Identify the median class for the following grouped data:
\[\begin{array}{|c|c|} \hline \textbf{Class interval} & \textbf{Frequency} \\ \hline 5-10 & 5 \\ 10-15 & 15 \\ 15-20 & 22 \\ 20-25 & 25 \\ 25-30 & 10 \\ 30-35 & 3 \\ \hline \end{array}\]
Identify the median class for the following grouped data:
\[\begin{array}{|c|c|} \hline \textbf{Class interval} & \textbf{Frequency} \\ \hline 5-10 & 5 \\ 10-15 & 15 \\ 15-20 & 22 \\ 20-25 & 25 \\ 25-30 & 10 \\ 30-35 & 3 \\ \hline \end{array}\]
Show Hint
- 20-25
- 25-30
- 5-10
- 15-20
The Correct Option is D
Solution and Explanation
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.
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