Question

in the data set below, what is the mean absolute deviation? -2 9 -6 -8 -9 -9 -2 -5 if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad):

Explanation:

Step1: Calculate the mean

First, sum the data values: $-2 + 9+( - 6)+( - 8)+( - 9)+( - 9)+( - 2)+( - 5)=-2 + 9-6 - 8-9 - 9-2 - 5=-32$. There are $n = 8$ data - points. The mean $\bar{x}=\frac{-32}{8}=-4$.

Step2: Calculate the absolute deviations

Find the absolute deviation of each data - point from the mean:
$| - 2-( - 4)|=| - 2 + 4| = 2$;
$|9-( - 4)|=|9 + 4| = 13$;
$| - 6-( - 4)|=| - 6 + 4| = 2$;
$| - 8-( - 4)|=| - 8 + 4| = 4$;
$| - 9-( - 4)|=| - 9 + 4| = 5$;
$| - 9-( - 4)|=| - 9 + 4| = 5$;
$| - 2-( - 4)|=| - 2 + 4| = 2$;
$| - 5-( - 4)|=| - 5 + 4| = 1$.

Step3: Calculate the mean of the absolute deviations

Sum the absolute deviations: $2+13 + 2+4+5+5+2+1 = 34$.
The mean absolute deviation (MAD) is $\frac{34}{8}=4.25$. Rounding to the nearest tenth, we get $4.3$.

Answer:

$4.3$