A life insurance agent found the following data for the distribution of ages of 100 policyholders. Calculate the median age, if policies are given only to persons having age 18 years onwards but lets than 60 years.
Age (in years) No. of policyholders (cf)
Below 20 2
Below 25 6
Below 30 24
Below 35 45
Below 40 78
Below 45 89
Below 50 92
Below 55 98
Below 60 100

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Solution

Given the cumulative frequency distribution table convert into a frequency distribution table
Cumulative greater than $\frac{n}{2} = \frac{100}{2} = 50$ is $78$ .
$∴$ Median class is 35 - 40
$l = 35, h = 5, f = 33 a n d c f = 45$
$M e d i a n = l + ⎡ ⎢ ⎢ ⎢ ⎣ \frac{\frac{N}{2} - c f}{f} ⎤ ⎥ ⎥ ⎥ ⎦ \times h$
$= 35 + ⎡ ⎢ ⎢ ⎢ ⎣ \frac{\frac{100}{2} - 45}{33} ⎤ ⎥ ⎥ ⎥ ⎦ \times 5$
$= 35 + \frac{5}{33} \times 5$
$= 35 + 0.76$
$= 35.76$
$∴$ Median age is 35.76 years $

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Similar questions

A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onwards but less than 60 years.
$\begin{matrix} Age in years & Number of policy holders Below 20 & 2 Below 25 & 6 Below 30 & 24 Below 35 & 45 Below 40 & 78 Below 45 & 89 Below 50 & 92 Below 55 & 98 Below 60 & 100 \end{matrix}$

Q. A life insurance agent found the following data for distribution of ages of

100

policy holders. Calculate the median age, if policies are only given to person having age

18

years onwards but less than

60

years.

Age (in years)	No. of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

Q. A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onward but less than 60 years.

Age in years	Number of policy holders
Below 20 Below 25 Below 30 Below 35 Below 40 Below 45 Below 50 Below 55 Below 60	2 6 24 45 78 89 92 98 100

The Life insurance agent found the following data for the distribution of ages of 100 policyholders. Calculate the median age, if policies are given only to the

persons whose age is 18 years onwards but less than 60 years.

Age in years	No. of Policy holders
$Below 20$	$2$
$Below 25$	$6$
$Below 30$	$24$
$Below 35$	$45$
$Below 40$	$78$
$Below 45$	$89$
$Below 50$	$92$
$Below 55$	$98$
$Below 60$	$100$

Question 3
A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.

$\begin{matrix} A g e (i n y e a r s) & N u m b e r o f p o l i c y h o l d e r s B e l o w 20 & 2 B e l o w 25 & 6 B e l o w 30 & 24 B e l o w 35 & 45 B e l o w 40 & 78 B e l o w 45 & 89 B e l o w 50 & 92 B e l o w 55 & 98 B e l o w 60 & 100 \end{matrix}$

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Age (in years)	No. of policyholders (cf)
Below 20	2
Below 25	6
Below 30	24
Below 35	45
Below 40	78
Below 45	89
Below 50	92
Below 55	98
Below 60	100