Question

The scores of batsmen(S) in a cricket series is tabulated below. The mean deviation about mean for the scores is
$\begin{array}{ccccccc}S& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ f_i& 12& 18& 27& 20& 17& 6\end{array}$

• A. 15
• B. 99
• C. 10
• D. 50

Answer 1

The correct option is C 10

We write the midpoints of each given class and proceed as for a discrete frequency to find mean deviation.

$\begin{array}{cccccc}Score& f_i& x_i& f_i{x}_i& |x_i-\overline{x}|& f_i|x_i-\overline{x}|\\ 10-20& 2& 15& 30& 30& 60\\ 20-30& 3& 25& 75& 20& 60\\ 30-40& 8& 35& 250& 10& 80\\ 40-50& 14& 45& 630& 0& 0\\ 50-60& 8& 55& 440& 10& 80\\ 60-70& 3& 65& 195& 20& 60\\ 70-80& 2& 75& 150& 30& 60\\ & 40& & 1800& & 400\end{array}$

$N=\sum _{i=1}^7{f}_i=40\sum _{i=1}^7{f}_i{x}_i=1800\overline{x}=\frac{1}{N}\sum _{i=1}^7{f}_i{x}_i=\frac{1800}{40}=45$

$\sum _{i=1}7f_i|x_i-\overline{x}|=400$

$MD\left(\overline{x}\right)=\frac{1}{N}{\sum }_{i=1}^7{f}_i|x_i-\overline{x}|=\frac{1}{40}\left(400\right)=10$