Measures of Central Tendency and DispersionMCQMTP Nov 21Question 3178 of 473
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If all the observations are decreased by 4, find the relation between new SD and old SD.

Options

ANew SD = Old SD/2
BNew SD = Old SD - 2
CNew SD = Old SD - 4
DRemains unchanged
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Correct Answer

✅ Option d — Remains unchanged

All Options:

  • ANew SD = Old SD/2
  • BNew SD = Old SD - 2
  • CNew SD = Old SD - 4
  • DRemains unchanged

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Detailed Solution & Explanation

**Concept:** SD is independent of change of origin. Subtracting a constant from all observations does NOT change the SD. **Proof:** If xi′=xi−4\displaystyle x_i' = x_i - 4, then xˉ′=xˉ−4\displaystyle \bar{x}' = \bar{x} - 4. xi′−xˉ′=(xi−4)−(xˉ−4)=xi−xˉx_i' - \bar{x}' = (x_i - 4) - (\bar{x} - 4) = x_i - \bar{x} Deviations unchanged ⇒\displaystyle \Rightarrow Variance unchanged ⇒\displaystyle \Rightarrow SD unchanged. **New SD = Old SD** (Remains unchanged). The given `correct_option` 'b' (New SD = Old SD - 2) is incorrect. Hence, **Option D** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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