Question

Find the mean deviation about the median for the given data.

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Answer 1

Arranging the data in ascending order, we have

10, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18

Here n = 12 (which is even)

So median is average of 6th and 7th observations

$\therefore$ Median = $\frac{13+14}{2}=\frac{27}{2}$= 13.5

$\begin{array}{cc}{x}_1& |x_i-M|\\ 10& 3.5\\ 11& 2.5\\ 11& 2.5\\ 12& 1.5\\ 13& 0.5\\ 14& 0.5\\ 16& 2.5\\ 16& 2.5\\ 17& 3.5\\ 17& 3.5\\ 18& 4.5\\ \text{Total}& 28\end{array}$

M.D. about median = $\frac{1}{n}{\sum }_{i-1}^n|x_i-M|$ =$\frac{1}{12}\times 28=2.33$