Question

Following data represents the age wise distribution of employees in office.

Age in years	$25-30$	$30-35$	$35-40$	$40-45$	$45-50$	$50-55$	$55-60$
Number of employees	$4$	$16$	$19$	$28$	$22$	$8$	$3$

Find the median age of employees.

• A. $41$ years
• B. $42$ years
• C. $44$ years
• D. $46$ years

Answer 1

Answer: (B)

$42$ years

Total number of elements($n$) $=4+16+19+28+22+8+3=100$

So, median group will be group of ${50}^{th}$ and ${51}^{th}$ elements.

Which is $40-45$ age interval.

Now, median $=L+\frac{\frac{n}{2}-c{f}_b}{f_m}\times w$

Where,

$L=$ Lower class boundary of the modal group,

$f_m=$ Frequency of the median group

$n=$ Total number of the median group

$c{f}_b=$ Cumulative frequency of the groups before the median class

$w=$ Group width.

Median $=40+\frac{50-(4+16+19)}{38}\times 5$

Median $=40+1.96\equiv 42$

Hence, median is $42$ years.

Hence, option B.