EX 13.3 (Question: 3)

EX 13.3 (Question: 3) A life insurance agent found the following data for 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 year. 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

Solution: Given data: Total 𝑛=100 𝑛/2=50 Median class = 35 – 40 (since cumulative frequency just greater than 50 is 78) 𝑙 = 35 (lower limit) 𝐹 = 45 (cumulative frequency before median class) 𝑓 = 78 − 45 = 33 (frequency of median class) ℎ = 40 − 35= 5 (class width)Using formula: Median = 𝑙 + ( "n/2−F" /"𝑓" )"×h" Where: 𝑙 = 35, 𝐹 = 45, 𝑓 = 33, ℎ = 5. Median = 35 + ("(50−45" /20)"× 5" "=" 35 + 5/33 "× 5" "=" 35 + 25/33 "= 35. 76"

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