Question

Assertion (A) : Median of a data is the value of \(\frac{N}{2}\), where N represents sum of all frequencies.
Reason (R) : Median divides the whole distribution in two equal parts.

• A. Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

In Assertion-Reason questions, if you can clearly identify that the Assertion is false, you can immediately choose option (D) without spending much time analyzing the reason in depth.
This is a highly reliable shortcut because standard formats only have one option where the assertion is false!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This is an Assertion-Reason style question from the topic Statistics, focusing on the definition and concept of the "Median".
We need to verify the truth of the statements regarding what the median represents and how it is computed.

Step 2: Key Formula or Approach:
1. Median: The median of a distribution is the value of the middle-most observation when the data is arranged in ascending or descending order. It divides the total frequency into two equal halves.
2. Calculation: For a grouped frequency distribution, \(\frac{N}{2}\) is used to locate the cumulative frequency corresponding to the median class, but the median value itself is given by the formula: \[ \text{Median} = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \times h \] Thus, the median is not simply equal to the value of \(\frac{N}{2}\).

Step 3: Detailed Explanation:
1. Analyze the Assertion (A):
- The assertion states that the median of a data is the value of \(\frac{N}{2}\).
- This is incorrect. The value \(\frac{N}{2}\) represents the half-way point of the total frequency count. It is a tool used to find the position of the median, but it is not the value of the median itself.
- For example, if we have observations with a total frequency \(N = 100\), \(\frac{N}{2} = 50\). The median is the value of the \(50^{\text{th}}\) observation, not the number 50 itself.
- Thus, Assertion (A) is false.
2. Analyze the Reason (R):
- The reason states that the median divides the whole distribution into two equal parts.
- By definition, the median is the central value of a data set. Fifty percent of the observations lie below the median, and fifty percent of the observations lie above the median.
- Thus, Reason (R) is true.

Step 4: Final Answer:
Since Assertion (A) is false but Reason (R) is true, the correct choice is option (D).
Therefore, the correct option is (D).