Question

in the data set below, what is the mean absolute deviation? -36 73 -31 55 -85 -85 -51 13 -96 if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad):

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{-36 + 73-31 + 55-85-85-51 + 13-96}{9}=\frac{-143}{9}\approx - 15.9$

Step2: Calculate the absolute - deviations

$| - 36-(-15.9)|=| - 36 + 15.9| = 20.1$
$|73-(-15.9)|=|73 + 15.9| = 88.9$
$| - 31-(-15.9)|=| - 31 + 15.9| = 15.1$
$|55-(-15.9)|=|55 + 15.9| = 70.9$
$| - 85-(-15.9)|=| - 85 + 15.9| = 69.1$
$| - 85-(-15.9)|=| - 85 + 15.9| = 69.1$
$| - 51-(-15.9)|=| - 51 + 15.9| = 35.1$
$|13-(-15.9)|=|13 + 15.9| = 28.9$
$| - 96-(-15.9)|=| - 96 + 15.9| = 80.1$

Step3: Calculate the mean of the absolute - deviations

$MAD=\frac{20.1 + 88.9+15.1 + 70.9+69.1+69.1+35.1+28.9+80.1}{9}=\frac{477.3}{9}\approx53.0$

Answer:

$53.0$