Question

in the data set below, what is the mean absolute deviation? 57 82 89 69 70 if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad):

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, $n = 5$, $x_1=57$, $x_2 = 82$, $x_3=89$, $x_4=69$, $x_5=70$.
$$\bar{x}=\frac{57 + 82+89+69+70}{5}=\frac{367}{5}=73.4$$

Step2: Calcular las desviaciones absolutas

Calculamos $|x_i-\bar{x}|$ para cada $i$:

• $|57 - 73.4|=16.4$
• $|82 - 73.4|=8.6$
• $|89 - 73.4|=15.6$
• $|69 - 73.4|=4.4$
• $|70 - 73.4|=3.4$

Step3: Calcular la MAD

La MAD se calcula como $\text{MAD}=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$$\text{MAD}=\frac{16.4 + 8.6+15.6+4.4+3.4}{5}=\frac{48.4}{5}=9.68\approx9.7$$

Answer:

$9.7$