Question

Find the median of the following data:$$\begin{array}{cccccccc}\text{Class interval}& 25-35& 35-45& 45-55& 55-65& 65-75& 75-85& 85-95\\ \text{Frequency}& 12& 16& 17& 15& 8& 19& 13\end{array}$$

• A. 58.33
• B. 54.3
• C. 32.33
• D. 51.67

Answer 1

The correct option is A 58.33

$$\begin{array}{ccc}\text{Class Interval}& \text{Frequency}& \text{Cumulative}\\ & & Frequency\\ 25-35& 12& 12\\ 35-45& 16& 28\\ 45-55& 17& 45\\ 55-65& 15& 60\\ 65-75& 8& 68\\ 75-85& 19& 87\\ 85-95& 13& 100\end{array}$$

In the above distribution the total number of observations is 100.
Hence, n = 100.

$\frac{n}{2}=50$.

The cumulative frequency that is greater than 50 but closest to 50 is 60. The class corresponding to this frequency is 55 - 65. This is the median class.

$\text{Median}=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
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.

$\therefore Median=55+\frac{50-45}{15}\times 10=58.33$