Question

Calculate the number of students against the class 30−40 of the following data, where $\overline{X}$ = 28.

Marks	0−10	10−20	20−30	30−40	40−50	50−60
Frequency	12	18	27	?	17	6

Answer 1

Class Interval (Marks)	Mid-Values (m)	Frequency (f)	fm
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60	5 15 25 35 45 55	12 18 27 f 17 6	60 270 675 35f 765 330
		$\mathit{\Sigma }\mathit{f}$=80 + f	$\mathit{\Sigma }\mathit{f}\mathit{m}$=2100 + 35f

Let the missing frequency be f

Given:
Mean, $\overline{\mathit{X}}$=28

$$\begin{gathered} \overline{X}=\frac{\Sigma fm}{\Sigma f} \\ or,28=\frac{2100+35f}{80+f} \\ or,2240+28f=2100+35f \\ or,7f=140 \\ \Rightarrow f=\frac{140}{7}=20 \end{gathered}$$

Hence, the missing frequency is 20.