Question

The upper limit of the median class of the above data is :

• A. 10
• B. 20
• C. 30
• D. 40

Hint:

Always double-check your cumulative frequency sum against the total frequency to ensure no arithmetic errors were made during addition.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The median class is the class interval whose cumulative frequency is just greater than or equal to \(N/2\), where \(N\) is the total frequency.
Step 2: Key Formula or Approach:
1. Find total frequency \(N = \sum f\).
2. Calculate cumulative frequencies (cf).
3. Identify the class corresponding to \(cf \geq N/2\).
Step 3: Detailed Explanation:
1. Calculate Cumulative Frequency:
- 0-10: 3
- 10-20: 3 + 5 = 8
- 20-30: 8 + 7 = 15
- 30-40: 15 + 9 = 24
- 40-50: 24 + 11 = 35
2. Find \(N/2\): Total \(N = 35\), so \(N/2 = 17.5\).
3. Identify Median Class: The cumulative frequency just greater than 17.5 is 24, which corresponds to the class 30-40.
4. Identify Upper Limit: For the class 30-40, the upper limit is 40.
Step 4: Final Answer:
The upper limit of the median class is 40.