Question

The following frequency distribution gives the monthly consumption of $68$ consumers of a locality. Find the median.

Monthly Consumption	$65-85$	$85-105$	$105-125$	$125-145$	$145-165$	$165-185$	$185-205$
No. of consumers	$4$	$5$	$13$	$20$	$14$	$8$	$4$

Answer 1

Monthly Consumption	$65-85$	$85-105$	$105-125$	$125-145$	$145-165$	$165-185$	$185-205$
No.of customers	$4$	$5$	$13$	$20$	$14$	$8$	$4$
Cumulative frequency	$4$	$9$	$22$	$42$	$56$	$64$	$68$

From the above table,

$\frac{N}{2}=\frac{68}{2}=34$

So, Median class is $125-145$

Median $=L+\left(\frac{\frac{N}{2}-c}{f}\right)\times h$

Here,

$L=125,c=22,f=42,h=(145-125)=20$

Median $=L+\left(\frac{\frac{N}{2}-c}{f}\right)\times h$

$=125+\left(\frac{34-22}{42}\right)\times 20$

$=125+\frac{12}{42}\times 20$

$=125+5.714$

$=130.714$

So, Median $=130.714$