Question

# 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.Age in yearsNo. of policy holdersBelow 202Below 256Below 3024Below 3545Below 4078Below 4589Below 5092Below 5598Below 60100

A
47.12 years
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B
15.65 years
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C
25.17 years
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D
35.76 years
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Solution

## The correct option is D 35.76 years Class IntervalNo. of policy HoldersFreq (Fi) XI 18 to 20 2 2 20 to 25 4 6 25 to 30 18 24 30 to 35 21 45 35 to 40 33 78 40 to 45 11 89 45 to 50 3 92 50 to 55 6 98 55 to 60 2 100 N=100 For continuous data, median=L+(N2−Cf)×H Where N = Total cumulative frequencyL = lower limit of the median class Interval; Median Class = the class interval having cumulative freq≥N2 C= cumulative frequency of the class interval just before the median class intervalf= frequency of the median class interval; H= width of the median class intervalHere N=100N2=50this cumulative freq lies within interval (35−40);L=35;C=45;f=33;H=5Hence median =35+⎛⎜ ⎜ ⎜⎝1002−4533×5⎞⎟ ⎟ ⎟⎠=35+(50−4533×5)=35+(2533)=35+0.7575=35+.76=35.76

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