Question

The mean deviation about the mean for the following data :
$\begin{array}{cccccccc}{x}_i& 2& 3& 4& 5& 6& 7& 8\\ f_i& 5& 2& 3& 4& 5& 4& 2\end{array}$
is

• A. $2.3$
• B. $3.4$
• C. $4$
• D. $1.66$

Answer 1

The correct option is D $1.66$

$\begin{array}{ccccc}{x}_i& f_i& f_i{x}_i& |x_i-\overline{x}|& f_i|x_i-\overline{x}|\\ 2& 5& 10& 2.88& 14.4\\ 3& 2& 6& 1.88& 3.76\\ 4& 3& 12& 0.88& 2.64\\ 5& 4& 20& 0.12& 0.48\\ 6& 5& 30& 1.12& 5.6\\ 7& 4& 28& 2.12& 8.48\\ 8& 2& 16& 3.12& 6.24\\ & \sum f_i=25& \sum f_i{x}_i=122& & \sum f_i|x_i-\overline{x}|=41.6\end{array}$

$\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{122}{25}=4.88$
Mean deviation $=\frac{\sum f_i|x_i-\overline{x}|}{\sum f_i}=\frac{41.6}{25}=1.66$