Question

The following table gives the frequency distribution of married women by age at marriage:

Age (in years)	Frequency	Age (in years)	Frequency
$15-19$	$53$	$40-44$	$9$
$20-24$	$140$	$45-49$	$5$
$25-29$	$98$	$50-54$	$3$
$30-34$	$32$	$55-59$	$3$
$35-39$	$12$	$60$ and above	$2$

Calculate the median and interpret the results.

Answer 1

$Age$	$Frequency$	$Cumulativefrequency$
$14.5-19.5$	$53$	$53$
$19.5-24.5$	$140$	$193$
$24.5-29.5$	$98$	$291$
$29.5-34.5$	$32$	$323$
$34.5-39.5$	$12$	$335$
$39.5-44.5$	$9$	$344$
$44.5-49.5$	$5$	$349$
$49.5-54.5$	$3$	$352$
$54.5-59.5$	$3$	$355$
$59.5andabove$	$2$	$357$
	$N=357$

$\Rightarrow$ $N=357$ then, $\frac{N}{2}=\frac{357}{2}=178.5$

The cumulative frequency just greater than $\frac{N}{2}$ is $193$, then the median class is $20-24$ such that

$l=19.5,f=140,F=53,h=24.5-19.5=5$.

$\Rightarrow$ $Median=l+\frac{\frac{N}{2}-F}{f}\times h$

$\Rightarrow$ $Median=19.5+\frac{178.5-53}{140}\times 5$

$\Rightarrow$ $Median=23.98$

Nearly half the women were married between the ages of $15$ and $25$.