Question

The runs scored by batsmen in a game are given below
$\begin{array}{ccccc}x& 10& 20& 30& 40\\ f& 2& 3& 1& 4\end{array}$
Find the standard deviation of the runs scored by Assumed mean method.

• A. 11.87
• B. 12.89
• C. 14.25
• D. 15.65

Answer 1

The correct option is A 11.87

Let the Assumed mean, A = 20
$\begin{array}{ccccc}xi& fi& di=xi-A& fidi& fid{i}^2\\ 10& 2& -10& -20& 200\\ 20& 3& 0& 0& 0\\ 30& 1& 10& 10& 100\\ 40& 4& 20& 80& 1600\\ & n=10& & \sum fidi=70& \sum fid{i}^2=1900\end{array}$

Standard Deviation

$\sigma =\sqrt{\frac{\sum fid{i}^2}{N}-(\frac{\sum fidi}{N}{)}^2}=\sqrt{\frac{1900}{10}-(\frac{70}{10}{)}^2}$

$=\sqrt{190-49}=\sqrt{141}$

= 11.87