Question

The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is Rs. 18, find the missing frequency f.
$\begin{array}{cccccccc}\text{Daily pocket}& & & & & & & \\ \text{allowance(in Rs)}& 11-13& 13-15& 15-17& 17-19& 19-21& 21-23& 23-25\\ \text{Frequency}& 7& 6& 9& 13& f& 5& 4\end{array}$

Answer 1

The given data is shown as follows:

Daily pocket allowance (in Rs.)	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		∑(fi×xi)=752+20f

The mean of given data is given by

$\overline{x}$= ∑(fi×xi)/∑fi

⇒ 18 = $\frac{752+20f}{44+f}$

⇒ 18(44 + f) = 752 + 20f

⇒ 792 + 18f = 752 + 20f

⇒ 20f - 18f = 792 - 752

⇒ 2f = 40

⇒ f = 20

Hence, the value of f is 20.