Question

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency $f$.

Answer 1

To find the class mark $\left(x_i\right)$ for each interval, using the following relation:
$\left(x_i\right)=\frac{\text{Upper class limit}+\text{Lower class limit}}{2}$
Given that, mean pocket allowance, $\overline{x}=Rs.18$
Taking 18 as assumed mean $\left(a\right),d_i$ and $f_i{d}_i$ are calculated as:
From the table:
$\sum f_i=44+f$
$\sum f_i{d}_i=2f-40$
$\overline{x}=a+\frac{\sum f_i{d}_i}{\sum f_i}$
$18=18+\left(\frac{2f-40}{44+f}\right)$
$0=\frac{2f-40}{44+f}$
$2f-40=0$
$2f=40$
$f=20$
$\therefore$ the missing frequency, $f$, is $20$.