Question

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

$$\begin{array}{cc}Agelessthan& Numberofpeople\\ 15& 3\\ 16& 11\\ 17& 21\\ 18& 31\\ 19& 36\\ 20& 40\end{array}$$

• A. 15, 16
• B. 16, 17
• C. 18, 19
• D. 14,15

Answer 1

The correct option is B

16, 17

The given distribution is a cumulative distribution. What does this mean? For example let us ask what the $4^{th}$ observation is. The observations (ages) are in order. The first 3 observations (people) have age less than 15. From $4^{th}$ to ${11}^{th}$ observations ages are less than 16 but not less than 15. Since all ages are integral numbers in years, all observations from $4^{th}$ to ${11}^{th}$ observations will have age as 15. Thus, age of $4^{th}$ observation is 15.

Using the same idea as above, all observations numbered from 21 to 30 have an age of 16. Thus the ${27}^{th}$ observation has age 16.

Similarly, the ${32}^{nd}$ observation has age equal to 17.