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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 person having age $$18$$ years onwards but less than $$60$$ years.
Age (in years)
No. 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 $$60$$
$$100$$


A
62.12 years
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B
53.53 years
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C
35.76 years
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D
None of these
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Solution

The correct option is D $$35.76$$ years
Age (in years)       
Number of policy holders     $$f_1$$
Cumulative frequency
Below $$20$$
$$2=2$$
$$2$$
$$20-25$$
$$(6-2)=4$$
$$6$$
$$25-30$$
$$(24-6)=18$$
$$24$$
$$30-35$$
$$(45-24)=21$$
$$45$$
$$35-40$$
$$(78-45)=33$$
$$78$$
$$40-45$$
$$(89-78)=11$$
$$89$$
$$45-50$$
$$(92-89)=3$$
$$92$$
$$50-55$$
$$(98-92)=6$$
$$98$$
$$55-60$$
$$(100-98)=2$$
$$100$$
Total
$$n=100$$

Here, $$l=35, n=100, f=33, cf=45, h=5$$ Median$$=l+\left \{\cfrac {\frac {n}{2}-cf}{f}\right \}\times h$$
$$=35+\left \{\cfrac {50-45}{33}\right \}\times 5$$
$$=35+\cfrac {25}{33}$$
$$=35+0.76$$
$$=35.76$$ years

Mathematics
RS Agarwal
Standard X

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