[{"data":1,"prerenderedAt":1662},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/representacion-grafica-de-datos-y-variables-estadisticas-visualizacion-de-datos-graficos-estadisticos-diagramas-estadisticos:0":3},{"page":4,"book":25,"news":1656,"questionSent":19,"questions":1657,"formData":1658,"attachments":22,"chartData":22,"pending":19,"chartOptions":1659,"afspec":19,"aflink":1661},{"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},4087,2,0,"Representacion gráfica de datos y variables estadísticas (visualizacion de datos, gráficos estadísticos, diagramas estadísticos)","representacion-grafica-de-datos-y-variables-estadisticas-visualizacion-de-datos-graficos-estadisticos-diagramas-estadisticos","\u003Cp id=\"bkmrk-la-representaci%C3%B3n-gr\">La \u003Cstrong>representación gráfica de datos o variables estadísticas\u003C/strong> es el recurso a diagramas de llíneas, barras, puntos y formas geométricas simples para representar gráficamente variables estadísticas o más en general conjuntos de datos con el fin de realizar una exploración visul y poder extraer una primeras conclusiones sobre sus características. La ventaja de su utilización consisten en su simple interpretación, de acuerdo al adagio que afirma que una imagen vale más que mil palabras. \u003C/p>\r\n\u003Cp id=\"bkmrk-el-diagrama-o-gr%C3%A1fic\">El diagrama o gráfico estadístico a utilizar en cada caso dependerá de la naturaleza de los datos y del tipo variable. Como primer aproximación, la utilización de gráficos estadísticos puede responder a esta clasificación:\u003C/p>\r\n\u003Cp id=\"bkmrk-1%3A-variables-cualita\">\u003Cstrong>1: \u003Ca href=\"https://ikusmira.org/p/variable-cualitativa-variable-categorica\">VARIABLES CUALITATIVAS\u003C/a>\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-diagrama-de-sectores\">\r\n\u003Cli class=\"null\" style=\"font-weight: bold;\">\u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/diagrama-de-sectores-grafico-circular\">Diagrama de sectores\u003C/a>\u003C/strong>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/diagrama-de-barras-grafico-de-columnas\">Diagrama de barras\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-2%3A-variables-cuantit\">\u003Cstrong>2: \u003Ca href=\"https://ikusmira.org/p/variable-cuantitativa\">VARIABLES CUANTITATIVAS\u003C/a>\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-2.1%3A-variable-cuanti\">\u003Cstrong>2.1: Variable cuantitativa discreta\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-diagrama-de-barras\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/diagrama-de-barras-grafico-de-columnas\">\u003Cstrong>Diagrama de barras\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-2.2%3A-variable-cuanti\">\u003Cstrong>2.2: Variable cuantitativa continua\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-2.2.1%3A-n%C3%BAmero-de-dat\">\u003Cstrong>2.2.1: Número de datos pequeño: \u003Ca href=\"https://ikusmira.org/p/grafico-de-puntos-diagrama-de-puntos\">Diagrama de puntos\u003C/a>\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-2.2.2%3A-n%C3%BAmero-de-dat\">\u003Cstrong>2.2.2: Número de datos grande: \u003Ca href=\"https://ikusmira.org/p/histograma\">Histograma\u003C/a>, \u003Ca href=\"https://ikusmira.org/p/poligono-de-frecuencias\">polígono de frecuencias\u003C/a>, \u003Ca href=\"https://ikusmira.org/p/ojiva-estadistica\">ojiva\u003C/a>.\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\"> \u003C/p>",332,"2026-03-08T08:02:35.000000Z","2026-03-08T08:30:33.000000Z",{"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-la-representaci%C3%B3n-gr\">La \u003Cstrong>representación gráfica de datos o variables estadísticas\u003C/strong> es el recurso a diagramas de llíneas, barras, puntos y formas geométricas simples para representar gráficamente variables estadísticas o más en general conjuntos de datos con el fin de realizar una exploración visul y poder extraer una primeras conclusiones sobre sus características. La ventaja de su utilización consisten en su simple interpretación, de acuerdo al adagio que afirma que una imagen vale más que mil palabras. \u003C/p>\r\n\u003Cp id=\"bkmrk-el-diagrama-o-gr%C3%A1fic\">El diagrama o gráfico estadístico a utilizar en cada caso dependerá de la naturaleza de los datos y del tipo variable. Como primer aproximación, la utilización de gráficos estadísticos puede responder a esta clasificación:\u003C/p>\r\n\u003Cp id=\"bkmrk-1%3A-variables-cualita\">\u003Cstrong>1: \u003Ca href=\"https://ikusmira.org/p/variable-cualitativa-variable-categorica\">VARIABLES CUALITATIVAS\u003C/a>\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-diagrama-de-sectores\">\r\n\u003Cli class=\"null\" style=\"font-weight: bold;\">\u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/diagrama-de-sectores-grafico-circular\">Diagrama de sectores\u003C/a>\u003C/strong>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/diagrama-de-barras-grafico-de-columnas\">Diagrama de barras\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-2%3A-variables-cuantit\">\u003Cstrong>2: \u003Ca href=\"https://ikusmira.org/p/variable-cuantitativa\">VARIABLES CUANTITATIVAS\u003C/a>\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-2.1%3A-variable-cuanti\">\u003Cstrong>2.1: Variable cuantitativa discreta\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-diagrama-de-barras\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/diagrama-de-barras-grafico-de-columnas\">\u003Cstrong>Diagrama de barras\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-2.2%3A-variable-cuanti\">\u003Cstrong>2.2: Variable cuantitativa continua\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-2.2.1%3A-n%C3%BAmero-de-dat\">\u003Cstrong>2.2.1: Número de datos pequeño: \u003Ca href=\"https://ikusmira.org/p/grafico-de-puntos-diagrama-de-puntos\">Diagrama de puntos\u003C/a>\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-2.2.2%3A-n%C3%BAmero-de-dat\">\u003Cstrong>2.2.2: Número de datos grande: \u003Ca href=\"https://ikusmira.org/p/histograma\">Histograma\u003C/a>, \u003Ca href=\"https://ikusmira.org/p/poligono-de-frecuencias\">polígono de frecuencias\u003C/a>, \u003Ca href=\"https://ikusmira.org/p/ojiva-estadistica\">ojiva\u003C/a>.\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\"> \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":1649},"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},2646,"Coeficiente Q de Yule","coeficiente-q-de-yule","\u003Cp id=\"bkmrk-el-coeficiente-q-de-\">El \u003Cstrong>coeficiente Q de Yule \u003C/strong>es una medida de asociación nominal y ordinal entre dos \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/variable-dicotomica-variable-binaria\">variables dicotómicas o binarias\u003C/a>\u003C/strong>, calculado a partir de la tabla de contingencia 2x2 que forman los datos referidos a las dos variables. Dada la siguiente tabla de contingencia:\u003C/p>\r\n\u003Ctable id=\"bkmrk-tabla-de-contingenci\" style=\"border-collapse: collapse; width: 62.381%; height: 97px; border-width: 3px;\" border=\"1\">\u003Ccolgroup>\u003Ccol style=\"width: 41.1392%;\">\u003Ccol style=\"width: 23.2068%;\">\u003Ccol style=\"width: 20.8861%;\">\u003Ccol style=\"width: 14.9789%;\">\u003C/colgroup>\r\n\u003Ctbody>\r\n\u003Ctr>\r\n\u003Ctd style=\"border-width: 3px;\">Tabla de contingencia\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border-width: 3px;\">\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border-width: 3px;\">\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border-width: 3px;\">Totales\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr>\r\n\u003Ctd style=\"border-width: 3px;\">\u003Cbr>\u003C/td>\r\n\u003Ctd>a\u003Cbr>\u003C/td>\r\n\u003Ctd>b\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border-width: 3px;\">a+b\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr>\r\n\u003Ctd style=\"border-width: 3px;\">\u003Cbr>\u003C/td>\r\n\u003Ctd>c\u003Cbr>\u003C/td>\r\n\u003Ctd>d\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border-width: 3px;\">c+d\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr>\r\n\u003Ctd style=\"border-width: 3px;\">Totales\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border-width: 3px;\">a+c\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border-width: 3px;\">b+d\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border-width: 3px;\">a+b+c+d\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003C/tbody>\r\n\u003C/table>\r\n\u003Cp id=\"bkmrk-%24%24%5Cphi%3D%5Ccfrac%7Bac-bd%7D\">el coeficiente Q de Yule se calcula de esta forma:\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24q%3D%5Ccfrac%7Bad-bc%7D%7Bad\">$$Q=\\cfrac{ad-bc}{ad+bc}\u003C/p>\r\n\u003Cp id=\"bkmrk-el-coeficiente-toma-\">El coeficiente toma valores en el intervalo [-1,1], indicando un valor cercano a 1 en el caso de asociación ordinal una asociación directa entre las dos variables (cuando una sube de nivel, la otra también, en términos generales), mientras que un valor cercano a -1 indicaría una asociación inversa (cuando una variable sube de nivel, la otra baja, siempre en términos generales).  En este sentido de asociación ordinal, el coeficiente Q de Yule es equivalente al coeficiente de correlación ordinal gamma de Goodman y Kruskal cuando la tabla de contingencia es 2x2. \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-cuando-el-coeficient\">Cuando el coeficiente se utiliza para medir la asociación entre variables nominales, la interpretación del valor de la Q de Yule debe realizarse a partir de su valor absoluto, de modo que tomará valores en el intervalo [0,1], interpretánodse como asociación alta un valor del coeficiente cercano a 1. \u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-phi-%28coeficiente-de-\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/phi-coeficiente-de-correlacion-y-asociacion\">\u003Cstrong>Phi (coeficiente de correlación y asociación)\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/v-de-cramer\">\u003Cstrong>V de Cramér\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-referencias\">\u003Cstrong>Referencias\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-on-the-association-o\">\r\n\u003Cli class=\"null\">\r\n\u003Cp class=\"citation__title\">\u003Ca href=\"https://royalsocietypublishing.org/doi/10.1098/rsta.1900.0019\">On the association of attributes in statistics, George Udny Yule, 1900\u003C/a>\u003Cbr>\u003C/p>\r\n\u003C/li>\r\n\u003C/ul>\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},2731,"Muestreo estadístico","muestreo-estadistico","\u003Cp id=\"bkmrk-muestreo-estad%C3%ADstico\">\u003Cstrong>Muestreo estadístico \u003C/strong>es el conjunto de metodologías y procedimientos desarrollados para la selección y análisis de \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/muestra-estadistica\">muestras estadísticas\u003C/a>\u003C/strong> con el objeto de realizar inferencias o extraer conclusiones sobre una población estadística a partir de los resultados de dichas muestras, examinando y controlando además el error cometido a la hora de realizar dichas inferencias. \u003C/p>",{"id":42,"name":43,"slug":44,"html":45},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":47,"name":48,"slug":49,"html":50},138,"Media cuadrática","media-cuadratica","\u003Cp id=\"bkmrk-la-media-cuadr%C3%A1tica-\">La \u003Cstrong>media cuadrática\u003C/strong> es un promedio utilizado principalmente para situaciones en la que en un mismo conjunto de datos existen datos positivos y negativos. Por ello, es un promedio especialmente adecuado para calcular el valor medio de una serie de errores, que pueden tanto negativos como positivos, por defecto o por exceso. Para los datos $x_1,x_2,\\ldots,x_n$, se calcula de acuerdo a esta formula:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24c%3D%5Csqrt%7B%5Ccfrac%7B%5Csu\">$$C=\\sqrt{\\cfrac{\\sum_{i=1}^nx_i^2}{n}}$$\u003C/p>\r\n\u003Cp id=\"bkmrk-si-utilizamos-la-med\">Si utilizamos la media aritmética para el conjunto de errores -2/-3/1/6, la media aritmética da como resultado 0.5, valor que evidentemente no refleja adecuadamente el error promedio, y ello por un efecto de compensación entre datos negativos y positivos. La media cuadrática resuelve ese obstáculo sumando los cuadrados de los valores, de forma que tanto los datos positivos y negativos quedan transformados en positivos; se suman dichos cuadrados; se calcula su media, y finalmente para deshacer la transformación cuadrática se calcula la raíz cuadrada del resultado:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24c%3D%5Csqrt%7B%5Ccfrac%7B%28-2\">$$C=\\sqrt{\\cfrac{(-2)^2+(-3)^2+1^2+6^2}{4}}=3.53$$\u003C/p>\r\n\u003Cp id=\"bkmrk-este-valor-s%C3%AD-que-re\">Este valor sí que refleja adecuadamente el error medio representativo de los errores medidos.\u003C/p>\r\n\u003Cp id=\"bkmrk-dicha-aplicaci%C3%B3n-de-\">Dicha aplicación de la media cuadrática para el cálculo del error medio, encuentra su lugar en otra medida habitual en estadística, la desviación típica, medida de dispersión que no es más que la media cuadrática de las distancias de cada dato a la media aritmética.\u003C/p>\r\n\u003Cp id=\"bkmrk-el-inconveniente-de-\">El inconveniente de la media cuadrática radica en su sensibilidad a los valores extremos y atípicos, que exageran su resultado y por lo tanto restan representatividad como promedio. Así pues, se trata de una \u003Ca href=\"https://sigmalitika.hirusta.io/termino/robustez-estadistica/\">medida no robusta\u003C/a>.\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>\r\n\u003Cp id=\"bkmrk-\">\u003C/p>\r\n\u003Ctable id=\"bkmrk-demografia-biztanler\" style=\"border: 1px solid rgb(170, 170, 170); border-collapse: collapse; background-color: rgb(249, 249, 249); width: 877px; margin: 2em auto; height: 148.6px; font-size: 13px;\">\r\n\u003Ctbody>\r\n\u003Ctr style=\"height: 26.6px;\">\r\n\u003Ctd class=\"align-left\" style=\"border: 1px solid rgb(170, 170, 170); background-color: rgb(204, 204, 255); font-weight: bold; padding: 5px; text-align: center; height: 26.6px; width: 865px;\" colspan=\"2\">\u003Ca href=\"https://ikusmira.org/p/medidas-de-tendencia-central\">Medidas de tendencia central\u003C/a>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 26.6px;\">\r\n\u003Ctd class=\"align-left\" style=\"border: 1px solid rgb(170, 170, 170); background-color: rgb(230, 230, 255); font-weight: bold; padding: 5px; width: 432.5px; height: 26.6px;\">\u003Cbr>Medidas de tendencia central clásicas\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); padding: 5px; height: 26.6px; width: 432.5px;\">\r\n\u003Cdiv style=\"display: flex; flex-wrap: wrap; gap: 0.5em; align-items: center;\"> \u003Ca href=\"https://ikusmira.org/p/media-aritmetica-simple\">Media aritmética simple\u003C/a>(\u003Ca href=\"https://ikusmira.org/p/media-aritmetica-para-datos-agrupados\">media aritmética para datos agrupados\u003C/a>) \u003Cbr>\u003C/div>\r\n\u003Cdiv style=\"display: flex; flex-wrap: wrap; gap: 0.5em; align-items: center;\"> – \u003Ca href=\"https://ikusmira.org/p/mediana-estadistica\">Mediana \u003C/a>(\u003Ca href=\"https://ikusmira.org/p/mediana-para-datos-agrupados-calculo\">mediana para datos agrupados en intervalos\u003C/a>–\u003Cbr>\u003C/div>\r\n\u003Cdiv style=\"display: flex; flex-wrap: wrap; gap: 0.5em; align-items: center;\">\u003Ca href=\"https://ikusmira.org/p/clase-mediana\">clase mediana\u003C/a>) –  \u003Ca href=\"https://ikusmira.org/p/moda-estadistica\">Moda\u003C/a> (\u003Ca href=\"https://ikusmira.org/p/moda-absoluta-y-moda-relativa\">moda absoluta y moda relativa\u003C/a>–\u003Cbr>\u003Ca href=\"https://ikusmira.org/p/calculo-de-la-moda-estadistica-para-datos-agrupados-en-intervalos\">moda para datos agrupados en intervalos\u003C/a>)\u003C/div>\r\n\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 42.2px;\">\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); background-color: rgb(230, 230, 255); font-weight: bold; padding: 5px; width: 432.5px; height: 42.2px;\">Otras medidas de tendencia central\u003C/td>\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); padding: 5px; height: 42.2px; width: 432.5px;\">\r\n\u003Cdiv style=\"display: flex; flex-wrap: wrap; gap: 0.5em; align-items: center;\">\u003Ca href=\"https://ikusmira.org/p/media-ponderada\">Media ponderada\u003C/a> (\u003Ca href=\"https://ikusmira.org/p/media-aritmetica-ponderada\">media aritmética ponderada\u003C/a>) –\u003Ca href=\"https://ikusmira.org/p/media-cuadratica\">Media cuadrática\u003C/a>– Medias pitagóricas (\u003Ca href=\"https://ikusmira.org/p/media-geometrica\">media geométrica\u003C/a>, \u003Ca href=\"https://ikusmira.org/p/media-armonica\">media armónica\u003C/a>) – \u003Ca href=\"https://ikusmira.org/p/media-cubica\">Media cúbica\u003C/a> – \u003Ca href=\"https://ikusmira.org/p/media-generalizada\">Media generalizada\u003C/a>\u003Cbr>\u003C/div>\r\n\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 26.6px;\">\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); background-color: rgb(230, 230, 255); font-weight: bold; padding: 5px; width: 432.5px; height: 26.6px;\">Conceptos relacionados\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); padding: 5px; height: 26.6px; width: 432.5px;\">\r\n\u003Cdiv style=\"display: flex; flex-wrap: wrap; gap: 0.5em; align-items: center;\">\u003Ca href=\"https://ikusmira.org/p/promedio\">Promedios\u003C/a> – \u003Ca href=\"https://ikusmira.org/p/media-de-medias-media-general-media-agregada\">Media de medias\u003C/a> – Desigualdades entre medias\u003Cbr>\u003C/div>\r\n\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr>\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); background-color: rgb(230, 230, 255); font-weight: bold; padding: 5px; width: 432.5px;\">Medias en inferencia estadística\u003C/td>\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); padding: 5px; width: 432.5px;\">\r\n\u003Cdiv style=\"display: flex; flex-wrap: wrap; gap: 0.5em; align-items: center;\">\u003Ca href=\"https://ikusmira.org/p/media-poblacional\">Media poblacional\u003C/a> –  \u003Ca href=\"https://ikusmira.org/p/media-muestral\">Media muestral \u003C/a>\u003C/div>\r\n\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 26.6px;\">\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); background-color: rgb(230, 230, 255); font-weight: bold; padding: 5px; width: 432.5px; height: 26.6px;\">\u003Ca href=\"https://ikusmira.org/p/robustez-estadistica\">Medidas robustas\u003C/a> de tendencia central\u003C/td>\r\n\u003Ctd style=\"border: 1px solid rgb(170, 170, 170); padding: 5px; height: 26.6px; width: 432.5px;\">\r\n\u003Cdiv style=\"display: flex; flex-wrap: wrap; gap: 0.5em; align-items: center;\">\u003Ca href=\"https://ikusmira.org/p/medias-recortadas-medias-truncadas\">Medias recortadas\u003C/a> (\u003Ca href=\"https://ikusmira.org/p/promedio-intercuartil\">promedio intercuartil\u003C/a>) – \u003Ca href=\"https://ikusmira.org/p/media-winsorizada\">Medias winsorizadas\u003C/a> – \u003Ca href=\"https://ikusmira.org/p/medio-rango\">Medio rango\u003C/a> – \u003Ca href=\"https://ikusmira.org/p/medio-rango-intercuartil\">Medio rango intercuartil\u003C/a> – \u003Ca href=\"https://ikusmira.org/p/trimedia\">Trimedia \u003C/a>\u003Cbr>\u003C/div>\r\n\u003C/td>\r\n\u003C/tr>\r\n\u003C/tbody>\r\n\u003C/table>",{"id":52,"name":53,"slug":54,"html":55},2229,"Variable politómica","variable-politomica","\u003Cp id=\"bkmrk-una-variable-polit%C3%B3m\">Una \u003Cstrong>variable politómica o variable policotómica\u003C/strong> es aquella \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/variable-cualitativa-variable-categorica\">variable estadística cualitativa\u003C/a>\u003C/strong> que incluye más de dos modalidades o categorías, a diferencia de las \u003Ca href=\"https://ikusmira.org/p/variable-dicotomica-variable-binaria\">\u003Cstrong>variables dicotómicas\u003C/strong>\u003C/a> que únicamente tienen dos categorías. Por ejemplo, son variables politómicas el nivel educativo (primaria/secundaria/bachillerato/universidad) y el grado universitario que se está cursando (ciencias sociales/ciencias puras/humanidades/tecnología).\u003C/p>",{"id":57,"name":58,"slug":59,"html":60},2066,"Diagrama de tallo y hojas","diagrama-de-tallo-y-hojas","\u003Cp id=\"bkmrk-el-diagrama-de-tallo\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2025-03/99Awp0Z0ZKPCIZWJ-tallo-hojas.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2025-03/scaled-1680-/99Awp0Z0ZKPCIZWJ-tallo-hojas.png\" alt=\"tallo_hojas.png\" width=\"461\" height=\"250\">\u003C/a>El \u003Cstrong>diagrama de tallo y hojas o gráfico (gŕafica) de tallo y hojas, también llamado representación de tronco y hojas, \u003C/strong>es un diagrama que se utiliza para presentar los datos originales de una \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/variable-cuantitativa-continua\">variable estadística cuantitativa continua\u003C/a>\u003C/strong>, proporcionando al mismo tiempo una representación gráfica de la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/distribucion-de-frecuencias\">distribución de frecuencias\u003C/a>\u003C/strong> de dichos datos, de forma similar a un \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/histograma\">histograma \u003C/a>\u003C/strong>con barras horizontales. Para ello, se toman como tallos las diferentes primeras cifras significativas de los datos, en forma de líneas, a las que van añadiendo las siguientes cifras significativas correspondientes a cada dato en el tallo que le corresponda, de modo que a medida tras unas primeras cifras significativas se encuentran más datos, la línea de hojas detrás de cada tallo se va alargando, de modo que los tallos más largos indican una mayor frecuencia de datos. La ventaja del diagrama de tallos y hojas es que realiza la agrupación de datos y por tanto establece la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/distribucion-de-frecuencias-agrupada-en-intervalos\">distribución de frecuencias por intervalos\u003C/a>\u003C/strong> sin que haya pérdida de información respecto de los datos originales. \u003C/p>\r\n\u003Cp id=\"bkmrk-el-diagrama-de-talol\">El diagrama de tallo y hojas fue desarrollado por el estadístico estadounidense John Tukey en la década de 1970. \u003C/p>",{"":62},[63,67,71,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,177,182,187,192,197,202,207,212,217,222,227,232,236,241,245,250,255,260,265,270,274,278,283,288,293,298,302,307,312,317,322,327,332,337,342,344,349,354,359,364,369,374,379,384,389,394,399,404,409,414,418,423,428,433,438,443,448,453,458,462,467,472,476,481,486,491,496,501,506,511,516,521,525,530,535,540,545,550,555,560,565,570,575,580,585,590,595,600,605,610,615,620,625,630,635,640,645,650,655,660,665,670,675,680,685,690,695,700,705,710,715,720,725,730,735,739,744,749,754,758,762,767,772,776,780,784,789,794,799,804,806,811,816,821,826,831,836,841,845,850,855,860,865,870,875,880,885,890,895,899,904,909,914,919,924,929,934,939,944,948,953,957,962,967,972,977,982,986,991,993,998,1003,1007,1012,1017,1021,1026,1031,1036,1040,1045,1050,1055,1060,1064,1069,1074,1079,1084,1089,1094,1099,1104,1109,1113,1118,1123,1128,1132,1137,1142,1147,1151,1155,1160,1165,1170,1175,1180,1184,1188,1193,1198,1203,1208,1212,1217,1219,1222,1226,1231,1236,1240,1245,1250,1255,1260,1265,1270,1275,1280,1285,1290,1295,1300,1304,1309,1314,1319,1324,1329,1334,1339,1344,1346,1351,1356,1361,1366,1371,1376,1379,1383,1388,1393,1398,1402,1406,1410,1415,1419,1423,1428,1433,1438,1443,1448,1453,1458,1463,1468,1473,1478,1483,1488,1492,1497,1502,1506,1511,1516,1521,1526,1530,1534,1538,1543,1548,1553,1558,1563,1568,1573,1578,1583,1588,1593,1598,1603,1608,1613,1618,1623,1628,1633,1638,1643,1648],{"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":32,"name":33,"slug":34,"priority":176,"chapter_name":22},23,{"id":178,"name":179,"slug":180,"priority":181,"chapter_name":22},2218,"Comprobación de Charlier","comprobacion-de-charlier",24,{"id":183,"name":184,"slug":185,"priority":186,"chapter_name":22},2095,"Concepto de estadística","concepto-de-estadistica",25,{"id":188,"name":189,"slug":190,"priority":191,"chapter_name":22},2607,"Constante estadística","constante-estadistica",26,{"id":193,"name":194,"slug":195,"priority":196,"chapter_name":22},2087,"Corrección de Bessel","correccion-de-bessel",27,{"id":198,"name":199,"slug":200,"priority":201,"chapter_name":22},308,"Corrección de Sheppard","correccion-de-sheppard",28,{"id":203,"name":204,"slug":205,"priority":206,"chapter_name":22},1080,"Corrección de Yates","correccion-de-yates",29,{"id":208,"name":209,"slug":210,"priority":211,"chapter_name":22},49,"Corrección por continuidad","correccion-por-continuidad",30,{"id":213,"name":214,"slug":215,"priority":216,"chapter_name":22},2685,"Correlación","correlacion",31,{"id":218,"name":219,"slug":220,"priority":221,"chapter_name":22},1624,"Correlación espuria (correlación espúrea)","correlacion-espuria-correlacion-espurea",32,{"id":223,"name":224,"slug":225,"priority":226,"chapter_name":22},2684,"Correlación por rangos","correlacion-por-rangos",33,{"id":228,"name":229,"slug":230,"priority":231,"chapter_name":22},1665,"Correlograma","correlograma",34,{"id":233,"name":234,"slug":235,"priority":101,"chapter_name":22},148,"Covariación","covariacion",{"id":237,"name":238,"slug":239,"priority":240,"chapter_name":22},44,"Covarianza","covarianza",36,{"id":242,"name":243,"slug":244,"priority":171,"chapter_name":22},1652,"Criterio (variable)","criterio-variable",{"id":246,"name":247,"slug":248,"priority":249,"chapter_name":22},2135,"Cuartiles (primer cuartil, segundo cuartil, tercer cuartil)","cuartiles-primer-cuartil-segundo-cuartil-tercer-cuartil",38,{"id":251,"name":252,"slug":253,"priority":254,"chapter_name":22},2159,"Cuasivarianza (varianza corregida)","cuasivarianza-varianza-corregida",39,{"id":256,"name":257,"slug":258,"priority":259,"chapter_name":22},1669,"Curtosis (estadística)","curtosis-estadistica",40,{"id":261,"name":262,"slug":263,"priority":264,"chapter_name":22},2072,"Datos agregados","datos-agregados",41,{"id":266,"name":267,"slug":268,"priority":269,"chapter_name":22},1732,"Datos agrupados","datos-agrupados",42,{"id":271,"name":272,"slug":273,"priority":81,"chapter_name":22},2692,"Datos aislados (datos no agrupados)","datos-aislados-datos-no-agrupados",{"id":275,"name":276,"slug":277,"priority":237,"chapter_name":22},2745,"Datos bivariados","datos-bivariados",{"id":279,"name":280,"slug":281,"priority":282,"chapter_name":22},73,"Datos blandos","datos-blandos",45,{"id":284,"name":285,"slug":286,"priority":287,"chapter_name":22},2315,"Datos cualitativos","datos-cualitativos",46,{"id":289,"name":290,"slug":291,"priority":292,"chapter_name":22},2900,"Datos desagregados","datos-desagregados",47,{"id":294,"name":295,"slug":296,"priority":297,"chapter_name":22},241,"Datos estructurados y datos no estructurados","datos-estructurados-y-datos-no-estructurados",48,{"id":299,"name":300,"slug":301,"priority":208,"chapter_name":22},2726,"Datos no agrupados","datos-no-agrupados",{"id":303,"name":304,"slug":305,"priority":306,"chapter_name":22},2038,"Deciles","deciles",50,{"id":308,"name":309,"slug":310,"priority":311,"chapter_name":22},142,"Desigualdad de Markov","desigualdad-de-markov",51,{"id":313,"name":314,"slug":315,"priority":316,"chapter_name":22},1609,"Desviación media absoluta","desviacion-media-absoluta",52,{"id":318,"name":319,"slug":320,"priority":321,"chapter_name":22},1923,"Desviación típica (desviación estándar)","desviacion-tipica-desviacion-estandar",53,{"id":323,"name":324,"slug":325,"priority":326,"chapter_name":22},2055,"Diagrama de barras (gráfico de columnas)","diagrama-de-barras-grafico-de-columnas",54,{"id":328,"name":329,"slug":330,"priority":331,"chapter_name":22},2945,"Diagrama de caja y bigotes","diagrama-de-caja-y-bigotes",55,{"id":333,"name":334,"slug":335,"priority":336,"chapter_name":22},2765,"Diagrama de frecuencias","diagrama-de-frecuencias",56,{"id":338,"name":339,"slug":340,"priority":341,"chapter_name":22},1854,"Diagrama de sectores (gráfico circular)","diagrama-de-sectores-grafico-circular",57,{"id":57,"name":58,"slug":59,"priority":343,"chapter_name":22},58,{"id":345,"name":346,"slug":347,"priority":348,"chapter_name":22},775,"Diseño experimental","diseno-experimental",59,{"id":350,"name":351,"slug":352,"priority":353,"chapter_name":22},279,"Distribución asimétrica negativa (a la izquierda)","distribucion-asimetrica-negativa-a-la-izquierda",60,{"id":355,"name":356,"slug":357,"priority":358,"chapter_name":22},3180,"Distribución asimétrica positiva (a la derecha)","distribucion-asimetrica-positiva-a-la-derecha",61,{"id":360,"name":361,"slug":362,"priority":363,"chapter_name":22},3172,"Distribución bimodal","distribucion-bimodal",62,{"id":365,"name":366,"slug":367,"priority":368,"chapter_name":22},307,"Distribución bivariada","distribucion-bivariada",63,{"id":370,"name":371,"slug":372,"priority":373,"chapter_name":22},795,"Distribución conjunta","distribucion-conjunta",64,{"id":375,"name":376,"slug":377,"priority":378,"chapter_name":22},1702,"Distribución de frecuencias","distribucion-de-frecuencias",65,{"id":380,"name":381,"slug":382,"priority":383,"chapter_name":22},2634,"Distribución de frecuencias acumuladas","distribucion-de-frecuencias-acumuladas",66,{"id":385,"name":386,"slug":387,"priority":388,"chapter_name":22},1693,"Distribución de frecuencias agrupada en intervalos","distribucion-de-frecuencias-agrupada-en-intervalos",67,{"id":390,"name":391,"slug":392,"priority":393,"chapter_name":22},349,"Distribución de llegadas","distribucion-de-llegadas",68,{"id":395,"name":396,"slug":397,"priority":398,"chapter_name":22},2880,"Distribución dicotómica","distribucion-dicotomica",69,{"id":400,"name":401,"slug":402,"priority":403,"chapter_name":22},1818,"Distribución mesocúrtica, distribución platicúrtica y distribución leptocúrtica","distribucion-mesocurtica-distribucion-platicurtica-y-distribucion-leptocurtica",70,{"id":405,"name":406,"slug":407,"priority":408,"chapter_name":22},2897,"Distribución monomodular o equiespaciada","distribucion-monomodular-o-equiespaciada",71,{"id":410,"name":411,"slug":412,"priority":413,"chapter_name":22},2275,"Distribución muestral de un 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