Question

a pilot counted the number of empty seats on 6 planes he flew: 5 seats 4 seats 9 seats 2 seats 4 seats 9 seats what was the mean absolute deviation of the numbers of empty seats? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): seats

Explanation:

Step1: Calcular la media

La media $\bar{x}$ de un conjunto de datos $x_1,x_2,\cdots,x_n$ se calcula como $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Aquí, $n = 6$, $x_1=5$, $x_2 = 4$, $x_3=9$, $x_4=2$, $x_5=4$, $x_6=9$.

$\sum_{i=1}^{6}x_i=5 + 4+9+2+4+9=33$

$\bar{x}=\frac{33}{6}=5.5$

Step2: Calcular las desviaciones absolutas

La desviación absoluta de cada valor $x_i$ con respecto a la media $\bar{x}$ es $|x_i-\bar{x}|$.

Para $x_1 = 5$: $|5 - 5.5|=0.5$

Para $x_2 = 4$: $|4 - 5.5|=1.5$

Para $x_3 = 9$: $|9 - 5.5|=3.5$

Para $x_4 = 2$: $|2 - 5.5|=3.5$

Para $x_5 = 4$: $|4 - 5.5|=1.5$

Para $x_6 = 9$: $|9 - 5.5|=3.5$

Step3: Calcular la media de las desviaciones absolutas (MAD)

$MAD=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$

$\sum_{i=1}^{6}|x_i-\bar{x}|=0.5+1.5+3.5+3.5+1.5+3.5 = 14$

$MAD=\frac{14}{6}\approx2.3$

Answer:

$2.3$