Measures of Central Tendency and DispersionMCQMTP May 18Question 3158 of 473
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The SD is independent of change of

Options

AOrigin
BScale
CBoth (a) & (b)
DNone of these
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Correct Answer

✅ Option a — Origin

All Options:

  • AOrigin
  • BScale
  • CBoth (a) & (b)
  • DNone of these

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Detailed Solution & Explanation

**Properties of Standard Deviation:** 1. **Change of Origin (adding/subtracting a constant):** SD is INDEPENDENT of change of origin. If xi′=xi+c\displaystyle x_i' = x_i + c, then σx′=σx\displaystyle \sigma_{x'} = \sigma_x. 2. **Change of Scale (multiplying/dividing by a constant):** SD is NOT independent of change of scale. If xi′=kxi\displaystyle x_i' = kx_i, then σx′=∣k∣σx\displaystyle \sigma_{x'} = |k|\sigma_x. **Therefore:** SD is independent only of change of **origin**, not of scale. The given `correct_option` is 'b' (Scale), which is WRONG because SD is actually AFFECTED by change of scale. SD is independent of change of **origin** (Option A). Hence, **Option A** 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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