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: Evaluate Assertion (A).
Assertion A states: Median of data is the value of \(\frac{N}{2}\), where N is the sum of all frequencies. This is INCORRECT. \(\frac{N}{2}\) is the cumulative frequency threshold used to locate the median class, not the median value itself. Assertion A is FALSE.
Step 2: Evaluate Reason (R).
Reason R states: Median divides the whole distribution in two equal parts. This is the correct definition of the median. Reason R is TRUE.
Step 3: Match with the options.
We need the option where A is false but R is true.
Step 4: Identify option 4.
Option 4 says: Assertion (A) is false, but Reason (R) is true. This matches our findings.
Step 5: Confirm by reviewing the median formula.
The actual median formula for grouped data is \(M = l + \frac{\frac{N}{2} - cf}{f} \times h\). Here \(\frac{N}{2}\) is only a step in the calculation, not the median itself.
Step 6: Select the correct option.
Option 4 is correct.
\[ \boxed{\text{Assertion (A) is false, but Reason (R) is true.}} \]