Question

in the data set below, what is the mean absolute deviation? -17 -25 -11 -28 -93 -72 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 the data - set $x_1=-17,x_2 = - 25,x_3=-11,x_4=-28,x_5=-93,x_6=-72$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$, where $n = 6$.
$\sum_{i=1}^{6}x_i=-17-25 - 11-28-93-72=-246$. Then $\bar{x}=\frac{-246}{6}=-41$.

Step2: Calculate the absolute - deviations

The absolute - deviation of each data point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
$| - 17-(-41)|=| - 17 + 41| = 24$;
$| - 25-(-41)|=| - 25 + 41| = 16$;
$| - 11-(-41)|=| - 11 + 41| = 30$;
$| - 28-(-41)|=| - 28 + 41| = 13$;
$| - 93-(-41)|=| - 93 + 41| = 52$;
$| - 72-(-41)|=| - 72 + 41| = 31$.

Step3: Calculate the mean of the absolute - deviations

The mean absolute deviation (MAD) is $\text{MAD}=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i=1}^{6}|x_i-\bar{x}|=24 + 16+30+13+52+31 = 166$.
Then $\text{MAD}=\frac{166}{6}\approx27.7$.

Answer:

$27.7$