Question

The distribution of the number of hours per week spent studying by a group of 50 students is given below. Calculate the standard deviation using the assumed mean method.

$\begin{array}{cccccc}\text{No. of hours}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{No. of students}& 20& 10& 8& 7& 5\end{array}$

• A. 11.6
• B. 13.8
• C. 14.4
• D. 15.2

Answer 1

The correct option is B

13.8

Let the assumed mean be 25 i.e. A = 25

$\begin{array}{ccccc}X& F& D=X-A& FD& F{D}^2\\ 5& 20& -20& -400& 8000\\ 15& 10& -10& -100& 1000\\ 25& 8& 0& 0& 0\\ 35& 7& 10& 70& 700\\ 45& 5& 20& 100& 2000\\ & \sum F=50& & \sum FD=-330& \sum F{D}^2=11700\end{array}$

$\sigma =\sqrt{\frac{\sum F{D}^2}{\sum F}-{\left(\frac{\sum FD}{\sum F}\right)}^2}=\sqrt{\frac{11700}{50}-{\left(\frac{-330}{50}\right)}^2}=\sqrt{234-43.56}=\sqrt{190.44}=13.8$