Question

Find the Mean of the following frequency table by step - deviation method :

$\begin{array}{cc}\text{Class Interval}& \text{Frequency}\\ 10-15& 10\\ 15-20& 5\\ 20-25& 6\\ 25-30& 8\\ 30-35& 4\\ 35-40& 7\end{array}$

• A. 30
• B. 24
• C. 26.5
• D. 27.5

Answer 1

The correct option is B

24

$\begin{array}{ccccc}\text{Class Interval}& \text{Mid value (x)}& \text{Frequency (f)}& \mu =\frac{x-A}{i}& fu\\ 10-15& 12.5& 10& -3& -30\\ 15-20& 17.5& 5& -2& -10\\ 20-25& 22.5& 6& -1& -6\\ 25-30& 27.5=A& 8& 0& 0\\ 30-35& 32.5& 4& 1& 4\\ 35-40& 37.5& 7& 2& 14\\ \text{Total}& & \sum \text{f}=40& & \sum \text{fu}=-28\end{array}$

Here we Choose A = 27.5 and i = 5.

We can arrange the data as given :

$\therefore$ Mean = A + $\left(\frac{\Sigma fu}{\Sigma f}\right)\times i$

= 27.5 +$(\frac{-28}{40}\times 5)$

= 27.5 - 3.5

= 24