Q1. [1] § 13.2 Mean of Grouped Data
If every term of the statistical data consisting of $n$ terms is decreased by 2, then the mean of the data :
- (a) decreases by 2
- (b) remains unchanged
- (c) decreases by $2n$
- (d) decreases by 1
Previously asked in CBSE board exam
2023 30/5/1 Q18
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
(a) decreases by 2
When every term is decreased by 2, the new mean = old mean − 2, so the mean also decreases by 2.
Explanation
If original mean is $\bar{x} = \dfrac{\sum x_i}{n}$, and each term becomes $(x_i - 2)$, new mean $= \dfrac{\sum(x_i-2)}{n} = \bar{x} - 2$. The mean shifts by exactly the same constant subtracted from every term. Examiners expect you to state the correct option and give a one-line reason.
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