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2.3. Despejando

Una nube de datos

Nubes con datos

Xurxo tiene que organizar la "nube de datos" que ha recogido.

Se pone manos a la obra y recuerda que, en un curso anterior, le explicaron una forma de hacerlo con una tabla llamada "tabla de frecuencias".

Haciendo memoria, este era el proceso...

Organizando el tiempo

Para organizar datos es necesario identificar cuántos hay diferentes y clasificarlos en una tabla.

Estas son las columnas habituales:

1. La variable

La primera columna de la tabla es la más importante, en ella se pone lo que vas a estudiar, la variable estadística que, habitualmente, se representa por la letra mayúscula X.

Sólo se ponen los valores distintos que, en general, se identifican con una letra minúscula y un número en la parte inferior que indica su orden.

Por ejemplo \(\thinspace x_1\) significa que es el primer dato de X.

2. La frecuencia absoluta

La segunda columna contiene el recuento de cada dato. Este número se llama frecuencia absoluta, o simplemente frecuencia.

Se representa por \(f_i\).

La suma de las frecuencias absolutas es el número total de datos: \(N\).

\(N=f_1+f_2+...+f_n=\sum_{i=1}^{n} f_i\)

3. La frecuencia relativa

Para saber si el dato es muy representativo o poco, lo comparamos con el total de datos mediante una división.

Este resultado es la frecuencia relativa.

Para calcularlo se divide la frecuencia absoluta de \(x_i\) entre el total de datos, \(h_i=\displaystyle \frac{f_i}{N}\).

La suma de las frecuencias relativas vale \(1\).

\(\sum_{i=1}^{n} h_i=h_1+h_2+...+h_n=\displaystyle \frac{f_1+f_2+...+f_n}{N}=\displaystyle \frac{N}{N}=1\)

4. El porcentaje

A veces, además de la frecuencia relativa, se añade otra columna, la del porcentaje.

Para calcularlo, se multiplica la frecuencia relativa \(h_i\) por \(100\), es decir, \(p_i=h_i·100\).

Obviamente, la suma de los porcentajes vale \(100\).

Se pueden añadir más columnas, esto lo estudiarás en el siguiente capítulo.

Ordena

Has ordenado muy bien la variable cuantitativa.

Cubre los huecos, ordenando los datos de la temperatura media diaria, de menor a mayor:

 19, 20, 19, 21, 20, 17, 16, 17, 18, 18, 18, 18, 18, 16, 17, 18, 19, 19, 21, 18, 17, 22, 24, 23, 21, 21, 22, 24, 25, 24, 19.

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Ba%FC%A8%B2%B7%E1%B0%BE%B0%FF%E1%F5%C6%EB%E2%F7%D5%F3%FF%F7%B0%A8%B0%D1%FD%FF%E2%FE%F7%E6%F3%B0%EF%EF
Tablas de datos

Temperatura \(x_i\)

Estado del cielo \(x_i\)
@@16@@ Despejado
@@17@@ Nubes y claros
@@18@@ Cubierto
@@19@@ Lluvia
@@20@@
@@21@@
@@22@@
@@23@@
@@24@@
@@25@@

La variable cualitativa, en este caso, no tiene orden.

Su navegador no es compatible con esta herramienta.

Cuenta

Muy bien hecho, sigue así en los siguientes pasos.

Con los datos que consiguió Xurxo, introduce en tabla la frecuencia absoluta.

Los datos de la temperatura media diaria: 19, 20, 19, 21, 20, 17, 16, 17, 18, 18, 18, 18, 18, 16, 17, 18, 19, 19, 21, 18, 17, 22, 24, 23, 21, 21, 22, 24, 25, 24, 19

Los datos del estado del cielo: Despejado, Despejado, Despejado, Despejado, Despejado, Nubes y claros, Despejado, Lluvia, Lluvia, Lluvia, Lluvia, Despejado, Despejado, Lluvia, Nubes y claros, Nubes y claros, Despejado, Despejado, Despejado, Lluvia, Despejado, Despejado, Despejado, Despejado, Despejado, Nubes y claros, Despejado, Despejado, Nubes y claros, Despejado, Cubierto.

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Tabla de frecuencias                                              Tabla de frecuencias
Temperatura                                                             Estado del cielo
Temperatura \(x_i\) Número de días \(f_i\) Estado del cielo \(x_i\) Número de días \(f_i\)
16 @@2@@ Despejado @@19@@
17 @@4@@ Nubes y claros @@5@@
18 @@7@@ Cubierto @@1@@
19 @@5@@ Lluvia @@6@@
20 @@2@@ N=\(\displaystyle \sum_{i=1}^{4}f_{i} \)=@@31@@
21 @@4@@
22 @@2@@
23 @@1@@
24 @@3@@
25 @@1@@
N=\(\displaystyle \sum_{i=1}^{10}f_{i} \)=@@31@@
Su navegador no es compatible con esta herramienta.

Organiza la temperatura

Están todos los datos muy bien organizados en la tabla de frecuencias, esto te ayudará a entender los siguientes apartados.

Completa la tabla, ten en cuenta que debes completar el porcentaje con dos cifras decimales, redondeando cuando sea necesario:

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Tabla de frecuencias
Temperatura \(x_i\) Número de días \(f_i\) Frecuencia relativa \(h_i\) Porcentaje \(p_i\)
16 2 @@2@@/@@31@@ @@6@@,@@45@@
17 4 @@4@@/@@31@@ @@12@@,@@90@@
18 7 @@7@@/@@31@@ @@22@@,@@58@@
19 5 @@5@@/@@31@@ @@16@@,@@13@@
20 2 @@2@@/@@31@@ @@6@@,@@45@@
21 4 @@4@@/@@31@@ @@12@@,@@90@@
22 2 @@2@@/@@31@@ @@6@@,@@45@@
23 1 @@1@@/@@31@@ @@3@@,@@23@@
24 3 @@3@@/@@31@@ @@9@@,@@68@@
25 1 @@1@@/@@31@@ @@3@@,@@23@@
N=\(\displaystyle \sum_{i=1}^{10}f_{i} \)=31 \(\displaystyle \sum_{i=1}^{10}h_{i} \)=@@1@@ \(\displaystyle \sum_{i=1}^{10}p_{i} \)=@@100@@

Su navegador no es compatible con esta herramienta.

Organiza el estado del cielo

Están todos los datos muy bien organizados en la tabla de frecuencias, esto te ayudará a entender los siguientes apartados.

Completa la tabla, ten en cuenta que debes completar el porcentaje con dos cifras decimales, redondeando cuando sea necesario:

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Tabla de frecuencias
Estado del cielo \(x_i\)

Número de días \(f_i\)

 Frecuencia relativa \(h_i\) Porcentaje \(p_i\)
Despejado 19 @@19@@/@@31@@ @@61@@,@@29@@
Nubes y claros 5 @@5@@/@@31@@ @@16@@,@@13@@
Cubierto 1 @@1@@/@@31@@ @@3@@,@@23@@
Lluvia 6 @@6@@/@@31@@ @@19@@,@@35@@
N=\(\displaystyle \sum_{i=1}^{4}f_{i} \)=31 \(\displaystyle \sum_{i=1}^{4}h_{i} \)=@@1@@ \(\displaystyle \sum_{i=1}^{4}p_{i} \)=@@100@@
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