Q1. [1] § STATISTICS § 13.2 Mean of Grouped Data § 13.4 Median of Grouped Data
Assertion (A) : The mean of first 'n' natural numbers is $\frac{n-1}{2}$.
Reason (R): The sum of first 'n' natural numbers is $\frac{n(n+1)}{2}$.
Select the correct answer from the options (A), (B), (C) and (D).
- 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.
Previously asked in CBSE board exam
2026 30/2/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
(D) Assertion (A) is false, but Reason (R) is true.
The sum of first n natural numbers is $\frac{n(n+1)}{2}$ (R is true), so Mean $= \frac{n(n+1)/2}{n} = \frac{n+1}{2}$, not $\frac{n-1}{2}$. Hence A is false.
Explanation
- R is true: The standard formula $1+2+\cdots+n = \frac{n(n+1)}{2}$ is correct.
- A is false: Dividing the sum by n gives mean $= \frac{n+1}{2}$, not $\frac{n-1}{2}$ (e.g., mean of 1, 2, 3 is 2 = $\frac{3+1}{2}$, not $\frac{3-1}{2} = 1$).
- In Assertion–Reason questions, always verify A independently before checking if R explains it.
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