Question

The number of goals scored by Messi in champion's league for past 10 years is a follows: {1, 1, 6, 9, 8, 12, 14, 8, 8, 10}. Find the mean deviation about the median.

Answer 1

First we have to calculate the median of the goals.
Arranging the given values, we get,
1, 1, 6, 8, 8, 8, 9, 10, 12, 14,

5^th and 6^th values are 8 and 8.

Therefore, median = $\frac{8+8}{2}$ = 8 = M
Absolute deviations respectively are {7,7,2,1,0,4,6,0,0,2}

$\Rightarrow {\sum }_{i=1}^{10}|x_i-M|$ = 7+7+2+1+0+4+6+0+0+2 = 29

$MD\left(M\right)=\frac{{\sum }_{i=1}^{10}|x_i-M|}{10}=\frac{29}{10}=2.9$