Question

Find the mean deviation about median for the following data.
$18,23,9,11,26,4,14,21$

Answer 1

First arranging data in ascending order

$4,9,11,14,18,21,23,26$

No. of terms $n=8$ ( even)

Since $n$ is even,

median $=\left(\frac{n}{2}\right)$th term,

$=\left(\frac{8}{2}\right)$th term,

$=4$th term,

$=14$

Now, We calculate mean deviation about median

median $\left(M\right)=14$

mean deviation about median $=\frac{\sum |x_i-M|}{8}$

$M.d.=\frac{(|4-14|+|9-14|+|11-14|+|14-14|+|18-14|+|21-14|+|23-14|+|26-14|)}{8}$

$=\frac{(|-10|+|-5|+|-3|+|0|+|4|+|7|+|9|+|12|)}{8}$

$=\frac{10+5+3+4+7+9+12}{8}$

$=\frac{50}{8}$

$=6.25$