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A life insurance agent found the following data for distribution of ages of 100 policy holders - Mathematics

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
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Solution

Here, class width is not the same. There is no requirement of adjusting the frequencies according to class intervals. The given frequency table is of less than type represented with upper class limits. The policies were given only to persons with age 18 years onwards but less than 60 years. Therefore, class intervals with their respective cumulative frequency can be defined as below

 

Age (in years) Number of policy holders (fi) 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 98 - 92 = 6 98
55 - 60 100 - 98 = 2 100
Total (n)    

From the table, it can be observed that n = 100.

Cumulative frequency (cf) just greater than `n/2(100/2 = 50)` is 78, belonging to interval 35 - 40.
Therefore, median class = 35 - 40
Lower limit (l) of median class = 35
Class size (h) = 5
Frequency (f) of median class = 33
Cumulative frequency (cf) of class preceding median class = 45

`"Median" = l + ((n/2-cf)/f)xxh`

`= 35 + ((50-45)/33)xx5`

`= 35 + 25/33`

= 35.76

Therefore, median age is 35.76 years.

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APPEARS IN

NCERT Class 10 Maths
Chapter 14 Statistics
Exercise 14.3 | Q 3 | Page 287
RD Sharma Class 10 Maths
Chapter 15 Statistics
Exercise 15.4 | Q 17 | Page 36
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