Question

In the given frequency distribution, which is the median age?
$\begin{array}{cc}\text{Age in years}& \text{Number of people}\\ 15& 3\\ 16& 8\\ 17& 10\\ 18& 10\\ 19& 5\\ 20& 4\end{array}$

• A. 18 years
• B. 17 years
• C. 19 years
• D. 20 years

Answer 1

The correct option is B

17 years

$\begin{array}{ccc}\text{Age in years}& \text{Number of people}& \text{Cumulative frequency}\\ 15& 3& 3\\ 16& 8& 11\\ 17& 10& 21\\ 18& 10& 31\\ 19& 5& 36\\ 20& 4& 40\end{array}$
The total number of people is 40.
Since it is an even number,
there will be two median terms :
$(\frac{n}{2}{)}^{th}=\frac{40}{2}=20$ and ​$(\frac{n}{2}+1=\frac{40}{2}+1)={21}^{st}$ terms.
The median age will be the average of the two terms.

$(20{)}^{th}$ term = 17 and $(21{)}^{st}$ = 17.

So, the median = $\frac{17+17}{2}=17$

Hence, the median age is 17 years.