Question

The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is ₹18, find the missing frequency f.

Daily pocket allowance (in ₹)	11−13	13−15	15−17	17−19	19−21	21−23	23−25
Number of children	7	6	9	13	f	5	4

Answer 1

The given data is shown as follows:

Daily pocket allowance (in ₹)	Number of children (fi)	Class mark (xi)	fixi
11−13	7	12	84
13−15	6	14	84
15−17	9	16	144
17−19	13	18	234
19−21	f	20	20f
21−23	5	22	110
23−25	4	24	96
Total	∑ fi = 44 + f		∑ fixi = 752 + 20f

The mean of given data is given by

$$\begin{gathered} \overline{x}=\frac{{\displaystyle \sum _i}{f}_i{x}_i}{{\displaystyle \sum _i}{f}_i} \\ \Rightarrow 18=\frac{752+20f}{44+f} \\ \Rightarrow 18(44+f)=752+20f \\ \Rightarrow 792+18f=752+20f \\ \Rightarrow 20f-18f=792-752 \\ \Rightarrow 2f=40 \\ \Rightarrow f=20 \end{gathered}$$

​Hence, the value of f is 20.