Question

Estimate the median for the following data$:$

Daily wages	$22-24$	$24-26$	$26-28$	$28-30$	$30-32$
Number of workers	$23$	$120$	$100$	$110$	$105$

• A. $27.72$
• B. $26.67$
• C. $36.67$
• D. $66.67$

Answer 1

The correct option is A $27.72$

Daily wages	Number of workers(f)	Cumulative frequency (cf)
$22-24$	$23$	$23$
$24-26$	$120$	$23+120=143$
$26-28$	$100$	$143+100=243$
$28-30$	$110$	$243+110=353$
$30-32$	$105$	$353+105=458$

Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$

$n=\Sigma f=$ Total number of frequency $=458$

$\frac{n}{2}=\frac{458}{2}=229$

So, the median class is $26-28$

L$=$ Lower limit of the median class $=26$

cf$=$ Cumulative frequency of the class preceding the median class

$=143$

f$=$ Frequency of the median class $=100$

h$=$ class width$=2$

Therefore, Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$

$=26+\left(\frac{\frac{458}{2}-143}{100}\right)\times 2$

$=26+\left(\frac{229-143}{100}\right)\times 2$

$=26+1.72$

$=27.72$

Hence, the median is $27.72$.