A life insurance agent found the following data for distribution of ages of 100 policyholders.Calculate the median age, if policies are given only to persons having age 18 years onwards and below 60 years.
Age (in years)
Number of policyholders
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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35.76 years

38.76 years

36.78 years

34.97years

answer is A.

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Detailed Solution

Age (in years)	Number of Policyholders (𝑓)	Cumulative frequency (𝑐𝑓)
18 − 20	2	2
20 − 25	6 − 2 = 4	6
25 − 30	24 − 6 = 18	24
30 − 35	45 − 24 = 21	45
35 − 40	78 − 45 = 33	78
40 − 45	89 − 78 = 11	89
45 − 50	92 − 89 = 3	92
50 − 55	96 − 92 = 4	96
55 − 60	100 − 96 = 4	100
	𝑛 = 𝛴𝑓 = 100

For, the table, we got 𝑛 = 100
Therefore, 𝑛 = 100 = 50
2 2
Now,
𝑛
Cumulative frequency (𝑐𝑓) 𝑗𝑢𝑠𝑡 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛
Therefore,
Median class = 35 − 40
Lower limit of the median class (𝑙) = 35 Frequency of the median class (𝑓) = 33 Cumulative frequency (𝑐𝑓) = 45
Class size (ℎ) = 5

= 50 𝑖𝑠 78, which lies in the interval 35 − 40.
2
Now, we know the formula for median,

𝑛 − 𝑐𝑓
𝑀𝑒𝑑𝑖𝑎𝑛 = 𝑙 + ( 2 ) × ℎ
𝑓
Put the above written values,

⇒ 𝑀𝑒𝑑𝑖𝑎𝑛 = 35 + (

50 − 45
33
5

) × 5
⇒ 𝑀𝑒𝑑𝑖𝑎𝑛 = 35 + × 5
33
⇒ 𝑀𝑒𝑑𝑖𝑎𝑛 =

1155 + 25
33
1180
⇒ 𝑀𝑒𝑑𝑖𝑎𝑛 =
33
Therefore, the median age = 35.76 years.

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