Question

The median class of the following frequency distribution will be: 
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-Interval} & \text{$0$--$10$} & \text{$10$--$20$} & \text{$20$--$30$} & \text{$30$--$40$} & \text{$40$--$50$} \\ \hline \text{Frequency} & \text{$7$} & \text{$8$} & \text{$15$} & \text{$10$} & \text{$5$} \\ \hline \end{array}\]

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

Hint:

For the median class, compute $N/2$ and pick the first class with cumulative frequency $\ge N/2$. No formula is needed to identify the class.

Answer 1

The Correct Option is C

 

Step 1: Total frequency and median position 
Total $N = 7+8+15+10+5 = 45$. Median position $= \dfrac{N}{2} = \dfrac{45}{2} = 22.5$. 
 

Step 2: Cumulative frequencies (c.f.) 
$0$--$10:7$,  $10$--$20:7+8=15$,  $20$--$30:15+15=30$,  $30$--$40:40$,  $40$--$50:45$. 
 

Step 3: Locate the median class 
Find the first class whose c.f. $\ge 22.5$. Here, c.f. just exceeding $22.5$ is $30$ for the class $20$--$30$ $\Rightarrow$ Median class is $20$--$30$. 
\[ \boxed{\text{Median class }=\,20\text{--}30} \]