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Question

Which of the following are the possible ages of 27th and 32nd observations in the given grouped distribution in increasing order of age? All the persons (observations) part of the distribution have exact integral ages.

Age less thanNumber of people15316111721183119362040


A
15, 16
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B
17, 18
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C
18, 19
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D
14, 15
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Solution

The correct option is B 17, 18

The given distribution is a cumulative distribution.
The observations (ages) are in order.
The first 3 observations (people) have age less than 15.
From 4th to 11th observations ages are less than 16 but not less than 15. Since all ages are integral numbers in years, all observations from 4th to 11th observations will have age as 15. Thus the age of 4th observation is 15.

Using the same idea as above, all observations numbered from 22 to 31 have age as 17. Thus the 27th observation is 17 years old. Similarly, the 32nd observation has age equal to 18.


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