Question

A batsman scores $38,76,34,48,44,54,46,55,63,42$ runs in $10$ innings. Find the value of mean deviation about the median.

Answer 1

Answer: 9.2

On arranging the given data in ascending order we get,
$34,38,42,44,46,48,54,55,63,76$
Here, $N=10$. (even.)
$\Rightarrow$ Median $=$ Average of ${\left(\frac{N}{2}\right)}^{\text{th }}$ and
${\left(\frac{N}{2}+1\right)}^{\text{th }}$ terms
$=\frac{46+48}{2}$
$=47$
$\Rightarrow$ Mean deviation about median
$\Rightarrow \frac{\sum \mid x-\text{ Median }\mid }{N}$
$\iff \frac{\sum |x-47|}{10}$
$\iff \frac{13+9+5+3+1+1+7+8+16+29}{10}$
$\Rightarrow \frac{92}{10}\iff 9.2$