Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 3088 of 473
All Questions

Which of the following is a correct statement?

Options

ARange is unaffected by the change in origin or change in scale
BRange is affected by the change in origin or change in scale
CRange is unaffected by the change in origin but affected by change in scale
DRange is affected by the change in origin but unaffected by change in scale
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Correct Answer

✅ Option c — Range is unaffected by the change in origin but affected by change in scale

All Options:

  • ARange is unaffected by the change in origin or change in scale
  • BRange is affected by the change in origin or change in scale
  • CRange is unaffected by the change in origin but affected by change in scale
  • DRange is affected by the change in origin but unaffected by change in scale

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Detailed Solution & Explanation

A fundamental property of the measures of dispersion (such as Range, Mean Deviation, Quartile Deviation, and Standard Deviation) is that they are independent of change of origin but dependent on change of scale. This means that if a constant is added or subtracted from all observations, the measures of dispersion remain unaffected. However, if all observations are multiplied or divided by a constant, the measures of dispersion are also multiplied by the absolute value of that constant. Hence, **Option C** 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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