Question

in the data - set below, what is the mean absolute deviation? -60 -22 -57 -14 -19 -86 -64 if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad):

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 7$, $x_1=-60,x_2=-22,x_3=-57,x_4=-14,x_5=-19,x_6=-86,x_7=-64$.
$\sum_{i=1}^{7}x_i=-60 - 22-57 - 14-19 - 86-64=-322$.
$\bar{x}=\frac{-322}{7}=-46$.

Step2: Calculate the absolute deviations

The absolute deviation of each data - point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
$| - 60-(-46)|=| - 60 + 46| = 14$;
$| - 22-(-46)|=| - 22 + 46| = 24$;
$| - 57-(-46)|=| - 57 + 46| = 11$;
$| - 14-(-46)|=| - 14 + 46| = 32$;
$| - 19-(-46)|=| - 19 + 46| = 27$;
$| - 86-(-46)|=| - 86 + 46| = 40$;
$| - 64-(-46)|=| - 64 + 46| = 18$.

Step3: Calculate the mean absolute deviation

The mean absolute deviation (MAD) is $\text{MAD}=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i = 1}^{7}|x_i-\bar{x}|=14 + 24+11 + 32+27 + 40+18 = 166$.
$\text{MAD}=\frac{166}{7}\approx23.7$.

Answer:

$23.7$