Question

Find the median of the following data:
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 23& 2\\ 45& 3\\ 49& 5\\ 53& 16\\ 60& 14\\ 67& 13\\ 70& 7\end{array}$$

• A. 53
• B. 60
• C. 49
• D. 51

Answer 1

The correct option is B 60

$\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{median}\mathrm{we}\mathrm{must}\mathrm{first}\mathrm{find}\mathrm{the}\mathrm{cumulative}\mathrm{frequency},\mathrm{then}\mathrm{look}\mathrm{where}\mathrm{the}\mathrm{middle}\mathrm{most}\mathrm{term}\mathrm{lies}.\mathrm{The}\mathrm{corresponding}\mathrm{value}\mathrm{is}\mathrm{the}\mathrm{median}.$
$$\begin{array}{ccc}\text{Value}& \text{Frequency}& \text{cf}\\ 23& 2& 2\\ 45& 3& 5\\ 49& 5& 10\\ 53& 16& 26\\ 60& 14& 40\\ 67& 13& 53\\ 70& 7& 60\end{array}$$
The ${30}^{th}$ and ${31}^{th}$ term lies between ${26}^{th}$ and ${40}^{th}$ term and is 60 as can be seen from the table. Median is average of ${30}^{th}$ and ${31}^{th}$ terms that is 60.