Question

Find the mean deviation about the mean for the following data.

$\begin{array}{cccccc}{x}_i& 10& 30& 50& 70& 90\\ f_i& 4& 24& 28& 16& 8\end{array}$

Answer 1

Given data:

$\begin{array}{cccccc}{x}_i& 10& 30& 50& 70& 90\\ f_i& 4& 24& 28& 16& 8\end{array}$

Lets form the frequency distribution table to find mean and mean deviation about the mean.

$\begin{array}{ccccc}{x}_i& f_i& f_i{x}_i& |x_i-50|& f_i|x_i-50|\\ 10& 4& 40& 40& 160\\ 30& 24& 720& 20& 480\\ 50& 28& 1400& 0& 0\\ 70& 16& 1120& 20& 320\\ 90& 8& 720& 40& 320\\ & \sum f_i=80& \sum f_i{x}_i=4000& & \sum f_i|x_i-50|=1280\end{array}$

Mean $\left(\overline{x}\right)=\frac{1}{N}\sum f_i{x}_i=\frac{1}{80}\times 4000=50$

Mean deviation about mean

$=\frac{1}{N}{\sum }_{i=1}^n{f}_i|x_i-\overline{x}|$

$=\frac{1}{80}\times 1280$

$=16$

Therefore, Mean deviation about the mean is $16$.