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

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

Step 3: Compute 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 first class with a cumulative frequency greater than or equal to the median position (40). The cumulative frequency 42 is the first one greater than 40, corresponding to the class interval 15-20.