[{"data":1,"prerenderedAt":1672},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/puntuacion-diferencial:0":3},{"page":4,"book":26,"news":1666,"questionSent":19,"questions":1667,"formData":1668,"attachments":23,"chartData":23,"pending":19,"chartOptions":1669,"afspec":19,"aflink":1671},{"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":21,"template":19,"owned_by":22,"editor":20,"trends":23,"raw_html":24,"tags":25},4106,2,0,"Puntuación diferencial","puntuacion-diferencial","\u003Cp id=\"bkmrk-una-puntuaci%C3%B3n-difer\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2026-03/azvoxVg5PZHOkX7J-puntuacion-diferencial-1.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2026-03/scaled-1680-/azvoxVg5PZHOkX7J-puntuacion-diferencial-1.png\" alt=\"puntuacion_diferencial_1.png\" width=\"165\" height=\"80\">\u003C/a>Una \u003Cstrong>puntuación diferencial\u003C/strong> es un dato observado, esto es, una \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/puntuacion-directa\">puntuación directa\u003C/a>\u003C/strong>, al que se ha sustraido la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/media-aritmetica-simple\">media aritmética\u003C/a>\u003C/strong> de la muestra o población en el que se encuentra, con el objeto de conocer su posición relativa, por debajo o por encima, de dicha media. \u003C/p>\r\n\u003Cp id=\"bkmrk-un-t%C3%B1ermino-sin%C3%B3nimo\">Un término sinónimo en estadística es el desviaciones respecto a la media, pero mientras el término \u003Cem>puntuación diferencial \u003C/em>es más común en psicometría, el término \u003Cem>desviaciones respecto a la media\u003C/em> se utiliza más en econometría. \u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-puntuaci%C3%B3n-t%C3%ADpica\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/puntuacion-estandar-puntuacion-tipificada-valor-z\">\u003Cstrong>Puntuación típica\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>",334,"2026-03-12T07:46:38.000000Z","2026-03-12T08:07:53.000000Z",{"id":15,"name":16,"slug":17},1,"Admin","admin",{"id":15,"name":16,"slug":17},false,"",5,{"id":15,"name":16,"slug":17},null,"\u003Cp id=\"bkmrk-una-puntuaci%C3%B3n-difer\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2026-03/azvoxVg5PZHOkX7J-puntuacion-diferencial-1.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2026-03/scaled-1680-/azvoxVg5PZHOkX7J-puntuacion-diferencial-1.png\" alt=\"puntuacion_diferencial_1.png\" width=\"165\" height=\"80\">\u003C/a>Una \u003Cstrong>puntuación diferencial\u003C/strong> es un dato observado, esto es, una \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/puntuacion-directa\">puntuación directa\u003C/a>\u003C/strong>, al que se ha sustraido la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/media-aritmetica-simple\">media aritmética\u003C/a>\u003C/strong> de la muestra o población en el que se encuentra, con el objeto de conocer su posición relativa, por debajo o por encima, de dicha media. \u003C/p>\r\n\u003Cp id=\"bkmrk-un-t%C3%B1ermino-sin%C3%B3nimo\">Un término sinónimo en estadística es el desviaciones respecto a la media, pero mientras el término \u003Cem>puntuación diferencial \u003C/em>es más común en psicometría, el término \u003Cem>desviaciones respecto a la media\u003C/em> se utiliza más en econometría. \u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-puntuaci%C3%B3n-t%C3%ADpica\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/puntuacion-estandar-puntuacion-tipificada-valor-z\">\u003Cstrong>Puntuación típica\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>",[],{"id":6,"name":27,"slug":28,"description":20,"created_at":29,"updated_at":30,"created_by":15,"updated_by":15,"owned_by":15,"default_template_id":23,"pages":31,"index":62,"shelves":1659},"Estadística general","estadistica-general","2023-05-06T08:26:42.000000Z","2023-05-16T06:24:05.000000Z",[32,37,42,47,52,57],{"id":33,"name":34,"slug":35,"html":36},1870,"Universo (estadística)","universo-estadistica","\u003Cp id=\"bkmrk-el%C2%A0universo-estad%C3%ADst\">El \u003Cstrong>universo estadístico\u003C/strong> es el conjunto de elementos, personas, cosas u otro tipo de entidad, del que se quiere indagar algo. Frecuentemente, se consideran sinónimos universo y \u003Ca href=\"https://ikusmira.org/p/poblacion-estadistica\">población estadística\u003C/a>, pero frecuentemente existen situaciones en que ambos conceptos son diferentes. Por ejemplo, si se desea realizar una investigación sobre los trabajadores de un país, este conjunto de trabajadores constituye el universo de la investigación e incluiría a trabajadores formales, informales y aquellas personas que realizan algún tipo de actividad asimilable a lo que se considera como trabajo; sin embargo, para poder limitar el estudio necesitamos un conjunto más concreto del que se extraerá una muestra y que puede venir dado por los trabajadores afiliados a la Seguridad Social y que por tanto tienen un número de afiliación; este conjunto más concreto que va a a ser objeto de observación y estudio es el que conforma la población, en este ejemplo a través de una lista de afiliados que es lo que se denomina \u003Ca href=\"https://ikusmira.org/p/marco-muestral\">marco muestral\u003C/a>.\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-fuentes-de-informaci\">\r\n\u003Cli class=\"null\" style=\"font-weight: bold;\">\u003Ca href=\"https://ikusmira.org/p/censo-estadistico\">\u003Cstrong>Censo estadístico\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":38,"name":39,"slug":40,"html":41},2607,"Constante estadística","constante-estadistica","\u003Cp id=\"bkmrk-una-constante-estad%C3%AD\">Una \u003Cstrong>constante estadística\u003C/strong> es una característica que se observa o mide entre los elementos de una población y que presenta una única modalidad, esto es, es la misma para todos los elementos. Se opone al concepto de \u003Ca href=\"https://ikusmira.org/p/variable-estadistica\">variable estadística\u003C/a>, como caracterísitcas con modalidades variable entre los elementos a analizar. \u003C/p>",{"id":43,"name":44,"slug":45,"html":46},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":48,"name":49,"slug":50,"html":51},2075,"Estadística bayesiana (inferencia bayesiana)","estadistica-bayesiana-inferencia-bayesiana","\u003Cp id=\"bkmrk-la-estad%C3%ADstica-bayes\">La \u003Cstrong>estadística bayesiana y más concretamente la inferencia bayesiana \u003C/strong>es un conjunto de métodos estadísticos que en base al teorema de Bayes, realiza estimaciones actualizadas de las distribuciones de probabilidad de parámetros desconocidos a partir probabilidades subjetivas iniciales relativas a ellos, en base a la evidencia proporcionada por los datos.\u003C/p>",{"id":53,"name":54,"slug":55,"html":56},3043,"Media generalizada","media-generalizada","\u003Cp id=\"bkmrk-la-media-generalizad\">La\u003Cstrong> media generalizada\u003C/strong> es la expresión general de una familia o conjunto de medias, entre las que se encuentran las \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/promedio\">medias o promedios\u003C/a>\u003C/strong> más utilizados habitualmente. Se calcula de la siguiente forma, para diferentes valores de un parámetro \\(p\\):\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24mg_p%28x_1%2C%5Cdots%2Cx_n\">$$MG_p(x_1,\\dots,x_n) = \\left( \\frac{1}{n} \\sum_{i=1}^n x_i^p \\right)^{{1}/{p}}$$\u003C/p>\r\n\u003Cp id=\"bkmrk-en-el-caso-especial-\">En el caso especial de \\(p=0\\), puede demostrarse que la media generalizada coincide con la media geométrica:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24m_0%28x_1%2C-%5Cdots%2C-x_\">$$M_0(x_1, \\dots, x_n) = \\left(\\prod_{i=1}^n x_i\\right)^{1/n}$$\u003C/p>\r\n\u003Cp id=\"bkmrk-para-%5C%28p%3D1%5C%29%2C-la-med\">Para \\(p=1\\), la media generalizada coincide con la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/media-aritmetica-simple\">media aritmética simple\u003C/a>\u003C/strong>; para \\(p=2\\); con la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/media-cuadratica\">media cuadrática\u003C/a>\u003C/strong>; y para \\(p=3\\); con la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/media-cubica\">media cúbica\u003C/a>\u003C/strong>. \u003Cbr>\u003C/p>",{"id":58,"name":59,"slug":60,"html":61},37,"Coeficiente de variación","coeficiente-de-variacion","\u003Cp id=\"bkmrk-el-coeficiente-de-va\">\u003Cstrong>El coeficiente de variación o desviación típica porcentual\u003C/strong> se calcula dividiendo la desviación típica entre la media aritmética simple:\u003C!-- /wp:paragraph -->\u003C!-- wp:paragraph -->\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24cv%3D%5Cfrac%7Bs_x%7D%7B%5Cove\">$$CV=\\frac{s_x}{\\overline{x}}$$\u003C!-- /wp:paragraph -->\u003C!-- wp:paragraph -->\u003C/p>\r\n\u003Cp id=\"bkmrk-se-trata-de-una-medi\">Se trata de una medida de dispersión relativa; es decir, se utiliza para comparar dispersiones de diferentes conjuntos de datos. Ciertamente, la desviación típica debe interpretarse siempre conjuntamente con la media aritmética, y es que la desviación típica indica la desviación media de cada dato respecto a la media.\u003C!-- /wp:paragraph -->\u003C!-- wp:paragraph -->\u003C/p>\r\n\u003Cp id=\"bkmrk-por-ejemplo%2C-no-son-\">Por ejemplo, no es lo mismo una desviación de 2 unidades alrededor de una media de 10 unidades que la misma desviación alrededor de una media de 100 unidades: en el primer caso, CV=2/10=0.2=20% y en el segundo caso CV=2/100=0.02=2%, de modo que a pesar de ser las desviaciones iguales las dispersión relativa es mayor en el primer caso.\u003C/p>",{"":63},[64,68,72,76,81,86,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,172,177,182,187,189,194,199,204,209,214,219,224,229,233,238,242,247,252,257,262,267,271,275,280,285,290,295,299,304,309,314,319,324,329,334,339,344,349,354,359,364,369,374,379,384,389,394,399,404,409,414,418,423,428,433,438,443,448,453,458,462,467,472,476,481,486,491,496,498,503,508,513,518,522,527,532,537,542,547,552,557,562,567,572,577,582,587,592,597,602,607,612,617,622,627,632,637,642,647,652,657,662,667,672,677,682,687,692,697,702,707,712,717,722,727,732,737,742,747,752,756,760,765,770,774,778,782,787,792,797,802,806,811,816,818,823,828,833,838,842,847,852,857,862,867,872,877,882,887,892,896,901,906,911,916,921,926,931,936,941,945,950,954,959,964,969,974,979,983,988,993,998,1003,1007,1012,1017,1021,1026,1031,1036,1040,1045,1050,1055,1060,1064,1069,1074,1079,1084,1089,1094,1099,1104,1109,1113,1118,1123,1128,1132,1134,1139,1144,1148,1152,1157,1162,1167,1172,1177,1181,1185,1190,1195,1200,1205,1209,1214,1219,1222,1226,1231,1236,1240,1245,1247,1252,1257,1262,1267,1272,1277,1282,1287,1292,1297,1301,1306,1311,1316,1321,1326,1331,1336,1341,1346,1351,1356,1361,1366,1371,1376,1379,1383,1388,1393,1398,1402,1406,1410,1415,1419,1423,1428,1433,1438,1443,1448,1453,1458,1463,1468,1473,1478,1483,1488,1492,1497,1502,1506,1511,1516,1521,1526,1530,1534,1538,1543,1548,1553,1558,1563,1568,1573,1578,1583,1588,1593,1598,1603,1608,1613,1618,1623,1628,1633,1638,1643,1648,1653,1658],{"id":65,"name":66,"slug":67,"priority":7,"chapter_name":23},3173,"Aleatorización (diseño de experimentos)","aleatorizacion-diseno-de-experimentos",{"id":69,"name":70,"slug":71,"priority":15,"chapter_name":23},631,"Amplitud de clase","amplitud-de-clase",{"id":73,"name":74,"slug":75,"priority":6,"chapter_name":23},387,"Análisis de trayectorias","analisis-de-trayectorias",{"id":77,"name":78,"slug":79,"priority":80,"chapter_name":23},624,"Arranque aleatorio","arranque-aleatorio",3,{"id":82,"name":83,"slug":84,"priority":85,"chapter_name":23},43,"Asociación estadística","asociacion-estadistica",4,{"id":87,"name":88,"slug":89,"priority":21,"chapter_name":23},2019,"Asociación no estadística","asociacion-no-estadistica",{"id":91,"name":92,"slug":93,"priority":94,"chapter_name":23},2948,"Banco de datos","banco-de-datos",6,{"id":96,"name":97,"slug":98,"priority":99,"chapter_name":23},1621,"Base del índice (periodo base)","base-del-indice-periodo-base",7,{"id":101,"name":102,"slug":103,"priority":104,"chapter_name":23},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":23},3063,"Característica cualitativa","caracteristica-cualitativa",9,{"id":111,"name":112,"slug":113,"priority":114,"chapter_name":23},2708,"Casos particulares","casos-particulares",10,{"id":116,"name":117,"slug":118,"priority":119,"chapter_name":23},2730,"Censo estadístico","censo-estadistico",11,{"id":121,"name":122,"slug":123,"priority":124,"chapter_name":23},2551,"Clase mediana","clase-mediana",12,{"id":126,"name":127,"slug":128,"priority":129,"chapter_name":23},1011,"Clase modal","clase-modal",13,{"id":131,"name":132,"slug":133,"priority":134,"chapter_name":23},2133,"Coeficiente de asimetría de Bowley","coeficiente-de-asimetria-de-bowley",14,{"id":136,"name":137,"slug":138,"priority":139,"chapter_name":23},1714,"Coeficiente de asimetría de Fisher","coeficiente-de-asimetria-de-fisher",15,{"id":141,"name":142,"slug":143,"priority":144,"chapter_name":23},1844,"Coeficiente de asimetría de Pearson","coeficiente-de-asimetria-de-pearson",16,{"id":146,"name":147,"slug":148,"priority":149,"chapter_name":23},2057,"Coeficiente de contingencia de Pearson","coeficiente-de-contingencia-de-pearson",17,{"id":151,"name":152,"slug":153,"priority":154,"chapter_name":23},2648,"Coeficiente de correlación biserial puntual","coeficiente-de-correlacion-biserial-puntual",18,{"id":156,"name":157,"slug":158,"priority":159,"chapter_name":23},1938,"Coeficiente de curtosis de Pearson","coeficiente-de-curtosis-de-pearson",19,{"id":161,"name":162,"slug":163,"priority":164,"chapter_name":23},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":23},2649,"Coeficiente de Tschuprow","coeficiente-de-tschuprow",21,{"id":58,"name":59,"slug":60,"priority":171,"chapter_name":23},22,{"id":173,"name":174,"slug":175,"priority":176,"chapter_name":23},2646,"Coeficiente Q de Yule","coeficiente-q-de-yule",23,{"id":178,"name":179,"slug":180,"priority":181,"chapter_name":23},2218,"Comprobación de Charlier","comprobacion-de-charlier",24,{"id":183,"name":184,"slug":185,"priority":186,"chapter_name":23},2095,"Concepto de estadística","concepto-de-estadistica",25,{"id":38,"name":39,"slug":40,"priority":188,"chapter_name":23},26,{"id":190,"name":191,"slug":192,"priority":193,"chapter_name":23},2087,"Corrección de Bessel","correccion-de-bessel",27,{"id":195,"name":196,"slug":197,"priority":198,"chapter_name":23},308,"Corrección de Sheppard","correccion-de-sheppard",28,{"id":200,"name":201,"slug":202,"priority":203,"chapter_name":23},1080,"Corrección de Yates","correccion-de-yates",29,{"id":205,"name":206,"slug":207,"priority":208,"chapter_name":23},49,"Corrección por continuidad","correccion-por-continuidad",30,{"id":210,"name":211,"slug":212,"priority":213,"chapter_name":23},2685,"Correlación","correlacion",31,{"id":215,"name":216,"slug":217,"priority":218,"chapter_name":23},1624,"Correlación espuria (correlación espúrea)","correlacion-espuria-correlacion-espurea",32,{"id":220,"name":221,"slug":222,"priority":223,"chapter_name":23},2684,"Correlación por rangos","correlacion-por-rangos",33,{"id":225,"name":226,"slug":227,"priority":228,"chapter_name":23},1665,"Correlograma","correlograma",34,{"id":230,"name":231,"slug":232,"priority":101,"chapter_name":23},148,"Covariación","covariacion",{"id":234,"name":235,"slug":236,"priority":237,"chapter_name":23},44,"Covarianza","covarianza",36,{"id":239,"name":240,"slug":241,"priority":58,"chapter_name":23},1652,"Criterio (variable)","criterio-variable",{"id":243,"name":244,"slug":245,"priority":246,"chapter_name":23},2135,"Cuartiles (primer cuartil, segundo cuartil, tercer cuartil)","cuartiles-primer-cuartil-segundo-cuartil-tercer-cuartil",38,{"id":248,"name":249,"slug":250,"priority":251,"chapter_name":23},2159,"Cuasivarianza (varianza corregida)","cuasivarianza-varianza-corregida",39,{"id":253,"name":254,"slug":255,"priority":256,"chapter_name":23},1669,"Curtosis (estadística)","curtosis-estadistica",40,{"id":258,"name":259,"slug":260,"priority":261,"chapter_name":23},2072,"Datos agregados","datos-agregados",41,{"id":263,"name":264,"slug":265,"priority":266,"chapter_name":23},1732,"Datos agrupados","datos-agrupados",42,{"id":268,"name":269,"slug":270,"priority":82,"chapter_name":23},2692,"Datos aislados (datos no agrupados)","datos-aislados-datos-no-agrupados",{"id":272,"name":273,"slug":274,"priority":234,"chapter_name":23},2745,"Datos bivariados","datos-bivariados",{"id":276,"name":277,"slug":278,"priority":279,"chapter_name":23},73,"Datos blandos","datos-blandos",45,{"id":281,"name":282,"slug":283,"priority":284,"chapter_name":23},2315,"Datos 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