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 $f$.

Daily pocket allowance (in $Rs.$)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-25$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

Answer 1

Lets take assumed mean, $A$ as $16$

Class interval $=2$

$\therefore u_i=\frac{x_i-A}{h}=\frac{x_i-16}{2}$

Now, we have $A=16,\overline{x}=18$ and $h=2$

We know that,

Mean, $\overline{x}=A+h(\frac{1}{N}\sum f_i{u}_i)$

$\Rightarrow 18=16+2\left(\frac{2f+24}{f+44}\right)$

$\Rightarrow \frac{2f+24}{f+44}=1$

$\Rightarrow f+44=2f+24$

$\Rightarrow f=20$

Hence, the value of missing frequency, $f=20$