Question

Calculate the median for the following frequency distribution.

$$\begin{array}{cccccccc}Class& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ f_i& 6& 8& 20& 25& 15& 10& 4\end{array}$$

• A. 34.2
• B. 32.4
• C. 32
• D. 34

Answer 1

The correct option is D 34

$$\begin{array}{cccccccc}ClassInterval& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ Frequency\left(f_i\right)& 6& 8& 20& 25& 15& 10& 4\\ CumulativeFrequency& 6& 14& 34& 59& 74& 84& 88\end{array}$$
In the above distribution the total number of observations is 88. Hence, n = 88.

$\frac{n}{2}=44$.

The cumulative frequency that is greater than 44 but closest to 44 is 59. The class corresponding to this frequency is 30-40. 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 the 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.

$⟹Median=30+\frac{44-34}{25}\times 10$
$\therefore Median=34$