[{"data":1,"prerenderedAt":1677},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/distribucion-marginal: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},4060,2,0,"Distribución marginal","distribucion-marginal","\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-una-\">En estadística, una \u003Cstrong>distribución marginal\u003C/strong> es la distribución de frecuencias de una variable estadística unidimensional X  o la distribución de probabilidad de una variable aleatoria unidimensional X sin tener en cuenta el valor que toman otras variables Y y calculada a partir de la distribución conjunta que presenta dicha variable junto con ese otro conjunto de variables.\u003C/p>\r\n\u003Cp id=\"bkmrk-para-cada-variable-x\">Para cada variable X, su distribución marginal se determina asignando a cada valor de dicha variable,\u003C/p>\r\n\u003Cul id=\"bkmrk-%C2%A0la-suma-de-frecuenc\">\r\n\u003Cli class=\"null\"> la suma de frecuencias para el resto de valores del resto de variables en la tabla de contigencia correspondiente, en el caso de una distribución de datos;\u003C/li>\r\n\u003Cli class=\"null\">la suma de probabilidades para todos los valores de las otras variables aleatorias en el caso de una distribución de probabilidad conjunta discreta;\u003C/li>\r\n\u003Cli class=\"null\">la integral en el conjunto de valores del resto de variables aleaorias, en el caso de una distribución de probabilidad conjunta continua. \u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-probabilidad-margina\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/probabilidad-marginal\">\u003Cstrong>Probabilidad marginal\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",330,"2026-03-03T16:02:52.000000Z","2026-03-03T16:18:04.000000Z",{"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-una-\">En estadística, una \u003Cstrong>distribución marginal\u003C/strong> es la distribución de frecuencias de una variable estadística unidimensional X  o la distribución de probabilidad de una variable aleatoria unidimensional X sin tener en cuenta el valor que toman otras variables Y y calculada a partir de la distribución conjunta que presenta dicha variable junto con ese otro conjunto de variables.\u003C/p>\r\n\u003Cp id=\"bkmrk-para-cada-variable-x\">Para cada variable X, su distribución marginal se determina asignando a cada valor de dicha variable,\u003C/p>\r\n\u003Cul id=\"bkmrk-%C2%A0la-suma-de-frecuenc\">\r\n\u003Cli class=\"null\"> la suma de frecuencias para el resto de valores del resto de variables en la tabla de contigencia correspondiente, en el caso de una distribución de datos;\u003C/li>\r\n\u003Cli class=\"null\">la suma de probabilidades para todos los valores de las otras variables aleatorias en el caso de una distribución de probabilidad conjunta discreta;\u003C/li>\r\n\u003Cli class=\"null\">la integral en el conjunto de valores del resto de variables aleaorias, en el caso de una distribución de probabilidad conjunta continua. \u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-probabilidad-margina\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/probabilidad-marginal\">\u003Cstrong>Probabilidad marginal\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",[],{"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},2726,"Datos no agrupados","datos-no-agrupados","\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cem>Puede interesarte también: \u003Ca href=\"https://ikusmira.org/p/datos-agrupados\">Datos agrupados\u003C/a>. \u003C/em>\u003C/p>\r\n\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-los-\">En estadística, los \u003Cstrong>datos no agrupados\u003C/strong> son aquellos que no se han reunido en una \u003Ca href=\"https://ikusmira.org/p/distribucion-de-frecuencias\">tabla de frecuencias\u003C/a>, en base a ciertas categorías, valores de variable o intervalos de clase, y que por tanto consisten simplemente en la lista de datos cualitativos o cuantitativos. Así pues, los datos no agrupados son los datos tal como aparecen en la masa de datos, esto es, los datos en bruto o en crudo. \u003C/p>\r\n\u003Cp id=\"bkmrk-la-distinci%C3%B3n-entre-\">La distinción entre datos agrupados y datos no agrupados es importante a la hora de establecer las fórmulas para el cálculo de los estadísticos muestrales. Por ejemplo, para calcular la media aritmética simple a partir de datos no agrupados (básicamente, una lista de datos numéricos), se utiliza esta fórmula, según la cual no hay más que sumar los datos individuales \\(x_i\\) y dividirlos por el número de datos \\(n\\):\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24%5Coverline%7Bx%7D%3D%5Ccfra\">$$\\overline{x}=\\cfrac{\\sum_ix_i}{n}$$\u003C/p>\r\n\u003Cp id=\"bkmrk-sin-embargo%2C-si-los-\">Sin embargo, si los datos se encuentran agrupados en base a los diferentes valores que toman los datos \\(x_i\\), correspondiendo a cada valor una frecuencia absoluta \\(n_i\\), el cálculo de la media aritmética se realiza de acuerdo a la siguiente fórmula:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24%5Coverline%7Bx%7D%3D%5Ccfra-1\">$$\\overline{x}=\\cfrac{\\sum_in_ix_i}{\\sum_in_i}$$\u003C/p>\r\n\u003Cp id=\"bkmrk-hay-que-tener-en-cue\">Hay que tener en cuenta por tanto que el valor \\(x_i\\) indica conceptos diferentes para datos no agrupados y agrupados: en datos no agrupados indica un dato numérico sin agrupar (y por tanto se puede repetir), mientras que en el contexto de datos agrupados indica el valor que toma una variable, siendo \\(n_i\\) el número de veces que se repite dicho valor. \u003C/p>",{"id":37,"name":38,"slug":39,"html":40},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>",{"id":42,"name":43,"slug":44,"html":45},1690,"Histograma","histograma","\u003Cp id=\"bkmrk-un-histograma-es-una\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2024-02/lAV5WXcPt4Vspqzv-tomate-histograma.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg src=\"https://es.gizapedia.org/uploads/images/gallery/2024-02/scaled-1680-/lAV5WXcPt4Vspqzv-tomate-histograma.png\" alt=\"tomate_histograma.png\" width=\"494\" height=\"494\">\u003C/a>\u003C/p>\r\n\u003Cp id=\"bkmrk-imagen%3A-histograma-d\">\u003Cem>Imagen: Histograma de los pesos en gramos de una muestra de 100 tomates. En el intervalo 200gr-220gr se encuentran 6 tomates. El histograma puede utilizarse para posicionar el centro de la distribución, en este caso alrededor de 260gr aproximadamente, y visualizar la amplitud total de la distribución.\u003C/em>\u003C/p>\r\n\u003Cp id=\"bkmrk-un%C2%A0histograma-es-una\">Un \u003Cstrong>histograma o más exactamente un histograma de frecuencias\u003C/strong> es una \u003Ca href=\"https://ikusmira.org/p/representacion-grafica\">representación gráfica\u003C/a> de una \u003Ca href=\"https://ikusmira.org/p/variable-estadistica-discreta-y-variable-estadistica-continua\">variable estadística continua\u003C/a> (es decir, que toma muchos diferentes valores) adecuada para aquellos casos en el tamaño de muestra o número de datos es alto, con generalidad puede decirse que mayor que 20, \u003Ca href=\"https://ikusmira.org/p/distribucion-de-frecuencias-agrupada-en-intervalos\">agrupando para ello los datos\u003C/a> en \u003Ca href=\"https://ikusmira.org/p/intervalo-de-clase\">intervalos de clase\u003C/a> consecutivos y representando las \u003Ca href=\"https://ikusmira.org/p/frecuencia-de-clase\">frecuencias de dichos intervalos\u003C/a> a través de barras contiguas. Por ejemplo, un histograma es un diagrama apropiado para representar las alturas o pesos de una muestra grande de jóvenes, o las rentas percibidas por una población de familias. No sería un gráfico adecuado para, por ejemplo, representar el número de hermanos por familia,  por ser en este caso la variable discreta (con pocos valores diferentes, sería más conveniente para esa situación un diagrama de barras) o los tiempos de una carrera de 1.500m de 12 atletas, por no disponer en este caso de un número insuficiente de datos (sería más oportuno un \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/diagrama-de-caja-y-bigotes\">diagrama de caja\u003C/a>\u003C/strong> o \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/grafico-de-puntos-diagrama-de-puntos\">diagrama de puntos\u003C/a>\u003C/strong>). \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-una-muestra-grande-d\">Una muestra grande de datos referidos a una variable continua resulta difícil de interpretar por sí sola, ya que agregados individualmente, los datos constituirán un conjunto heterogéneo e irregular. Sin embargo, a partir de la agrupación de los datos en intervalos, el histograma, construido de forma adecuada, nos ayudará a conocer como se distribuyen los datos a lo largo de los intervalos, visualizando características de los datos como su tendencia central y su dispersión. \u003C/p>\r\n\u003Cp id=\"bkmrk-conceptos-relacionad\">Conceptos relacionados: \u003Ca href=\"https://ikusmira.org/p/amplitud-de-clase\">amplitud de clase\u003C/a>, \u003Ca href=\"https://ikusmira.org/p/frecuencia-de-clase\">frecuencia de clase\u003C/a>, \u003Ca href=\"https://ikusmira.org/p/limite-de-clase\">límite de clase\u003C/a>, \u003Ca href=\"https://ikusmira.org/p/marca-de-clase\">marca de clase\u003C/a>\u003C/p>\r\n\u003Cp id=\"bkmrk-el-punto-de-partida%3A\">\u003Cstrong>El punto de partida: el número de intervalos\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-el-punto-de-partida-\">El punto de partida para la construcción de un histograma consiste en la determinación del número de intervalos de clase en los que se agruparán los datos. Para ello debe tenerse en cuenta que cuanto menor sea el número de intervalos de clase, mayor será la pérdida de información respecto a los datos originales. Más concretamente:\u003Cbr>\u003C/p>\r\n\u003Cul id=\"bkmrk-por-un-lado%2C-un-n%C3%BAme\">\r\n\u003Cli class=\"null\">por un lado, un número excesivamente alto de intervalos, generalmente más de 15 o 20, no resumirá los datos de forma adecuada, de modo que la información resultante seguirá siendo igual o similarmente confusa a la que poseíamos con los datos originales  o no agrupados;\u003C/li>\r\n\u003Cli class=\"null\">por otro lado, un número muy bajo, generalmente inferior a 5,  puede derivar en una excesiva simplificación o resumen de los datos, con la consiguiente pérdida de información relevante.\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-se-han-establecido-d\">Se han establecido diferentes reglas o fórmulas para el cálculo del número de intervalos más adecuado, generalmente como función creciente del tamaño de la muestra. Entre estas, la mñas utilizada es la \u003Ca href=\"https://ikusmira.org/p/regla-de-sturges-formula-de-sturges\">regla de Sturges\u003C/a> que calcula el número de intervalos de clase $k$ de esta forma, redondeando el resultado al siguiente número entero: \u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24k%3D%5Ccfrac%7B%5Cln-k%7D%7B%5Cl\">$$k=\\cfrac{\\ln k}{\\ln 2}+1$$\u003C/p>\r\n\u003Cp id=\"bkmrk-construcci%C3%B3n-de-los-\">\u003Cstrong>Construcción de los intervalos \u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-una-vez-determinado-\">Una vez determinado el número de intervalos de clase en los que se van a agrupar los datos, los pasos a desarrollar son los siguientes:\u003Cbr>\u003C/p>\r\n\u003Cul id=\"bkmrk-se-calcula-el-recorr\">\r\n\u003Cli class=\"null\">se calcula el \u003Ca href=\"https://ikusmira.org/p/recorrido-rango\">recorrido o rango\u003C/a> R de los datos, es decir, la diferencia entre el valor mayor y el valor menor de los datos;\u003C/li>\r\n\u003Cli class=\"null\">se divide el recorrido R entre el número de intervalos k, siendo el resultado la amplitud de clase teórica de cada intervalo de clase;\u003C/li>\r\n\u003Cli class=\"null\">se redondea por exceso dicha amplitud a un número significativo, por ejemplo 10, 20, 50, ...;\u003C/li>\r\n\u003Cli class=\"null\">se multiplica dicha amplitud final por el número de intervalos, obteniendo de esta forma el recorrido de los intervalos del histograma;\u003C/li>\r\n\u003Cli class=\"null\">el exceso de recorrido entre este recorrido final y el recorrido real se reparte de forma más o menos equitativa por debajo del valor menor de los datos y por encima del valor mayor (para mayor información, consulta \u003Ca href=\"https://ikusmira.org/p/amplitud-de-clase\">amplitud de clase\u003C/a>);\u003C/li>\r\n\u003Cli class=\"null\">se comienza a construir los intervalos desde el límite inferior de clase del primer intervalo, que coincide con el valor inferior disminuido por el exceso de recorrido considerado, hasta llegar al último intervalo, formando en total $k$ intervalos.\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-agrupamiento-de-los-\">\u003Cstrong>Agrupamiento de los datos\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-una-vez-construidos-\">Una vez construidos los intervalos, es hora de agrupar los datos en estos. Para ello debe tenerse en cuenta que por convenio, se supone que los intervalos de clase son  abiertos por la derecha y cerrados por la izquierda, es decir el intervalo de clase a-b se considera de esta forma:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24%5Ba%2Cb%29%24%24\">$$[a,b)$$\u003C/p>\r\n\u003Cp id=\"bkmrk-a-veces-para-evitar-\">A veces para evitar dicha suposición y dejar claro qué dato entra en cada intervalo, estos se establecen de forma consecutiva pero sin valores coincidentes: por ejemplo, a la hora de agrupar edades pueden establecerse como intervalos de clase 0-4, 5-9, 10-14, 15-19, ...\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-recomendaciones-gene\">\u003Cstrong>Recomendaciones generales sobre los intervalos\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-los-intervalos-deben\">\r\n\u003Cli class=\"null\">Los intervalos deben ser disjuntos, esto es, no deben solaparse.\u003C/li>\r\n\u003Cli class=\"null\">Como regla general, los intervalos serán de amplitud constante, pero en ciertas situaciones es mejor que se de amplitud diferente.\u003C/li>\r\n\u003Cli class=\"null\">Los extremos de los intervalos serán preferiblemente \u003Ca href=\"https://ikusmira.org/p/numeros-redondos\">números redondos\u003C/a>.\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-ejemplo\">\u003Cstrong>Ejemplo\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-se-han-recogidos-los\">Se han recogidos los datos sobre la altura de 100 jóvenes del sexo femenino en una región (cm):\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-170-174-170-168-168-\">\u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">174\u003C/span> \u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">168\u003C/span> \u003Cspan class=\"hljs-number\">168\u003C/span> \u003Cspan class=\"hljs-number\">163\u003C/span> \u003Cspan class=\"hljs-number\">184\u003C/span> \u003Cspan class=\"hljs-number\">173\u003C/span> \u003Cspan class=\"hljs-number\">164\u003C/span> \u003Cspan class=\"hljs-number\">168\u003Cbr>\u003C/span>\u003Cspan class=\"hljs-number\">169\u003C/span> \u003Cspan class=\"hljs-number\">164\u003C/span> \u003Cspan class=\"hljs-number\">163\u003C/span> \u003Cspan class=\"hljs-number\">173\u003C/span> \u003Cspan class=\"hljs-number\">166\u003C/span> \u003Cspan class=\"hljs-number\">169\u003C/span> \u003Cspan class=\"hljs-number\">164\u003C/span> \u003Cspan class=\"hljs-number\">176\u003C/span> \u003Cspan class=\"hljs-number\">171\u003C/span> \u003Cspan class=\"hljs-number\">171\u003Cbr>\u003C/span> \u003Cspan class=\"hljs-number\">165\u003C/span> \u003Cspan class=\"hljs-number\">178\u003C/span> \u003Cspan class=\"hljs-number\">179\u003C/span> \u003Cspan class=\"hljs-number\">161\u003C/span> \u003Cspan class=\"hljs-number\">180\u003C/span> \u003Cspan class=\"hljs-number\">169\u003C/span> \u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">157\u003C/span> \u003Cspan class=\"hljs-number\">177\u003C/span> \u003Cspan class=\"hljs-number\">168\u003C/span> \u003Cbr>\u003Cspan class=\"hljs-number\">172\u003C/span> \u003Cspan class=\"hljs-number\">174\u003C/span> \u003Cspan class=\"hljs-number\">163\u003C/span> \u003Cspan class=\"hljs-number\">169\u003C/span> \u003Cspan class=\"hljs-number\">168\u003C/span> \u003Cspan class=\"hljs-number\">178\u003C/span> \u003Cspan class=\"hljs-number\">180\u003C/span> \u003Cspan class=\"hljs-number\">184\u003C/span> \u003Cspan class=\"hljs-number\">172\u003C/span> \u003Cspan class=\"hljs-number\">172\u003Cbr>\u003C/span> \u003Cspan class=\"hljs-number\">179\u003C/span> \u003Cspan class=\"hljs-number\">172\u003C/span> \u003Cspan class=\"hljs-number\">163\u003C/span> \u003Cspan class=\"hljs-number\">177\u003C/span> \u003Cspan class=\"hljs-number\">158\u003C/span> \u003Cspan class=\"hljs-number\">163\u003C/span> \u003Cspan class=\"hljs-number\">171\u003C/span> \u003Cspan class=\"hljs-number\">174\u003C/span> \u003Cspan class=\"hljs-number\">167\u003C/span> \u003Cspan class=\"hljs-number\">161\u003Cbr>\u003C/span> \u003Cspan class=\"hljs-number\">179\u003C/span> \u003Cspan class=\"hljs-number\">173\u003C/span> \u003Cspan class=\"hljs-number\">183\u003C/span> \u003Cspan class=\"hljs-number\">169\u003C/span> \u003Cspan class=\"hljs-number\">166\u003C/span> \u003Cspan class=\"hljs-number\">163\u003C/span> \u003Cspan class=\"hljs-number\">175\u003C/span> \u003Cspan class=\"hljs-number\">169\u003C/span> \u003Cspan class=\"hljs-number\">167\u003C/span> \u003Cspan class=\"hljs-number\">169\u003Cbr>\u003C/span> \u003Cspan class=\"hljs-number\">167\u003C/span> \u003Cspan class=\"hljs-number\">161\u003C/span> \u003Cspan class=\"hljs-number\">169\u003C/span> \u003Cspan class=\"hljs-number\">181\u003C/span> \u003Cspan class=\"hljs-number\">165\u003C/span> \u003Cspan class=\"hljs-number\">156\u003C/span> \u003Cspan class=\"hljs-number\">167\u003C/span> \u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">170\u003Cbr>\u003C/span> \u003Cspan class=\"hljs-number\">167\u003C/span> \u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">174\u003C/span> \u003Cspan class=\"hljs-number\">173\u003C/span> \u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">168\u003C/span> \u003Cspan class=\"hljs-number\">165\u003C/span> \u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">173\u003C/span> \u003Cspan class=\"hljs-number\">157\u003Cbr>\u003C/span> \u003Cspan class=\"hljs-number\">166\u003C/span> \u003Cspan class=\"hljs-number\">170\u003C/span> \u003Cspan class=\"hljs-number\">159\u003C/span> \u003Cspan class=\"hljs-number\">176\u003C/span> \u003Cspan class=\"hljs-number\">166\u003C/span> \u003Cspan class=\"hljs-number\">169\u003C/span> \u003Cspan class=\"hljs-number\">171\u003C/span> \u003Cspan class=\"hljs-number\">172\u003C/span> \u003Cspan class=\"hljs-number\">174\u003C/span> \u003Cspan class=\"hljs-number\">178\u003Cbr>\u003C/span> \u003Cspan class=\"hljs-number\">173\u003C/span> \u003Cspan class=\"hljs-number\">178\u003C/span> \u003Cspan class=\"hljs-number\">174\u003C/span> \u003Cspan class=\"hljs-number\">176\u003C/span> \u003Cspan class=\"hljs-number\">171\u003C/span> \u003Cspan class=\"hljs-number\">162\u003C/span> \u003Cspan class=\"hljs-number\">166\u003C/span> \u003Cspan class=\"hljs-number\">162\u003C/span> \u003Cspan class=\"hljs-number\">165\u003C/span> \u003Cspan class=\"hljs-number\">164\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-buscamos-los-valores\">\u003Cspan class=\"hljs-number\">Buscamos los valores mínimo y máximo entre los datos: 156cm (mínimo)  y 184cm (máximo).\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-calculamos-el-recorr\">\u003Cspan class=\"hljs-number\">Calculamos el recorrido o diferencia los valores máximo y mínimo: R=184-156=28.\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-aplicamos-la-regla-d\">\u003Cspan class=\"hljs-number\">Aplicamos la regla de Sturges para calcular el número de intervalos más adecuado para este número de datos:\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24k%3D%5Ccfrac%7Bln-100%7D%7Bl\">\u003Cspan class=\"hljs-number\">$$k=\\cfrac{ln 100}{ln 2}+1=7.64 \\rightarrow 8$$\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-calculamos-la-amplit\">\u003Cspan class=\"hljs-number\">Calculamos la amplitud teórica de cada intervalo dividiendo el recorrido entre el número de intervalos fijado. Dado que es conveniente que la amplitud de los intervalos sea un \u003Ca href=\"https://ikusmira.org/p/numeros-redondos\">número redondo\u003C/a>, redondeamos la amplitud teórica por exceso, para poder cubrir todo el recorrido:\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24h%3D%5Ccfrac%7B28%7D%7B8%7D%3D3.\">\u003Cspan class=\"hljs-number\">$$h=\\cfrac{28}{8}=3.5 \\rightarrow 4$$\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-de-este-modo%2C-debemo\">\u003Cspan class=\"hljs-number\">De este modo, debemos construir 8 intervalos de amplitud 4cm, por lo que los intervalos cubren en total 32cm. Como el recorrido real es de 28cm, añadiremos 2cm por debajo del valor mínimo y 2cm por encima del valor máximo, de modo que los intervalos comenzarán en 156-2=154cm y terminarán en 184+2=186cm. Así pues, los intervalos serán: 154-158, 158-162, 162-166, 166-170, 170-174, 174-178, 178-182, 182-186. No nos queda más que realizar el conteo de datos para cada intervalo para obtener las frecuencias de clase que serán las alturas de las barras del histograma:\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-\">\u003Cspan class=\"hljs-number\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2024-07/gwWdIBXmgvbPYSTX-rplot01.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg src=\"https://es.gizapedia.org/uploads/images/gallery/2024-07/scaled-1680-/gwWdIBXmgvbPYSTX-rplot01.png\" alt=\"Rplot01.png\">\u003C/a>\u003C/span>\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>\r\n\u003Cp id=\"bkmrk--1\">\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-diagrama-de-sectores\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/diagrama-de-sectores-grafico-circular\">\u003Cstrong>Diagrama de sectores\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/vahttps://ikusmira.org/p/diagrama-de-barras-grafico-de-columnas\">\u003Cstrong>Diagrama de barras\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/poligono-de-frecuencias\">\u003Cstrong>Polígono de frecuencias\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/ojiva-estadistica\">\u003Cstrong>Ojiva (estadística)\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":47,"name":48,"slug":49,"html":50},280,"Sobremuestreo","sobremuestreo","\u003Cp id=\"bkmrk-el-sobremuestreo-es-\">El \u003Cstrong>sobremuestreo\u003C/strong> es c\u003Cspan id=\"bkmrk-ualquier-tipo-de-mue\" class=\"form-control-text textarea\" role=\"textbox\">ualquier tipo de muestreo que dé a algunos elementos de la población una mayor probabilidad que a otros de ser extraídos de ella, generalmente con el objetivo de corregir un desequilibrio natural y propio en la selección aleatoria.\u003C/span>\u003C/p>",{"id":52,"name":53,"slug":54,"html":55},5,"Tanto por uno","tanto-por-uno","\u003Cp id=\"bkmrk-un-tanto-por-uno-es-\">Un \u003Cstrong>tanto por uno\u003C/strong> es una proporción, promedio o valor de referencia, que expresa el valor de una cantidad o magnitud por cada unidad de medida de una cantidad total. Por ejemplo, si por cada 20 euros en una operación, se van a cobrar 2 euros de comisión, el tanto por uno es 2/20=0.1; es decir, se va a cobrar 0.1 euros por cada euro en la operación.\u003C/p>\r\n\u003Cp id=\"bkmrk-los-tantos-por-uno-s\">Los tantos por uno son fácilmente trasladables a tantos por ciento o porcentajes, sinplemente multiplicando los tantos por uno por 100, por ejemplo, en el ejemplo anterior el porcentaje de comisión sería 0.1x100=10%.\u003C/p>",{"id":57,"name":58,"slug":59,"html":60},3963,"Microdatos (datos individuales)","microdatos-datos-individuales","\u003Cp id=\"bkmrk-los-microdatos-o-dat\">Los \u003Cstrong>microdatos o datos individuales\u003C/strong> son aquellos datos que se refieren de forma concreta y exacta a una sola unidad de observación, frecuentemente para luego agregarlos de una u otra forma y formar \u003Ca href=\"https://ikusmira.org/p/macrodatos\">macrodatos\u003C/a> o \u003Ca href=\"https://ikusmira.org/p/agregado-estadistico\">agregados estadísticos\u003C/a>. \u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>",{"":62},[63,67,71,75,80,85,89,94,99,104,109,114,119,124,129,134,139,144,149,154,159,164,169,174,179,184,189,194,199,204,209,214,219,224,229,234,238,243,247,252,257,262,267,272,276,280,285,290,295,300,301,306,311,316,321,326,331,336,341,346,351,356,361,366,371,376,381,386,391,396,401,406,411,416,420,425,430,435,440,445,450,455,460,464,469,474,478,483,488,493,498,503,508,513,518,523,527,532,537,542,547,552,557,562,567,572,577,582,587,592,597,602,607,612,617,622,627,632,637,642,647,652,657,662,667,672,677,682,687,692,697,699,704,709,714,719,724,729,734,739,744,749,754,758,762,767,772,776,780,784,789,794,799,804,808,813,818,823,828,833,838,843,847,852,857,862,867,872,877,882,887,892,897,901,906,911,916,921,926,931,936,941,946,950,955,959,964,969,974,979,984,988,993,998,1003,1008,1012,1017,1022,1026,1031,1036,1041,1045,1050,1055,1060,1065,1069,1074,1079,1084,1089,1094,1099,1104,1109,1114,1118,1123,1128,1133,1137,1142,1147,1152,1156,1160,1165,1170,1175,1180,1185,1189,1193,1198,1203,1208,1210,1214,1219,1224,1225,1229,1234,1239,1243,1248,1253,1258,1263,1268,1273,1278,1283,1288,1293,1298,1303,1307,1312,1317,1322,1327,1332,1337,1342,1347,1352,1357,1362,1367,1372,1377,1382,1385,1389,1394,1399,1404,1408,1412,1416,1421,1425,1429,1434,1439,1444,1449,1454,1459,1464,1469,1474,1479,1484,1489,1494,1498,1503,1508,1512,1517,1522,1527,1529,1533,1537,1541,1546,1551,1556,1561,1566,1571,1576,1581,1586,1591,1596,1601,1606,1611,1613,1618,1623,1628,1633,1638,1639,1644,1649,1654,1659],{"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":52,"chapter_name":22},2019,"Asociación no estadística","asociacion-no-estadistica",{"id":90,"name":91,"slug":92,"priority":93,"chapter_name":22},2948,"Banco de datos","banco-de-datos",6,{"id":95,"name":96,"slug":97,"priority":98,"chapter_name":22},1621,"Base del índice (periodo base)","base-del-indice-periodo-base",7,{"id":100,"name":101,"slug":102,"priority":103,"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":105,"name":106,"slug":107,"priority":108,"chapter_name":22},3063,"Característica cualitativa","caracteristica-cualitativa",9,{"id":110,"name":111,"slug":112,"priority":113,"chapter_name":22},2708,"Casos particulares","casos-particulares",10,{"id":115,"name":116,"slug":117,"priority":118,"chapter_name":22},2730,"Censo estadístico","censo-estadistico",11,{"id":120,"name":121,"slug":122,"priority":123,"chapter_name":22},2551,"Clase mediana","clase-mediana",12,{"id":125,"name":126,"slug":127,"priority":128,"chapter_name":22},1011,"Clase modal","clase-modal",13,{"id":130,"name":131,"slug":132,"priority":133,"chapter_name":22},2133,"Coeficiente de asimetría de Bowley","coeficiente-de-asimetria-de-bowley",14,{"id":135,"name":136,"slug":137,"priority":138,"chapter_name":22},1714,"Coeficiente de asimetría de Fisher","coeficiente-de-asimetria-de-fisher",15,{"id":140,"name":141,"slug":142,"priority":143,"chapter_name":22},1844,"Coeficiente de asimetría de Pearson","coeficiente-de-asimetria-de-pearson",16,{"id":145,"name":146,"slug":147,"priority":148,"chapter_name":22},2057,"Coeficiente de contingencia de Pearson","coeficiente-de-contingencia-de-pearson",17,{"id":150,"name":151,"slug":152,"priority":153,"chapter_name":22},2648,"Coeficiente de correlación biserial puntual","coeficiente-de-correlacion-biserial-puntual",18,{"id":155,"name":156,"slug":157,"priority":158,"chapter_name":22},1938,"Coeficiente de curtosis de Pearson","coeficiente-de-curtosis-de-pearson",19,{"id":160,"name":161,"slug":162,"priority":163,"chapter_name":22},2032,"Coeficiente de determinación ajustado (coeficiente de determinación corregido)","coeficiente-de-determinacion-ajustado-coeficiente-de-determinacion-corregido",20,{"id":165,"name":166,"slug":167,"priority":168,"chapter_name":22},2649,"Coeficiente de Tschuprow","coeficiente-de-tschuprow",21,{"id":170,"name":171,"slug":172,"priority":173,"chapter_name":22},37,"Coeficiente de variación","coeficiente-de-variacion",22,{"id":175,"name":176,"slug":177,"priority":178,"chapter_name":22},2646,"Coeficiente Q de Yule","coeficiente-q-de-yule",23,{"id":180,"name":181,"slug":182,"priority":183,"chapter_name":22},2218,"Comprobación de Charlier","comprobacion-de-charlier",24,{"id":185,"name":186,"slug":187,"priority":188,"chapter_name":22},2095,"Concepto de estadística","concepto-de-estadistica",25,{"id":190,"name":191,"slug":192,"priority":193,"chapter_name":22},2607,"Constante estadística","constante-estadistica",26,{"id":195,"name":196,"slug":197,"priority":198,"chapter_name":22},2087,"Corrección de Bessel","correccion-de-bessel",27,{"id":200,"name":201,"slug":202,"priority":203,"chapter_name":22},308,"Corrección de Sheppard","correccion-de-sheppard",28,{"id":205,"name":206,"slug":207,"priority":208,"chapter_name":22},1080,"Corrección de Yates","correccion-de-yates",29,{"id":210,"name":211,"slug":212,"priority":213,"chapter_name":22},49,"Corrección por continuidad","correccion-por-continuidad",30,{"id":215,"name":216,"slug":217,"priority":218,"chapter_name":22},2685,"Correlación","correlacion",31,{"id":220,"name":221,"slug":222,"priority":223,"chapter_name":22},1624,"Correlación espuria (correlación espúrea)","correlacion-espuria-correlacion-espurea",32,{"id":225,"name":226,"slug":227,"priority":228,"chapter_name":22},2684,"Correlación por rangos","correlacion-por-rangos",33,{"id":230,"name":231,"slug":232,"priority":233,"chapter_name":22},1665,"Correlograma","correlograma",34,{"id":235,"name":236,"slug":237,"priority":100,"chapter_name":22},148,"Covariación","covariacion",{"id":239,"name":240,"slug":241,"priority":242,"chapter_name":22},44,"Covarianza","covarianza",36,{"id":244,"name":245,"slug":246,"priority":170,"chapter_name":22},1652,"Criterio (variable)","criterio-variable",{"id":248,"name":249,"slug":250,"priority":251,"chapter_name":22},2135,"Cuartiles (primer cuartil, segundo cuartil, tercer cuartil)","cuartiles-primer-cuartil-segundo-cuartil-tercer-cuartil",38,{"id":253,"name":254,"slug":255,"priority":256,"chapter_name":22},2159,"Cuasivarianza (varianza corregida)","cuasivarianza-varianza-corregida",39,{"id":258,"name":259,"slug":260,"priority":261,"chapter_name":22},1669,"Curtosis (estadística)","curtosis-estadistica",40,{"id":263,"name":264,"slug":265,"priority":266,"chapter_name":22},2072,"Datos agregados","datos-agregados",41,{"id":268,"name":269,"slug":270,"priority":271,"chapter_name":22},1732,"Datos agrupados","datos-agrupados",42,{"id":273,"name":274,"slug":275,"priority":81,"chapter_name":22},2692,"Datos aislados (datos no agrupados)","datos-aislados-datos-no-agrupados",{"id":277,"name":278,"slug":279,"priority":239,"chapter_name":22},2745,"Datos bivariados","datos-bivariados",{"id":281,"name":282,"slug":283,"priority":284,"chapter_name":22},73,"Datos blandos","datos-blandos",45,{"id":286,"name":287,"slug":288,"priority":289,"chapter_name":22},2315,"Datos cualitativos","datos-cualitativos",46,{"id":291,"name":292,"slug":293,"priority":294,"chapter_name":22},2900,"Datos desagregados","datos-desagregados",47,{"id":296,"name":297,"slug":298,"priority":299,"chapter_name":22},241,"Datos estructurados y datos no estructurados","datos-estructurados-y-datos-no-estructurados",48,{"id":32,"name":33,"slug":34,"priority":210,"chapter_name":22},{"id":302,"name":303,"slug":304,"priority":305,"chapter_name":22},2038,"Deciles","deciles",50,{"id":307,"name":308,"slug":309,"priority":310,"chapter_name":22},142,"Desigualdad de Markov","desigualdad-de-markov",51,{"id":312,"name":313,"slug":314,"priority":315,"chapter_name":22},1609,"Desviación media absoluta","desviacion-media-absoluta",52,{"id":317,"name":318,"slug":319,"priority":320,"chapter_name":22},1923,"Desviación típica (desviación estándar)","desviacion-tipica-desviacion-estandar",53,{"id":322,"name":323,"slug":324,"priority":325,"chapter_name":22},2055,"Diagrama de barras (gráfico de columnas)","diagrama-de-barras-grafico-de-columnas",54,{"id":327,"name":328,"slug":329,"priority":330,"chapter_name":22},2945,"Diagrama de caja y bigotes","diagrama-de-caja-y-bigotes",55,{"id":332,"name":333,"slug":334,"priority":335,"chapter_name":22},2765,"Diagrama de frecuencias","diagrama-de-frecuencias",56,{"id":337,"name":338,"slug":339,"priority":340,"chapter_name":22},1854,"Diagrama de sectores (gráfico circular)","diagrama-de-sectores-grafico-circular",57,{"id":342,"name":343,"slug":344,"priority":345,"chapter_name":22},2066,"Diagrama de tallo y hojas","diagrama-de-tallo-y-hojas",58,{"id":347,"name":348,"slug":349,"priority":350,"chapter_name":22},775,"Diseño 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