Question

Identify the median class for the following grouped data:

\[\begin{array}{|c|c|} \hline \textbf{Class interval} & \textbf{Frequency} \\ \hline 5-10 & 5 \\ 10-15 & 15 \\ 15-20 & 22 \\ 20-25 & 25 \\ 25-30 & 10 \\ 30-35 & 3 \\ \hline \end{array}\]
 

• A. 20-25
• B. 25-30
• C. 5-10
• D. 15-20

Hint:

To find the median class: 1. Find the total frequency, N. 2. Calculate the median position, N/2. 3. Compute the cumulative frequencies. 4. The median class is the first class where the cumulative frequency is \(\ge\) N/2.

Answer 1

The Correct Option is D

Step 1: Calculate the total frequency (N). \[ N = 5 + 15 + 22 + 25 + 10 + 3 = 80 \]

Step 2: Find the position of the median. The median is the value at the \( N/2 \)-th position. \[ \text{Median Position} = \frac{80}{2} = 40 \]

Step 3: Calculate the cumulative frequency (CF) for each class.

\[\begin{array}{|c|c|c|} \hline \text{Class interval} & \text{Frequency (f)} & \text{Cumulative Frequency (CF)} \\ \hline 5-10 & 5 & 5 \\ 10-15 & 15 & 20 \\ 15-20 & 22 & 42 \\ 20-25 & 25 & 67 \\ 25-30 & 10 & 77 \\ 30-35 & 3 & 80 \\ \hline \end{array}\]
 

Step 4: Identify the median class. The median class is the class whose cumulative frequency is the first to be greater than or equal to the median position (40). The cumulative frequency 42 is the first one greater than 40. The corresponding class interval is 15-20.