Mathematics

A life insurance agent found the following data of age distribution of 100 policy holders, where f is an unknown frequency.
Age in years No. of policy holders
15-20 7
20-25 12
25-30 15
30-35 22
35-40 f
40-45 14
45-50 8
50-55 4
(a) If the mean age of the policy holders is 35.65 years, find the unknown frequency f.
(b) Find the median class of the distribution.

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(a) Given,

Total no. of policy holders = 100

∴ 7 + 12 + 15 + 22 + f + 14 + 8 + 4 = 100

⇒ 82 + f = 100

⇒ f = 100 - 82 = 18.

Hence, f = 18.

(b) Cumulative frequency distribution table :

Since, n = 100, which is even.

Median = $\dfrac{n}{2}\text{ th term} = \dfrac{100}{2}$ = 50th term.

Steps of construction :

Plot class interval on x-axis and cumulative frequency on y-axis.
Mark points (20, 7), (25, 19), (30, 34), (35, 56), (40, 74), (45, 88), (50, 96) and (55, 100).
Draw a free hand curve passing through the points marked and starting from the lower limit of first class and terminating at upper limit of the last class.
From point A = 50 draw a line parallel to x-axis touching the graph at point B. From point B draw a line parallel to y-axis touching x-axis at C.

From graph,

C = 33.75, which lies between 30-35.

Hence, median class = 30-35.

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