# A batsman scores $38, 70, 48, 34, 42, 55, 63, 46, 54 \: and \: 44$ in 10 innings. Find his mean deviation from median.

$\begin {array} {1 1} (A)\;8 & \quad (B)\;8.6 \\ (C)\;8.9 & \quad (D)\;9 \end {array}$

Ans : (B)
Arranging the given data in ascending order we get
$34, 38, 42, 44, 46, 48, 54, 55, 63, 70$
Median = $\large\frac{1}{2}$ $(T+T_1) = \large\frac{46+48}{2}$
$= 47$
Mean deviation = $\large\frac{1}{n}$ $\Sigma | x_i-M_e |$
$\large\frac{1}{10}$ $\Sigma n|x_i-47|$
$\large\frac{1}{10}$ $( 13+9+5+3+1+1+7+8+6+23)$
$= \large\frac{1}{10}$$(86)$
$= 8.6$

edited Jan 25, 2014