Question

in the data set below, what is the mean absolute deviation? -7 -9 9 -7 -7 -6 if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad):

Explanation:

Step1: Calculate the mean

The sum of the data points $-7+( - 9)+9+( - 7)+( - 7)+( - 6)=-27$. There are $n = 6$ data - points. The mean $\bar{x}=\frac{-27}{6}=-4.5$.

Step2: Calculate the absolute deviations

$| - 7-( - 4.5)|=| - 7 + 4.5| = 2.5$; $| - 9-( - 4.5)|=| - 9 + 4.5| = 4.5$; $|9-( - 4.5)|=|9 + 4.5| = 13.5$; $| - 7-( - 4.5)|=| - 7 + 4.5| = 2.5$; $| - 7-( - 4.5)|=| - 7 + 4.5| = 2.5$; $| - 6-( - 4.5)|=| - 6 + 4.5| = 1.5$.

Step3: Calculate the mean of the absolute deviations

The sum of the absolute deviations is $2.5+4.5 + 13.5+2.5+2.5+1.5 = 27$. The mean absolute deviation $MAD=\frac{27}{6}=4.5$.

Answer:

$4.5$