[{"data":1,"prerenderedAt":1677},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/vector-aleatorio: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},4021,2,0,"Vector aleatorio","vector-aleatorio","\u003Cp id=\"bkmrk-un-vector-aleatorio-\">Un \u003Cstrong>vector aleatorio\u003C/strong> es un vector cuyos elementos son variables aleatorias, generalmente definidas a través de su distribución conjunta. El término es sinónimo de variable aleatoria multidimensional. \u003C/p>",327,"2026-02-20T15:56:25.000000Z","2026-02-20T15:59:27.000000Z",{"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-un-vector-aleatorio-\">Un \u003Cstrong>vector aleatorio\u003C/strong> es un vector cuyos elementos son variables aleatorias, generalmente definidas a través de su distribución conjunta. El término es sinónimo de variable aleatoria multidimensional. \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},3719,"Regla de Freedman-Diaconis","regla-de-freedman-diaconis","\u003Cp id=\"bkmrk-la-regla-de-freedman\">La \u003Cstrong>regla de Freedman-Diaconis\u003C/strong> es una regla para determinar la \u003Ca href=\"https://ikusmira.org/p/amplitud-de-clase\">amplitud óptima de intervalo\u003C/a> en una \u003Ca href=\"https://ikusmira.org/p/distribucion-de-frecuencias-agrupada-en-intervalos\">distribución agrupada por intervalos\u003C/a>, basándose en le recorrido intercuartílico (IQR) y el tamaño muestral (n):\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24%3A%5Ctext%7Bamplitud-de\">$$\\text{Amplitud de clase}=2\\, { \\text{IQR}(x) \\over{  \\sqrt[3]{n}  }}$$\u003Cbr>\u003Cbr>La regla proporciona la amplitud de clase que minimiza la suma de las distancias al cuadrado entre el histograma y una distribución teórica normal. En principio, la regla depende de la desviación típica de los datos, pero se hace depender del recorrido intercuartílico, como estimación robusta de la desviación. Originariamente, partiendo de una \u003Ca href=\"https://ikusmira.org/p/distribucion-normal\">distribución teórica normal\u003C/a>, en lugar del factor 2, debería utilizarse el factor 2.59, pero Freedman y Diaconis acabaron por establecer la regla con el factor 2 para adaptarla a todo tipo de distribuciones. Por todo ello, la regla de Freedman-Diaconis se utiliza especialmente cuando existen otuliers o datos atípicos o las distribución presenta una marcada asimetría. \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ad\">\u003Cstrong>Puede interesarte además\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-regla-de-sturges\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/regla-de-sturges-formula-de-sturges\">\u003Cstrong>Regla de Sturges\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":37,"name":38,"slug":39,"html":40},3939,"Teoría de colas","teoria-de-colas","\u003Cp id=\"bkmrk-la-teor%C3%ADa-de-colas-e\">La\u003Cstrong> teoría de colas \u003C/strong>es la rama que aunando matemática y estadística desarrolla y analiza modelos de colas (sistemas a los que llegan elementos a un servicio, deben esperar si este está ocupado y son atendidas en base a ciertas reglas), analizando tiempos de espera, longitud de cola y utilización de los recursos del sistema como variables principales, teniendo como objetivo principal la optimización de dichas variables. Se aplica en producción, servicio, transporte, redes de comunicaciones. El pionero en el desarrollo de este área fue el matemático e ingeniero danés Agner Krarup Erlang (1878 – 1929) y desde entonces se ha desarrollado como área con nombre propio dentro del ámibto de la investigación operativa. \u003C/p>",{"id":42,"name":43,"slug":44,"html":45},2031,"Nivel de confianza","nivel-de-confianza","\u003Cp id=\"bkmrk-en-relaci%C3%B3n-a-los-in\">En relación a los intervalos de confianza con una amplitud determinada que pueden resultar respecto a un parámetro, el \u003Cstrong>nivel de confianza\u003C/strong> es el porcentaje de veces que el parámetro a estimar se encontrará dentro de ese grupo de intervalos; por lo tanto, el nivel de confianza expresa la verosimilitud de que el parámetro se encuentre en un intervalo de confianza dado. Por ejemplo, cuando se establece que una media poblacional es estima que está entre 2 y 4 con un nivel de confianza del 90%, se está indicando que existe una verosimilitud del 90% de que el parámetro se encuentre en dicho intervalo. A veces se interpreta erróneamente el nivel de confianza como la probabilidad de que el parámetro se encuentre en un intervalo de confianza, cuando en realidad no podemos hablar de probabilidad en relación a si un parámetro está o no dentro de un intervalo, ya que el parámetro ya estará o no dentro de ese intervalo, lo que tenemos en realidad es desconocimiento sobre si está o no, por eso es más adecuado interpretar el nivel de confianza como un grado de verosimilitud. \u003C/p>\r\n\u003Cp id=\"bkmrk-normalmente%2C-un-inte\">Normalmente, un intervalo de confianza se construye a partir de un nivel de confianza dado, usualmente 90%, 95% o 99% . Cuanto mayor nivel de confianza deseemos, resultará un intervalo más amplio, para un tamaño muestral dado. \u003C/p>",{"id":47,"name":48,"slug":49,"html":50},2900,"Datos desagregados","datos-desagregados","\u003Cp id=\"bkmrk-en-estad%C3%ADstica%2C-los-\">En estadística, los \u003Cstrong>datos desagregados\u003C/strong> son aquellos datos que muestran un magnitud total o global, esto es, un \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/datos-agregados\">dato agregado\u003C/a>\u003C/strong>, dividida en sus diferentes partes o elementos. Por ejemplo, un dato agregado o global de paro puede mostrarse en forma de datos desagregados por provincia, edad, sexo o rama de actividad. Para partir de un dato agregado a datos desagregados generalmente hay que disponer de los denominados microdatos, que son los datos observados a nivel elemental o individual. \u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0\">\u003C/p>",{"id":52,"name":53,"slug":54,"html":55},52,"Macrodatos","macrodatos","\u003Cp id=\"bkmrk-los-macrodatos-son-l\">Los \u003Cstrong>macrodatos\u003C/strong> son los datos que resultan de la agregación u otro tipo de operaciones con datos más simples, en último extremo de microdatos. Por ejemplo, las calificaciones medias por aula son macrodatos obtenidos a partir de las calificaciones individuales de los estudiantes. El término \u003Cem>macrodato\u003C/em> puede considerarse cuasi-sinónimo de \u003Ca href=\"https://ikusmira.org/p/agregado-estadistico\">\u003Cem>agregado estadístico\u003C/em>\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-microdatos\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/microdatos-datos-individuales\">\u003Cstrong>Microdatos\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":57,"name":58,"slug":59,"html":60},1721,"Varianza muestral","varianza-muestral","\u003Cp id=\"bkmrk-este-art%C3%ADculo-es-sob\">\u003Cem>Este artículo es sobre la varianza muestral sin corregir para una serie de datos. Se denomina también varianza poblacional, aunque en Ikusmira utilizaremos el término de \u003Ca href=\"https://ikusmira.org/p/varianza-poblacional-distribuciones-de-probabilidad\">varianza poblacional para hacer referencia a la varianza de una distribución de probabilidad\u003C/a>.\u003C/em>\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-quiz%C3%A1s-est%C3%A9s-interes\">\u003Cem>Quizás estés interesado mñas exactamente en la \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/cuasivarianza-varianza-corregida\">cuasivarianza o varianza corregida\u003C/a>\u003C/strong>. \u003C/em>\u003C/p>\r\n\u003Cp id=\"bkmrk-la-varianza-es-una-m\">La \u003Cstrong>varianza muestral no corregida, a veces llamada también varianza de los datos o varianza poblacional,  \u003C/strong>es una \u003Ca href=\"https://ikusmira.org/p/medidas-de-dispersion-estadistica\">medida estadística de dispersión absoluta\u003C/a> para un conjunto de datos referidos a una \u003Ca href=\"https://ikusmira.org/p/variable-cuantitativa\">variable estadística cuantitativa\u003C/a>. Conceptualmente es la media de las distancias al cuadrado de los valores de la variable a la \u003Ca href=\"https://ikusmira.org/p/media-aritmetica-simple\">media aritmética simple\u003C/a> de la distribución; de esta forma, una varianza más alta que otra indica que la desviación de los datos o de los valores de una variable estadística o variable aleatoria respecto a la media es mayor y por tanto también es mayor la dispersión. Se utiliza cuando se desea determinar la varianza de una serie de datos sin ir mas allá, esto es, cuando el objetivo no es realizar a partir de la muestra una estimación o inferencia sobre la varianza de una población. Su resultado se mide en unidades de la variable al cuadrado.\u003C/p>\r\n\u003Cp id=\"bkmrk-la%C2%A0desviaci%C3%B3n-t%C3%ADpica\">La \u003Ca href=\"https://ikusmira.org/p/desviacion-tipica-desviacion-estandar\">desviación típica\u003C/a> es la raíz cuadrada de la varianza e indica en promedio la desviación media respecto a la media; así pues, la desviación típica tiene un significado más concreto e inmediato que la varianza como desviación al cuadrado media respecto a la media, pero aún así la varianza se utiliza frecuentemente en estadística debido a sus propiedades matemáticas. \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-hay-que-advertir-de-\">Hay que advertir de que se trata de una \u003Ca href=\"https://ikusmira.org/p/robustez-estadistica\">medida no robusta\u003C/a>, muy sensible a la existencia de datos atípicos en el conjunto de datos. \u003C/p>\r\n\u003Cp id=\"bkmrk-c%C3%A1lculo-para-una-ser\">\u003Cstrong>Cálculo para una serie de datos individuales\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-para-una-serie-de-da\">Para una serie de datos \\(x_1,x_2,\\ldots,x_n\\), la varianza \\(s_x^2\\) se calcula de acuerdo a la siguiente fórmula:\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24s_x%5E2%3D%5Ccfrac%7B%5Csum_\">$$s_x^2=\\cfrac{\\sum_i(x_i-\\overline{x})^2}{n}$$\u003C/p>\r\n\u003Cp id=\"bkmrk-por-ejemplo%2C-a-parti\">Por ejemplo, a partir de las puntuaciones \\(x_i\\) obtenidas por un grupo de alumnos en un examen recogidas en la primera columna se muestran a continuación los cálculos para la determinación de la varianza muestral:\u003C/p>\r\n\u003Cdiv style=\"text-align: center;\" id=\"bkmrk-distribuci%C3%B3n-del-tie\">\r\n\u003Ctable class=\"default\" style=\"width: 100%; height: 380px;\">\u003Ccaption> \u003C/caption>\r\n\u003Ctbody>\r\n\u003Ctr style=\"height: 46.6px;\">\r\n\u003Cth style=\"width: 17.7998%; height: 46.6px;\">\\(x_i\\)\u003Cbr>\u003C/th>\r\n\u003Cth style=\"width: 14.9567%; height: 46.6px;\">\\((x_i-\\overline{x})\\)\u003Cbr>\u003C/th>\r\n\u003Cth style=\"width: 16.5637%; height: 46.6px;\">\\((x_i-\\overline{x})^2\\)\u003Cbr>\u003C/th>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">1\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">-5\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">25\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">3\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">-3\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">9\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">4\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">-2\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">4\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 35.4px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 35.4px;\">4\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 35.4px;\">-2\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 35.4px;\">\r\n\u003Cp>4\u003Cbr>\u003C/p>\r\n\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">5\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">-1\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">1\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">7\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">1\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">1\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">8\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">2\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">4\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">9\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">3\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">9\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">9\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">3\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">9\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">10\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">4\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">16\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">Suma=60\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">Suma=0\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 16.5637%; height: 29.8px;\">Suma=82\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003C/tbody>\r\n\u003C/table>\r\n\u003C/div>\r\n\u003Cp id=\"bkmrk-calculamos-la-media-\">Calculamos en primer la media aritmética simple, siendo \\(n\\) el número de datos:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24%5Coverline%7Bx%7D%3D%5Ccfra\">$$\\overline{x}=\\cfrac{\\sum_ix_i}{n}=\\cfrac{60}{10}=6$$\u003C/p>\r\n\u003Cp id=\"bkmrk-en-la-segunda-column\">En la segunda columna calculamos las desviaciones respecto a la media. Su suma es siempre es 0. \u003C/p>\r\n\u003Cp id=\"bkmrk-en-la-tercera-column\">En la tercera columna calculamos las anteriores desviaciones al cuadrado, con el objetivo de que no se compensen unas con otras por tener signo distinto, y las sumamos. Dividiendo esa suma entre el tamaño de la muestra o  número de datos obtenemos la varianza, cuyas unidades son simepre la unidad de la variable al cuadrado:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24s_x%5E2%3D%5Ccfrac%7B%5Csum_-1\">$$s_x^2=\\cfrac{\\sum_i(x_i-\\overline{x})^2}{n}=\\cfrac{82}{10}=8.2\\ puntos^2$$\u003C/p>\r\n\u003Cp id=\"bkmrk-f%C3%B3rmula-simplificada\">\u003Cstrong>Fórmula simplificada para el cálculo de la varianza muestral\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-desarrollando-algebr\">Desarrollando algebráicamente la fórmula anterior se llega a esta fórmula simplificada  de la varianza muestral:\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24s%5E2%3D%5Ccfrac%7B%5Csum_ix\">$$s^2=\\cfrac{\\sum_ix_i^2}{n}-\\overline{x}^2$$\u003C/p>\r\n\u003Cp id=\"bkmrk-demostraci%C3%B3n\">\u003Cem>Demostración\u003C/em>\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24s_x%5E2%3D%5Ccfrac%7B%5Csum_-2\">$$s_x^2 = \\cfrac{\\sum_i (x_i - \\overline{x})^2}{n} = \\cfrac{\\sum_i x_i^2 - \\sum_i 2x_i \\overline{x} + \\sum_i \\overline{x}^2}{n} = \\cfrac{\\sum_i x_i^2 - 2 \\overline{x} \\sum_i x_i + \\sum_i \\overline{x}^2}{n}=$$\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24%5Ccfrac%7B%5Csum_i-x_i%5E\">$$\\cfrac{\\sum_i x_i^2}{n} - 2\\overline{x}\\cfrac{\\sum_i x_i}{n}+ \\cfrac{\\sum_i \\overline{x}^2}{n}=\\cfrac{\\sum_i x_i^2}{n}- 2\\overline{x}^2+\\cfrac{n\\overline{x}^2}{n}=\\cfrac{\\sum_i x_i^2}{n}- 2\\overline{x}^2+\\overline{x}^2=\\cfrac{\\sum_i x_i^2}{n}- \\overline{x}^2$$\u003C/p>\r\n\u003Cp id=\"bkmrk-ejemplo\">\u003Cstrong>Ejemplo\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-vamos-a-desarrollar-\">Vamos a desarrollar el cálculo de la fórmula simplificada para el ejemplo anterior:\u003C/p>\r\n\u003Cdiv style=\"text-align: center;\" id=\"bkmrk-%C2%A0-%5C%28x_i%5C%29-%5C%28%28x_i%5E2%5C%29\">\r\n\u003Ctable class=\"default\" style=\"width: 100%; height: 380px;\">\u003Ccaption> \u003C/caption>\r\n\u003Ctbody>\r\n\u003Ctr style=\"height: 46.6px;\">\r\n\u003Cth style=\"width: 17.7998%; height: 46.6px;\">\\(x_i\\)\u003Cbr>\u003C/th>\r\n\u003Cth style=\"width: 14.9567%; height: 46.6px;\">\\((x_i^2\\)\u003Cbr>\u003C/th>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">1\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">1\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">3\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">9\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">4\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">16\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 35.4px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 35.4px;\">4\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 35.4px;\">16\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">5\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">25\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">7\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">49\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">8\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">64\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">9\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">81\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">9\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">81\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">10\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">100\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003Ctr style=\"height: 29.8px;\">\r\n\u003Ctd style=\"width: 17.7998%; height: 29.8px;\">Suma=60\u003Cbr>\u003C/td>\r\n\u003Ctd style=\"width: 14.9567%; height: 29.8px;\">Suma=442\u003Cbr>\u003C/td>\r\n\u003C/tr>\r\n\u003C/tbody>\r\n\u003C/table>\r\n\u003C/div>\r\n\u003Cp id=\"bkmrk-y-finalmente-sustitu\">Y finalmente sustituimos en la fórmula simplificada:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24s%5E2%3D%5Ccfrac%7B%5Csum_ix-1\">$$s^2=\\cfrac{\\sum_ix_i^2}{n}-\\overline{x}^2=\\cfrac{442}{10}-6^2=8.2\\ puntos^2$$\u003C/p>\r\n\u003Cp id=\"bkmrk-el-resultado-es%2C-com\">El resultado es, como debe ser, el mismo. Pero en lugar de desarrollar tres columnas de cálculo, hemos desarrollado únicamente dos. \u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-cuasivarianza-%28varia\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/cuasivarianza-varianza-corregida\">\u003Cstrong>Cuasivarianza (varianza corregida)\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/correccion-de-bessel\">\u003Cstrong>Corrección de Bessel\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/correccion-de-sheppard\">\u003Cstrong>Corrección de Sheppard\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/comprobacion-de-charlier\">\u003Cstrong>Comprobación de Charlier\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/varianza-explicada\">\u003Cstrong>Varianza explicada\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://es.gizapedia.org/books/estadistica-general/page/matriz-de-varianzas-y-covarianzas-matriz-de-covarianzas\">\u003Cstrong>Matriz de varianzas y covarianzas\u003C/strong>\u003C/a>\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>\r\n\u003Cp id=\"bkmrk-%C2%A0-2\">\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0-3\">\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0-4\">\u003C/p>\r\n\u003Cp id=\"bkmrk-%C2%A0-5\">\u003C/p>",{"":62},[63,67,71,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,195,200,205,210,215,220,225,230,235,239,244,248,253,258,263,268,273,277,281,286,291,293,298,302,307,312,316,321,326,331,336,341,346,351,356,361,366,371,376,381,386,391,396,401,406,411,416,420,425,430,435,440,445,450,455,460,464,469,474,478,483,488,493,498,503,508,513,518,523,527,532,537,542,547,552,557,562,567,572,577,582,587,592,597,602,607,612,617,622,627,632,637,642,647,652,657,662,667,672,677,682,687,692,697,702,707,712,717,722,727,732,737,742,747,752,757,761,763,768,773,777,781,785,790,795,800,805,809,814,819,824,829,834,839,844,848,853,858,863,868,873,878,883,888,893,898,902,907,912,917,922,927,932,937,942,947,951,956,960,965,970,975,980,985,989,994,999,1001,1006,1010,1015,1020,1024,1029,1034,1039,1043,1048,1053,1058,1063,1067,1072,1077,1082,1087,1092,1097,1102,1107,1112,1116,1121,1126,1131,1135,1140,1145,1150,1154,1158,1163,1168,1173,1178,1183,1187,1191,1196,1201,1206,1211,1215,1220,1225,1228,1232,1237,1242,1246,1251,1256,1261,1266,1271,1276,1281,1286,1291,1296,1301,1306,1310,1315,1320,1325,1330,1335,1340,1345,1350,1355,1360,1365,1370,1375,1377,1382,1385,1389,1394,1399,1404,1408,1412,1416,1421,1425,1429,1434,1439,1444,1449,1454,1459,1464,1469,1474,1479,1484,1489,1494,1498,1503,1508,1509,1514,1519,1524,1529,1533,1537,1541,1546,1551,1556,1561,1566,1571,1576,1581,1586,1588,1593,1598,1603,1608,1613,1618,1623,1624,1629,1634,1639,1644,1649,1654,1659],{"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 (variable)","criterio-variable",{"id":249,"name":250,"slug":251,"priority":252,"chapter_name":22},2135,"Cuartiles (primer cuartil, segundo cuartil, tercer cuartil)","cuartiles-primer-cuartil-segundo-cuartil-tercer-cuartil",38,{"id":254,"name":255,"slug":256,"priority":257,"chapter_name":22},2159,"Cuasivarianza (varianza corregida)","cuasivarianza-varianza-corregida",39,{"id":259,"name":260,"slug":261,"priority":262,"chapter_name":22},1669,"Curtosis (estadística)","curtosis-estadistica",40,{"id":264,"name":265,"slug":266,"priority":267,"chapter_name":22},2072,"Datos agregados","datos-agregados",41,{"id":269,"name":270,"slug":271,"priority":272,"chapter_name":22},1732,"Datos agrupados","datos-agrupados",42,{"id":274,"name":275,"slug":276,"priority":81,"chapter_name":22},2692,"Datos aislados (datos no agrupados)","datos-aislados-datos-no-agrupados",{"id":278,"name":279,"slug":280,"priority":240,"chapter_name":22},2745,"Datos bivariados","datos-bivariados",{"id":282,"name":283,"slug":284,"priority":285,"chapter_name":22},73,"Datos blandos","datos-blandos",45,{"id":287,"name":288,"slug":289,"priority":290,"chapter_name":22},2315,"Datos cualitativos","datos-cualitativos",46,{"id":47,"name":48,"slug":49,"priority":292,"chapter_name":22},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":211,"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":52,"chapter_name":22},1609,"Desviación media 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