Question

The runs scored by a batsman in 60 innings are given below. Find the standard deviation of the runs using the assumed mean method.

$\begin{array}{ccccccc}Runs& 0-20& 20-40& 40-60& 60-80& 80-100& 100-120\\ No.ofinnings& 15& 20& 12& 5& 4& 4\end{array}$

• A. 24.68
• B. 27.85
• C. 29.05
• D. 31.33

Answer 1

The correct option is C

29.05

Let the assumed mean be 50 i.e. A = 50

$\begin{array}{ccccc}X& F& D=X-A& FD& F{D}^2\\ 10& 15& -40& -600& 240000\\ 30& 20& -20& -400& 8000\\ 50& 12& 0& 0& 0\\ 70& 5& 20& 100& 2000\\ 90& 4& 40& 160& 6400\\ 110& 4& 60& 240& 14400\\ & \sum F=60& & \sum FD=-500& \sum F{D}^2=54800\end{array}$

$\sigma =\sqrt{\frac{\sum F{D}^2}{\sum F}-{\left(\frac{\sum FD}{\sum F}\right)}^2}=\sqrt{\frac{54800}{60}-{\left(\frac{500}{60}\right)}^2}=\sqrt{913.33-69.39}=\sqrt{843.94}=29.05$