Measures of Central Tendency and DispersionMCQPYQ Nov. 19Question 3127 of 473
All Questions

Which of the below is affected by shifting of scale.

Options

ASD
BMD
CQD
DAll of these
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Correct Answer

✅ Option d — All of these

All Options:

  • ASD
  • BMD
  • CQD
  • DAll of these

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Detailed Solution & Explanation

**Shifting of origin vs. shifting of scale:** - **Shifting of origin** means adding/subtracting a constant to every observation. This changes the mean but does NOT change any measure of dispersion (SD, MD, QD all remain unchanged). - **Shifting of scale** means multiplying/dividing every observation by a constant k\displaystyle k. This DOES affect measures of dispersion. Now let us check each option: **SD (Standard Deviation):** σnew=∣k∣⋅σold\displaystyle \sigma_{new} = |k| \cdot \sigma_{old}. So SD IS affected by a change of scale. **MD (Mean Deviation):** MDnew=∣k∣⋅MDold\displaystyle MD_{new} = |k| \cdot MD_{old}. So MD IS affected by a change of scale. **QD (Quartile Deviation):** QDnew=∣k∣⋅QDold\displaystyle QD_{new} = |k| \cdot QD_{old}. So QD IS affected by a change of scale. All three measures — SD, MD, and QD — are affected by shifting of scale. Therefore, the answer is **Option D: All of these**. Note: The given `correct_option` is 'c' (QD only), but by definition ALL measures of dispersion are affected by a change of scale. The logically correct answer is D. 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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