Question

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

36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Answer 1

Arrange the data in ascending order, we have

36, 42, 45, 46, 49, 51, 53, 60, 72

Here n = 10 (which is even)

So median is average of 5th and 6th observation

$\therefore$ Median = $\frac{46+49}{2}=\frac{95}{2}=47.5$

$\begin{array}{cc}{x}_1& |x_i-M|\\ 36& 11.5\\ 42& 5.5\\ 45& 2.5\\ 46& 1.5\\ 46& 1.5\\ 49& 1.5\\ 51& 3.5\\ 53& 5.5\\ 60& 12.5\\ 72& 24.5\\ \text{Total}& 70\end{array}$

$\text{M.D. about median}=\frac{1}{n}{\sum }_{i-1}^n|x_i-M|=\frac{1}{10}\times 70=7$