Question

The following table gives weekly wages in rupees of workers in a certain commercial organisation. The frequency of class 49-52 is missing. It is known that the mean of the frequency is distribution is 47.2. Find the missing frequency.

Weekly wages (Rs.)	40-43	43-46	46-49	49-52	52-55
Number of workers:	31	58	60	?	27

Answer 1

Class-Intervals	mid-values $x_i$	$f_i$	$d_i=x_i-47.5$	$u_i=\frac{x_i=47.5}{3}$	$f_i{u}_i$
$40-43$	$41.5$	$31$	$-6$	$-2$	$-62$
$43-46$	$44.5$	$58$	$-3$	$-1$	$-58$
$46-52$	$47.5$	$60$	$0$	$0$	$0$
$49-52$	$50.5$	$f$	$3$	$1$	$f$
$52-55$	$53.5$	$27$	$6$	$2$	$54$
		$N=\sum f_i=176+f$			$\sum f_i{u}_i=f-66$

We have,

$\overline{X}$= 42.7 , A= 47. 5 and h=3

$\therefore \overline{X}=A+h[\frac{1}{N}\sum f_i{u}_i]$

$\Rightarrow 47.2=47.5+3\times \left[\frac{f-66}{176+f}\right]$

$\Rightarrow -0.3=3\times \left[\frac{f-66}{176+f}\right]$

$\Rightarrow \frac{-1}{10}=\frac{f-66}{176+f}$

$\Rightarrow -176-f=10f-660$

$\Rightarrow 11f=484\Rightarrow f=44$

Hence, the missing frequency is 44.