tag:blogger.com,1999:blog-72654658707410827102024-03-13T05:05:01.495-07:00medidas de tendencia central y variabilidadmedidadas de tendencia y variabilidadhttp://www.blogger.com/profile/07907215156790974391noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7265465870741082710.post-25634711382561097042010-11-25T19:05:00.001-08:002010-11-25T19:05:45.884-08:00<div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
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</div>medidadas de tendencia y variabilidadhttp://www.blogger.com/profile/07907215156790974391noreply@blogger.com0tag:blogger.com,1999:blog-7265465870741082710.post-8493007601814020342010-11-24T19:14:00.000-08:002010-11-26T07:02:35.455-08:00Medidas de tendencia central y variabilidad<strong>Medidas de tendencia central </strong><br />
<br />
Las medidas de tendencia central son llamadas asi porque "tienden" a localizarse en el centro de la información. las principales medidas de tendencia central son:<br />
<br />
*<strong>media</strong><br />
<strong>*mediana</strong><br />
<strong>*moda</strong><br />
<br />
La media de un conjunto de valores es igual a la suma de dichos valores dividida entre el número de ellos.<br />
<br />
La mediana es el valor que divide al grupo de datos en dos partes iguales, 50% por debajo de el y el otro 50% por arriba del mismo.<br />
<br />
La moda, es el dato o valore de la variable que ocurre con mayor frecuencia el simbolo que se utiliza es Mo.<br />
<br />
Se llama marca de clase de un intervalo al valor que esta justo enmedio del mismo y se obtiene promediando los limites del intervalo, es decir, sumandolos y dividiendolos entre dos.<br />
<br />
Se llama limites reales a los que se obtienen de restar y sumar media unidad alos limites inferior y superior del intervalo, respectivamente.<br />
<br />
Al tamaño del intervalo se le demonima amplitud o anchura del intervalo y se calcula obteniendo la diferencia entre los limites reales del intervalo.<br />
<br />
<br />
<strong>Medidas de variabilidad </strong><br />
<br />
<br />
<strong>Rango</strong><br />
Se calcula ayando la diferencia (resta) entre los valores maximo y minimo <br />
<br />
Rango<strong>=</strong> R=Valor maximo - valor minimo <br />
<br />
<br />
<strong>La desviación estandar </strong><br />
La desviación estandar es una medida de la variación de los valores con respecto a la media. Es una especie de desviación promedio respecto a la media.<br />
<br />
<strong>La varianza</strong><br />
La varianza es una medida de variabilidad que se obtiene elevando al cuadrado la deviación estandar.<br />
<br />
<br />
<br />
<br />
<strong>Ejercicio ( datos no agrupados)</strong><br />
<br />
<br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"></span></span></div><br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom: medium none; border-collapse: collapse; border-left: medium none; border-right: medium none; border-top: medium none; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 609px;"><tbody>
<tr style="height: 16.35pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: black 1pt solid; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">Calificaciones <i style="mso-bidi-font-style: normal;">x</i></span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: black 1pt solid; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">Núm. De alumnos <i style="mso-bidi-font-style: normal;">f</i></span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: black 1pt solid; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><br />
</div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: black 1pt solid; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div align="center" class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt; text-align: center;"><br />
</div></td></tr>
<tr style="height: 16.35pt; mso-yfti-irow: 1;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">3</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">2</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">2-5.8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">=14.4</span></span></div></td></tr>
<tr style="height: 16.35pt; mso-yfti-irow: 2;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">4</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">3</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">3-5.8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">=7.8</span></span></div></td></tr>
<tr style="height: 16.35pt; mso-yfti-irow: 3;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">5</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">3</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">3-5.8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">=7.8</span></span></div></td></tr>
<tr style="height: 16.35pt; mso-yfti-irow: 4;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">6</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">5</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">5-5.8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">=.64</span></span></div></td></tr>
<tr style="height: 16.35pt; mso-yfti-irow: 5;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">7</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">17</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">17-5.8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">=125.4</span></span></div></td></tr>
<tr style="height: 16.35pt; mso-yfti-irow: 6;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">9</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">9-5.8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">=10.6</span></span></div></td></tr>
<tr style="height: 16.35pt; mso-yfti-irow: 7;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">9</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">5</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">5-5.8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">=.64</span></span></div></td></tr>
<tr style="height: 16.35pt; mso-yfti-irow: 8;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">10</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">3</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">3-5.8</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 16.35pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">=7.8</span></span></div></td></tr>
<tr style="height: 15.6pt; mso-yfti-irow: 9; mso-yfti-lastrow: yes;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; height: 15.6pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">Total=</span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 15.6pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.1pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">n= 47 </span></span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 15.6pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><br />
</div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; height: 15.6pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 114.15pt;" valign="top" width="152"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">∑=174.68 </span></span></div></td></tr>
</tbody></table><br />
<div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><strong>Media</strong>: 47/8 = 5.8 </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><strong>Mediana:</strong> 7<span style="mso-spacerun: yes;"> </span></span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">N+1/2 = 47+1/2 = 24 </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">3 3 4 4 4 5 5 5 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 10 10 10 </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><strong>Moda:</strong> 7 </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><strong>Desviación estándar:</strong></span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><shapetype coordsize="21600,21600" filled="f" id="_x0000_t32" o:oned="t" o:spt="32" path="m,l21600,21600e"><path arrowok="t" fillok="f" o:connecttype="none"></path><lock shapetype="t" v:ext="edit"></lock></shapetype><shape id="_x0000_s1028" o:connectortype="straight" style="height: 0px; margin-left: 123.45pt; margin-top: 20.9pt; position: absolute; width: 52.5pt; z-index: 251677696;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><shape id="_x0000_s1027" o:connectortype="straight" style="height: 0.75pt; margin-left: 16.95pt; margin-top: 20.15pt; position: absolute; width: 51.75pt; z-index: 251676672;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><shape id="_x0000_s1026" o:connectortype="straight" style="flip: y; height: 0.75pt; margin-left: 49.2pt; margin-top: 4.4pt; position: absolute; width: 5.25pt; z-index: 251675648;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">S=√ ∑(x-x )²<span style="mso-spacerun: yes;"> </span>s= √174.68<span style="mso-spacerun: yes;"> </span>=13.2/8 = 1.6 </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>n <span style="mso-spacerun: yes;"> </span>8 </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><strong>Varianza:</strong></span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">s²= 1.6²=2.56 </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"></div></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><strong><span style="background-color: #f3f3f3; color: black;">Ejercicio (datos agrupados)</span></strong><br />
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<span style="color: black;"><br />
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<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom: medium none; border-collapse: collapse; border-left: medium none; border-right: medium none; border-top: medium none; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;"><tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: black 1pt solid; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">Intervalo</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: black 1pt solid; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">Frecuencia</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: black 1pt solid; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">M. de clase </span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: black 1pt solid; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">Fx</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: black 1pt solid; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><br />
</div></td></tr>
<tr style="mso-yfti-irow: 1;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">10-14</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">2</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">12</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">24</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">2</span></div></td></tr>
<tr style="mso-yfti-irow: 2;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">15-19</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">9</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">17</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">153</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">11</span></div></td></tr>
<tr style="mso-yfti-irow: 3;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">20-24</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">14</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">22</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">308</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">25</span></div></td></tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;"><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: black 1pt solid; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">25-29</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.75pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">6</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">27</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">162</span></div></td><td style="background-color: transparent; border-bottom: black 1pt solid; border-left: #f0f0f0; border-right: black 1pt solid; border-top: #f0f0f0; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 89.8pt;" valign="top" width="120"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-family: Calibri;">31</span></div></td></tr>
</tbody></table><br />
<div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">∑</span>31<span style="mso-spacerun: yes;"> </span><span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">∑</span><span style="mso-spacerun: yes;"> </span>647</span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Calibri;">Media</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><shapetype coordsize="21600,21600" filled="f" id="_x0000_t32" o:oned="t" o:spt="32" path="m,l21600,21600e"><path arrowok="t" fillok="f" o:connecttype="none"></path><lock shapetype="t" v:ext="edit"></lock></shapetype><shape id="_x0000_s1029" o:connectortype="straight" style="height: 0px; margin-left: 92.7pt; margin-top: 20.5pt; position: absolute; width: 27.75pt; z-index: 251661312;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><shape id="_x0000_s1028" o:connectortype="straight" style="height: 0px; margin-left: 77.7pt; margin-top: 0.95pt; position: absolute; width: 9.75pt; z-index: 251660288;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><shape id="_x0000_s1027" o:connectortype="straight" style="height: 0px; margin-left: 11.7pt; margin-top: 20.5pt; position: absolute; width: 32.25pt; z-index: 251659264;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><shape id="_x0000_s1026" o:connectortype="straight" style="height: 0px; margin-left: -0.3pt; margin-top: 0.95pt; position: absolute; width: 6.75pt; z-index: 251658240;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><span style="font-size: 14pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">X=∑ fx<span style="mso-spacerun: yes;"> </span>X= 647<span style="mso-spacerun: yes;"> </span>= 20.87</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 14pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>n<span style="mso-spacerun: yes;"> </span>31<span style="mso-spacerun: yes;"> </span></span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>Mediana: 22.5 </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><shape id="_x0000_s1034" o:connectortype="straight" style="height: 0.75pt; margin-left: 35.7pt; margin-top: 16.9pt; position: absolute; width: 34.5pt; z-index: 251678720;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">Me: L+(n/2-fa)a </span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>f</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">Moda : 20-24</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">Rango: 29-10 = 19</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">Desviación estándar:</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><shape id="_x0000_s1032" o:connectortype="straight" style="height: 0px; margin-left: 15.45pt; margin-top: 17.5pt; position: absolute; width: 51pt; z-index: 251664384;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><shape id="_x0000_s1031" o:connectortype="straight" style="height: 0px; margin-left: 19.95pt; margin-top: 0.25pt; position: absolute; width: 46.5pt; z-index: 251663360;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><shape id="_x0000_s1030" o:connectortype="straight" style="height: 0px; margin-left: 40.2pt; margin-top: 5.5pt; position: absolute; width: 7.5pt; z-index: 251662336;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">S= √ ∑(x-x) ²<br />
<span style="mso-spacerun: yes;"> </span>n</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><shape id="_x0000_s1033" o:connectortype="straight" style="height: 0px; margin-left: 11.7pt; margin-top: 15.2pt; position: absolute; width: 36pt; z-index: 251665408;" type="#_x0000_t32"><span style="font-family: Calibri;"></span></shape><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">S= 132.48 = 2.06</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>31</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">Varianza:</span></span></div><div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="font-family: Calibri;">S²<span style="mso-spacerun: yes;"> </span>2.06² = 4.2436</span></span></div><br />
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Integrantes:<br />
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Bortolotti Amador Talina<br />
Del Castillo Pulido Sandra Maribel<br />
Elos Mendez Edwin<br />
Llanes Tuxpan Ina Yuridia<br />
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</span></div>medidadas de tendencia y variabilidadhttp://www.blogger.com/profile/07907215156790974391noreply@blogger.com0