[{"data":1,"prerenderedAt":1677},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/distribucion-multimodal: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":6,"template":19,"owned_by":21,"editor":20,"trends":22,"raw_html":23,"tags":24},4008,2,0,"Distribución multimodal","distribucion-multimodal","\u003Cp id=\"bkmrk-una-distribuci%C3%B3n-mul\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2026-02/KKi0J1sna5ifML5F-bimodal-geological21.jpg\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2026-02/scaled-1680-/KKi0J1sna5ifML5F-bimodal-geological21.jpg\" alt=\"Bimodal_geological(2)(1).jpg\">\u003C/a>Una \u003Cstrong>distribución multimodal\u003C/strong> es una distribución de datos o distribución de probabilidad que presenta más de una \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/moda-estadistica\">moda\u003C/a>\u003C/strong>, indicando de esta forma la existencia de dos o más grupos con características diferentes en la distribución. Un caso especial de distribución multimodal es la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/distribucion-bimodal\">distribución bimodal\u003C/a>\u003C/strong>, con exactamente dos modas, como la que se muestra en la imagen contigua. \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0-1\">\u003C/p>",326,"2026-02-19T08:16:05.000000Z","2026-02-20T15:55:32.000000Z",{"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-una-distribuci%C3%B3n-mul\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2026-02/KKi0J1sna5ifML5F-bimodal-geological21.jpg\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2026-02/scaled-1680-/KKi0J1sna5ifML5F-bimodal-geological21.jpg\" alt=\"Bimodal_geological(2)(1).jpg\">\u003C/a>Una \u003Cstrong>distribución multimodal\u003C/strong> es una distribución de datos o distribución de probabilidad que presenta más de una \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/moda-estadistica\">moda\u003C/a>\u003C/strong>, indicando de esta forma la existencia de dos o más grupos con características diferentes en la distribución. Un caso especial de distribución multimodal es la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/distribucion-bimodal\">distribución bimodal\u003C/a>\u003C/strong>, con exactamente dos modas, como la que se muestra en la imagen contigua. \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0-1\">\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},2078,"Gráfico lineal (gráfico de línea)","grafico-lineal-grafico-de-linea","\u003Cp id=\"bkmrk-un-gr%C3%A1fico-lineal-o-\">Un \u003Cstrong>gráfico lineal, gráfico de línea  o diagrama de líneas\u003C/strong> es un gráfico estadístico bidimensional que une una serie de puntos que se han marcado previamente, con el objetivo de indicar una evolución en la magnitud expresada en los puntos o realizar una comparación de un conjunto de datos con otros. Puede complementarse con otros gráficos como el \u003Ca href=\"https://ikusmira.org/p/diagrama-de-barras-grafico-de-columnas\">diagrama de barras\u003C/a>.\u003C/p>\r\n\u003Cp id=\"bkmrk-el-gr%C3%A1fico-lineal-pa\">\u003Cstrong>El gráfico lineal para representar series temporales\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-la-aplicaci%C3%B3n-m%C3%A1s-co\">La aplicación más común del gráfico lineal es la representación de series temporales, marcando en el eje horizontal los periodos o momentos del tiempo en los que se observa la variable y en el eje vertical, los valores de la variable que se desea representar.\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2024-06/9q3PjFpB58pYyKfm-grafico-lineal.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg src=\"https://es.gizapedia.org/uploads/images/gallery/2024-06/scaled-1680-/9q3PjFpB58pYyKfm-grafico-lineal.png\" alt=\"grafico_lineal.png\">\u003C/a>\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0-1\">\u003C/p>",{"id":37,"name":38,"slug":39,"html":40},2029,"Tanto por mil","tanto-por-mil","\u003Cp id=\"bkmrk-tanto-por-mil%2C-tanto\">\u003Cstrong>Tanto por mil, tanto por millar o pormilaje\u003C/strong> es una magnitud o cantidad relativa o promedio de elementos o casos considerados,  respecto de un número total de mil. Por  ejemplo, si se dice que las unidades defectuosas son 4 por mil, quiere decir que en promedio cada 1000 unidades habrá 4 unidades defectuosas; si la remuneración que se ofrece como interés es de 80 por mil, esto quiere decir que por cada 1000 euros, se pagarán 80 euros de intereses en cada periodo.\u003C/p>",{"id":42,"name":43,"slug":44,"html":45},1667,"Estadísticos robustos","estadisticos-robustos","\u003Cp id=\"bkmrk-estad%C3%ADsticos-robusto\">\u003Cstrong>Estadísticos robustos\u003C/strong> son aquellos \u003Ca href=\"https://ikusmira.org/p/estadisticos-muestrales\">estadísticos muestrales\u003C/a> cuyos resultados y conclusiones no se ven afectadas por el incumplimiento de las condiciones que se exigen para su utilizacion en un procedimiento, como por ejemplo el muestreo aleatorio, el modelo estadístico que se ha establecido previamente, inexistencia de valores atípicos u homogeneidad en los datos.\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-robustez-estad%C3%ADstica\">\r\n\u003Cli>\u003Ca href=\"https://ikusmira.org/p/robustez-estadistica\">Robustez estadística\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":47,"name":48,"slug":49,"html":50},2690,"Mediala (medida de concentración y desigualdad)","mediala-medida-de-concentracion-y-desigualdad","\u003Cp id=\"bkmrk-la-mediala-o-valor-m\">La \u003Cstrong>mediala o valor medial\u003C/strong> es un indicador que se utiliza en el análisis de la concentración o desigualdad económica. Generalmente referida a una distribución de rentas, ingresos o salarios, y denominada en estos casos también renta medial, ingreso medial o salario medial, la mediala es el valor de la variable (renta, ingreso o salario) que acumula hasta dicho valor la mitad o el 50% del total acumulado de la variable (renta total, ingreso total o masa salarial, en cada caso).\u003C/p>\r\n\u003Cp id=\"bkmrk-la-mediala-por-s%C3%AD-so\">La mediala por sí sola no indica una mayor o menor concentración o desigualdad. Es su comparación con la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/mediana-estadistica\">mediana\u003C/a>\u003C/strong> la que proporciona un indicador de la mayor o menor concentración; más concretamente, siendo la mediala siempre mayor que que la mediana, cuanto mayor es la diferencia entre mediala y mediana, mayor es el nivel de concentración o desigualdad. Por otra parte, la mediala está relacionada de forma directa con la curva Lorenz: si llamamos \\(p_i\\) al número de individuos o elementos con valores de la variable inferiores a la mediala, el par \\((p_i,0.5)\\) es un punto de la curva de Lorenz. \u003C/p>\r\n\u003Cp id=\"bkmrk-ejemplo-%28datos-aisla\">\u003Cstrong>Ejemplo (datos aislados)\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-se-ha-realizado-una-\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2025-01/dlmQ4GBhWiP6CXSY-mediala.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2025-01/scaled-1680-/dlmQ4GBhWiP6CXSY-mediala.png\" alt=\"mediala.png\">\u003C/a>Se ha realizado una encuesta de salarios en una localidad obteniéndose los siguientes datos:  10-20-40-60-70. \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-para-determinar-la-m\">Para determinar la mediala se calcula el salario total:  10+20+40+60+70=200.\u003C/p>\r\n\u003Cp id=\"bkmrk-se-calcula-la-mitad-\">Se calcula la mitad del salario total: 200/2=100.\u003C/p>\r\n\u003Cp id=\"bkmrk-se-van-acumulando-lo\">Se van acumulando los salarios de menor a mayor: 10 (10) - 20 (30) - 40 (70) - 60 (130) - 70 (200).\u003C/p>\r\n\u003Cp id=\"bkmrk-se-llega-a-la-mitad-\">Se llega a la mitad del salario total con el salario de 60, luego la mediala es 60:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24ml%3D60%24%24\">$$Ml=60$$\u003C/p>",{"id":52,"name":53,"slug":54,"html":55},1619,"Variable cuasicuantitativa","variable-cuasicuantitativa","\u003Cp id=\"bkmrk-el-t%C3%A9rmino-variable-\">El término \u003Cstrong>variable cuasicuantitativa\u003C/strong> se utiliza con dos acepciones diferentes:\u003C/p>\r\n\u003Cul id=\"bkmrk-puede-referirse-a-un\">\r\n\u003Cli>puede referirse a una variable ordinal, por el hecho de situarse en relación a su escala de medida entre una variable nominal o cualitativa pura y una variable cuantitativa;\u003C/li>\r\n\u003Cli>por otro lado, puede ser un tipo concreto de variable ordinal, en la que los niveles o grados de la variables vienen dados por números que indican cierta medida de una característica.\u003C/li>\r\n\u003C/ul>",{"id":57,"name":58,"slug":59,"html":60},349,"Distribución de llegadas","distribucion-de-llegadas","\u003Cp id=\"bkmrk-\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2023-07/f8VGitI2Cd1D24ko-etorreren-banaketa.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-center\" src=\"https://es.gizapedia.org/uploads/images/gallery/2023-07/scaled-1680-/f8VGitI2Cd1D24ko-etorreren-banaketa.png\" alt=\"etorreren_banaketa.png\">\u003C/a>\u003C/p>\r\n\u003Cp id=\"bkmrk-imagen%3A-distribucion\">\u003Cem>Imagen: \u003C/em>\u003Cem>Distribuciones de llegadas en forma gráfica según un proceso de Poisson con diferentes tasas de llegadas: el proceso de abajo tiene una tasa de llegadas (parámetro lambda) mayor que el de\u003C/em> \u003Cem>arriba.\u003C/em>\u003C/p>\r\n\u003Cp id=\"bkmrk-una%C2%A0distribuci%C3%B3n-de-\">En teoría de colas, una \u003Cstrong>distribución de llegadas\u003C/strong> es la especificación en forma de distribución de probabilidad o distribución de frecuencias referidas número de unidades que llegan o acceden a un sistema de forma aleatoria a lo largo del tiempo. La distribución de llegadas utilizada con más frecuencia es la que se desarrolla en base a una \u003Ca href=\"https://ikusmira.org/p/distribucion-de-poisson\">distribución de Poisson\u003C/a> en la que los sujetos o elementos llegan de forma aleatoria en forma puntual a lo largo del tiempo a una tasa  constante y de forma independiente. La distribución de llegadas puede adoptar también la forma de distribución del tiempo entre llegadas consecutivas; por ejemplo si la distribución del número de llegadas sigue la distribución de Poisson, la distribución del tiempo entre llegadas sigue una  \u003Ca href=\"https://ikusmira.org/p/distribucion-exponencial\">distribución exponencial\u003C/a>.\u003C/p>\r\n\u003Cp id=\"bkmrk-en-cualquier-caso%2C-l\">En cualquier caso, la distribución de llegadas concreta en un sistema de colas se especifica a través de la notación de Kendall, distinguiéndose generalmente entre un proceso de Poisson (M), llegadas deterministas (D) y distribución general (G). \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-distribuci%C3%B3n-de-sali\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/distribucion-de-salidas-distribucion-de-tiempo-de-servicio\">\u003Cstrong>Distribución de salidas (distribución de tiempo de servicio)\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>",{"":62},[63,67,71,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,195,200,205,210,215,220,225,230,235,239,244,248,253,258,263,268,273,277,281,286,291,296,301,305,310,315,320,325,330,335,340,345,350,355,360,365,370,375,380,385,390,395,397,402,407,412,417,421,426,431,436,441,446,451,456,461,465,470,475,479,484,489,494,499,504,509,514,519,524,528,533,535,540,545,550,555,560,565,570,575,580,585,590,595,600,605,610,615,620,625,630,635,640,645,650,655,660,665,667,672,677,682,687,692,697,702,707,712,717,722,727,732,737,742,747,752,756,760,765,770,774,778,782,787,792,797,802,806,811,816,821,826,831,836,841,845,847,852,857,862,867,872,877,882,887,892,896,901,906,911,916,921,926,931,936,941,945,950,954,959,964,969,974,979,983,988,993,998,1003,1007,1012,1017,1021,1026,1031,1036,1040,1045,1050,1055,1060,1064,1069,1074,1079,1084,1089,1094,1099,1104,1109,1113,1118,1123,1128,1132,1137,1142,1147,1151,1155,1160,1165,1170,1175,1180,1184,1188,1193,1198,1203,1208,1212,1217,1219,1222,1226,1231,1236,1240,1245,1250,1255,1260,1265,1270,1275,1280,1285,1290,1295,1297,1301,1306,1311,1316,1321,1326,1331,1336,1341,1346,1351,1356,1361,1366,1371,1376,1379,1383,1388,1393,1398,1402,1406,1410,1415,1419,1423,1428,1433,1438,1443,1448,1453,1458,1463,1468,1473,1478,1483,1488,1492,1497,1502,1506,1511,1516,1521,1526,1530,1534,1538,1543,1548,1553,1558,1563,1568,1573,1578,1583,1588,1593,1598,1603,1608,1613,1618,1619,1624,1629,1634,1639,1644,1649,1654,1659],{"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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