Question

Find the mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17.

Answer 1

The given data is

4, 7, 8, 9, 10, 12, 13, 17

Mean of the data, $\bar{x}=\frac{4+7+8+10+12+13+17}{8}=\frac{80}{8}=10$

The deviations of the respective observations from the mean $\bar{x},i.e.x_i-\bar{x},$ are:

6, 3, 2, 1, 0, 2, 3, 7

The absolute values of the deviations, i.e. $|x_i-\bar{x}|$, are:

6, 3, 2, 1, 0, 2, 3, 7

The required mean deviation about the mean is

M.D.$\bar{x}=\frac{\sum_{i=1}^{8}|x_i-\bar{x}|}{8}=\frac{6+3+2+1+0+2+3+7}{8}$

$=\frac{24}{8}=3$