Question

The median for the following data is _____.

$$\begin{array}{ccccc}\text{Class interval}& 0-10& 10-20& 20-30& 30-40\\ \text{Frequency}& 7& 15& 16& 12\end{array}$$

• A. 25
• B. 21.875
• C. 20
• D. 22.5

Answer 1

The correct option is B 21.875

$$\begin{array}{ccc}\text{Class Interval}& \text{Frequency}& \text{Cumulative Frequency}\\ 0-10& 7& 7\\ 10-20& 15& 22\\ 20-30& 16& 38\\ 30-40& 12& 50\end{array}$$

In the above distribution the total number of observations is 50. Hence, n = 50.

$\therefore \frac{n}{2}=25$.

The cumulative frequency that is greater than 25 but closest to 25 is 38. The class corresponding to this frequency is 20 - 30.
This is the median class.

Using Median = $l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
Where $l$ is lower class limit of median class.
$n$ is total number of observations.
$cf$ is the cumulative frequency of the class preceding the median class.
$f$ is the frequency of the median class and h is the class size.
$\therefore Median=20+\frac{25-22}{16}\times 10=21.875$