Q1. [1] § 13.2 Mean of Grouped Data
If the value of each observation of a statistical data is increased by 3, then the mean of the data
- A remains unchanged
- B increases by 3
- C increases by 6
- D increases by 3n
Previously asked in CBSE board exam
2023 30/1/1 Q15
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
Option B: increases by 3
If each observation $x_i$ is increased by 3, the new mean $= \dfrac{\Sigma(x_i+3)}{n} = \dfrac{\Sigma x_i + 3n}{n} = \bar{x} + 3$.
Explanation
The mean is the sum of all observations divided by $n$. Adding 3 to every observation adds $3n$ to the total sum; dividing by $n$ gives an increase of exactly 3 in the mean. Options A, C, D are wrong because the mean does change, it changes by 3 (not 6 or 3n). This is a standard property of mean tested frequently in MCQs.
If a question refers to an image, map, graph or diagram that is not shown here, find the actual CBSE question paper on the CBSE website:
cbse.gov.in.