Question

If the mean of the following frequency distribution is 18 , find the missing frequency .

Class interval : 11-13 13-15 15-17 17-19 19-21 21-23 23-25

Frequency: 3 6 9 13 f 5 4

Answer 1

It is given that mean of the data is 18.
Let the assumed mean A = 18 and h = 2.

Marks	Mid-Value(xi)	Frequency	${\mathit{u}}_{\mathbf{i}}\mathbf{=}\frac{{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{18}}{\mathbf{2}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
11–13	12	3	−3	−9
13–15	14	6	−2	−12
15–17	16	9	−1	−9
17–19	18	13	0	0
19–21	20	f	1	f
21–23	22	5	2	10
23–25	24	4	3	12
		N = 40 + f		$\sum _{}{f}_i{u}_i=-8+f$

We know that mean,
Now, we have $N=\sum _{}{f}_i=40+f,h=2,A=18,\sum _{}{f}_i{u}_i=-8+f$
$$\begin{gathered} 18=18+2\left[\frac{1}{\left(40+f\right)}\times \left(-8+f\right)\right] \\ \Rightarrow 0=\frac{-16+2f}{40+f} \\ \Rightarrow -16+2f=0 \\ \Rightarrow f=8 \end{gathered}$$