Question

Median class of the following frequency distribution will be: 
\[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 0-10 & 7 \\ \hline 10-20 & 12 \\ \hline 20-30 & 18 \\ \hline 30-40 & 15 \\ \hline 40-50 & 10 \\ \hline 50-60 & 3 \\ \hline \end{array} \]

• A. 20-30
• B. 30-40
• C. 40-50
• D. 10-20

Hint:

To find the median class, always check $\tfrac{N}{2}$ against cumulative frequencies. The class where it lies is the median class.

Answer 1

The Correct Option is A

 

Step 1: Find total frequency ($N$) 
\[ N = 7 + 12 + 18 + 15 + 10 + 3 = 65 \]

Step 2: Find $\tfrac{N{2}$} 
\[ \frac{N}{2} = \frac{65}{2} = 32.5 \]

Step 3: Construct cumulative frequency (CF) 
\[ \begin{array}{|c|c|c|} \hline \text{Class Interval} & \text{Frequency} & \text{Cumulative Frequency} \\ \hline 0-10 & 7 & 7 \\ \hline 10-20 & 12 & 19 \\ \hline 20-30 & 18 & 37 \\ \hline 30-40 & 15 & 52 \\ \hline 40-50 & 10 & 62 \\ \hline 50-60 & 3 & 65 \\ \hline \end{array} \]

Step 4: Identify median class 
- The median class is the class interval where the cumulative frequency first becomes $\geq 32.5$. 
- Here, CF = 37 for class $20$-$30$. 
Thus, the median class is $20$-$30$. 
 

Step 5: Conclusion 
Therefore, the median class is $20$-$30$. 
The correct answer is option (A).