%C3%A9s-de-un-gr%C3%A1fi\">\r\n\u003Cli class=\"null\">a través de un gráfico de línea, indicando la línea los valores correspondientes a cada punto de dato;\u003C/li>\r\n\u003Cli class=\"null\">en una nube de puntos, simplemente como punto con una coordenadas cartesianas.;\u003C/li>\r\n\u003Cli class=\"null\">en un diagrama de punto, para puntos de datos unidimensionales o relativos a una sola variable. \u003C/li>\r\n\u003C/ul>",{"id":47,"name":48,"slug":49,"html":50},1711,"Prueba de hipótesis (contraste de hipótesis)","prueba-de-hipotesis-contraste-de-hipotesis","\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-una-\">En estadística, una \u003Cstrong>prueba de hipótesis  o contraste de hipótesis\u003C/strong> es un procedimiento por el cual se determina si a partir de los datos pertenecientes a una muestra puede rechazarse o no una proposición, denominada \u003Ca href=\"https://ikusmira.org/p/hipotesis-nula\">hipótesis nula\u003C/a>, referida a la población o naturaleza de los datos analizados. Para ello, el procedimiento general consiste en seleccionar un \u003Ca href=\"https://ikusmira.org/p/estadistico-de-prueba-estadistico-de-contraste\">estadístico de prueba\u003C/a>, es decir, un resultado cuantitativo derivado de los datos del cual ha de contrastarse o compararse su nivel de compatibilidad con lo afirmado por la hipótesis nula, Más concretamente se evalúa hasta que punto el valor que toma el estadístico de prueba para la muestra se explica por el mero azar de los datos de la muestra, en cuyo caso no se rechazaría o se aceptaría la hipótesiso nula, o si la diferencia es tan significativa o grande que la probabilidad de que se deba al azar de los datos es suficientemente pequeña, de modo que debamos rechazar la hipótesis nula. \u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-lema-de-neyman-pears\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/lema-de-neyman-pearson\">\u003Cstrong>Lema de Neyman-Pearson\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":52,"name":53,"slug":54,"html":55},307,"Distribución bivariada","distribucion-bivariada","\u003Cp id=\"bkmrk-una-distribuci%C3%B3n-biv\">Una \u003Cstrong>distribución bivariada\u003C/strong> es una \u003Ca href=\"https://ikusmira.org/p/distribucion-conjunta\">\u003Cstrong>distribución conjunta\u003C/strong>\u003C/a> de dos variables estadísticas, que especifica las frecuencias o probabilidades para cada par de valores de las variables consideradas.\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ad\">\u003Cstrong>Puede interesarte además\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-datos-bivariados-fre\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/datos-bivariados\">\u003Cstrong>Datos bivariados\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/frecuencia-conjunta\">\u003Cstrong>Frecuencia conjunta\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/tabla-de-contingencia\">\u003Cstrong>Tabla de contingencia\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>",{"id":57,"name":58,"slug":59,"html":60},3732,"Mapa de calor de correlaciones (correlograma)","mapa-de-calor-de-correlaciones-correlograma","\u003Cp id=\"bkmrk-\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2024-02/06RQrppGSVQIO9Vj-carmilagedata2.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg src=\"https://es.gizapedia.org/uploads/images/gallery/2024-02/scaled-1680-/06RQrppGSVQIO9Vj-carmilagedata2.png\" alt=\"CarMilageData(2).png\" width=\"335\" height=\"335\">\u003C/a>\u003C/p>\r\n\u003Cp id=\"bkmrk-imagen%3A-correlograma\">\u003Cem>Imagen: Correlograma que muestra las correlaciones mutuas entre 11 variables. Créditos: Jackverr-Commons.\u003C/em>\u003C/p>\r\n\u003Cp id=\"bkmrk-un%C2%A0correlograma-es-u\">En análisis multivariante, un \u003Cstrong>mapa de calor de correlaciones, también llamado a veces correlograma,\u003C/strong>  es una representación gráfica de los coeficientes de correlación entre los pares de variables de un grupo de variables.\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-correlograma%2C-en-la-\">\r\n\u003Cli class=\"null\">\u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/correlograma\">Correlograma\u003C/a>, en la acepción de autocorrelograma\u003C/strong>\u003C/li>\r\n\u003C/ul>",{"":62},[63,67,71,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,195,200,205,210,215,220,225,230,235,239,244,248,253,258,263,268,273,277,281,286,291,296,301,305,310,315,320,325,330,335,340,345,350,355,360,365,370,372,377,382,387,392,397,402,407,412,417,421,426,431,436,441,446,451,456,461,465,470,475,479,484,489,494,499,504,509,514,519,524,528,533,538,543,548,553,558,563,568,573,578,583,588,593,598,603,608,613,618,623,628,633,638,643,648,653,658,663,668,673,678,683,688,693,698,703,708,713,718,723,728,733,738,743,748,753,758,762,766,771,776,780,784,788,793,798,803,808,812,817,822,827,832,837,842,847,851,856,861,866,871,876,881,886,891,896,901,905,910,915,920,925,930,935,937,942,947,951,956,960,965,970,975,980,985,989,994,999,1004,1009,1013,1018,1023,1027,1032,1037,1042,1046,1051,1056,1061,1066,1070,1075,1080,1085,1090,1095,1100,1105,1110,1115,1119,1121,1126,1131,1135,1137,1142,1147,1151,1155,1160,1165,1170,1175,1180,1184,1188,1193,1198,1203,1208,1212,1217,1222,1225,1229,1234,1239,1243,1248,1253,1258,1263,1268,1273,1278,1283,1288,1293,1298,1303,1307,1312,1317,1322,1327,1332,1337,1342,1347,1352,1357,1362,1367,1372,1377,1382,1385,1389,1394,1399,1404,1408,1412,1416,1421,1425,1429,1434,1439,1444,1449,1454,1459,1464,1469,1474,1479,1484,1489,1494,1498,1500,1505,1509,1514,1519,1524,1526,1530,1534,1538,1543,1548,1553,1558,1563,1568,1573,1578,1583,1588,1593,1598,1603,1608,1613,1618,1623,1628,1633,1634,1639,1644,1649,1654,1659],{"id":64,"name":65,"slug":66,"priority":7,"chapter_name":22},3173,"Aleatorización (diseño de experimentos)","aleatorizacion-diseno-de-experimentos",{"id":68,"name":69,"slug":70,"priority":15,"chapter_name":22},631,"Amplitud de clase","amplitud-de-clase",{"id":72,"name":73,"slug":74,"priority":6,"chapter_name":22},387,"Análisis de trayectorias","analisis-de-trayectorias",{"id":76,"name":77,"slug":78,"priority":79,"chapter_name":22},624,"Arranque aleatorio","arranque-aleatorio",3,{"id":81,"name":82,"slug":83,"priority":84,"chapter_name":22},43,"Asociación estadística","asociacion-estadistica",4,{"id":86,"name":87,"slug":88,"priority":89,"chapter_name":22},2019,"Asociación no estadística","asociacion-no-estadistica",5,{"id":91,"name":92,"slug":93,"priority":94,"chapter_name":22},2948,"Banco de datos","banco-de-datos",6,{"id":96,"name":97,"slug":98,"priority":99,"chapter_name":22},1621,"Base del índice (periodo base)","base-del-indice-periodo-base",7,{"id":101,"name":102,"slug":103,"priority":104,"chapter_name":22},35,"Cálculo de la moda estadística para datos agrupados en intervalos","calculo-de-la-moda-estadistica-para-datos-agrupados-en-intervalos",8,{"id":106,"name":107,"slug":108,"priority":109,"chapter_name":22},3063,"Característica cualitativa","caracteristica-cualitativa",9,{"id":111,"name":112,"slug":113,"priority":114,"chapter_name":22},2708,"Casos particulares","casos-particulares",10,{"id":116,"name":117,"slug":118,"priority":119,"chapter_name":22},2730,"Censo estadístico","censo-estadistico",11,{"id":121,"name":122,"slug":123,"priority":124,"chapter_name":22},2551,"Clase mediana","clase-mediana",12,{"id":126,"name":127,"slug":128,"priority":129,"chapter_name":22},1011,"Clase modal","clase-modal",13,{"id":131,"name":132,"slug":133,"priority":134,"chapter_name":22},2133,"Coeficiente de asimetría de Bowley","coeficiente-de-asimetria-de-bowley",14,{"id":136,"name":137,"slug":138,"priority":139,"chapter_name":22},1714,"Coeficiente de asimetría de Fisher","coeficiente-de-asimetria-de-fisher",15,{"id":141,"name":142,"slug":143,"priority":144,"chapter_name":22},1844,"Coeficiente de asimetría de Pearson","coeficiente-de-asimetria-de-pearson",16,{"id":146,"name":147,"slug":148,"priority":149,"chapter_name":22},2057,"Coeficiente de contingencia de Pearson","coeficiente-de-contingencia-de-pearson",17,{"id":151,"name":152,"slug":153,"priority":154,"chapter_name":22},2648,"Coeficiente de correlación biserial puntual","coeficiente-de-correlacion-biserial-puntual",18,{"id":156,"name":157,"slug":158,"priority":159,"chapter_name":22},1938,"Coeficiente de curtosis de Pearson","coeficiente-de-curtosis-de-pearson",19,{"id":161,"name":162,"slug":163,"priority":164,"chapter_name":22},2032,"Coeficiente de determinación ajustado (coeficiente de determinación corregido)","coeficiente-de-determinacion-ajustado-coeficiente-de-determinacion-corregido",20,{"id":166,"name":167,"slug":168,"priority":169,"chapter_name":22},2649,"Coeficiente de Tschuprow","coeficiente-de-tschuprow",21,{"id":171,"name":172,"slug":173,"priority":174,"chapter_name":22},37,"Coeficiente de variación","coeficiente-de-variacion",22,{"id":176,"name":177,"slug":178,"priority":179,"chapter_name":22},2646,"Coeficiente Q de Yule","coeficiente-q-de-yule",23,{"id":181,"name":182,"slug":183,"priority":184,"chapter_name":22},2218,"Comprobación de Charlier","comprobacion-de-charlier",24,{"id":186,"name":187,"slug":188,"priority":189,"chapter_name":22},2095,"Concepto de estadística","concepto-de-estadistica",25,{"id":191,"name":192,"slug":193,"priority":194,"chapter_name":22},2607,"Constante estadística","constante-estadistica",26,{"id":196,"name":197,"slug":198,"priority":199,"chapter_name":22},2087,"Corrección de Bessel","correccion-de-bessel",27,{"id":201,"name":202,"slug":203,"priority":204,"chapter_name":22},308,"Corrección de Sheppard","correccion-de-sheppard",28,{"id":206,"name":207,"slug":208,"priority":209,"chapter_name":22},1080,"Corrección de Yates","correccion-de-yates",29,{"id":211,"name":212,"slug":213,"priority":214,"chapter_name":22},49,"Corrección por continuidad","correccion-por-continuidad",30,{"id":216,"name":217,"slug":218,"priority":219,"chapter_name":22},2685,"Correlación","correlacion",31,{"id":221,"name":222,"slug":223,"priority":224,"chapter_name":22},1624,"Correlación espuria (correlación espúrea)","correlacion-espuria-correlacion-espurea",32,{"id":226,"name":227,"slug":228,"priority":229,"chapter_name":22},2684,"Correlación por rangos","correlacion-por-rangos",33,{"id":231,"name":232,"slug":233,"priority":234,"chapter_name":22},1665,"Correlograma","correlograma",34,{"id":236,"name":237,"slug":238,"priority":101,"chapter_name":22},148,"Covariación","covariacion",{"id":240,"name":241,"slug":242,"priority":243,"chapter_name":22},44,"Covarianza","covarianza",36,{"id":245,"name":246,"slug":247,"priority":171,"chapter_name":22},1652,"Criterio 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