Measures of Central Tendency and DispersionMCQPYQ July 21Question 3095 of 473
All Questions

If every observation is increased by 7\displaystyle 7 then:

Options

AStandard deviation increased by 7\displaystyle 7
BMean deviation increased by 7\displaystyle 7
CNot affected at all
DQuartile deviation increased by 7\displaystyle 7.
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Correct Answer

✅ Option c — Not affected at all

All Options:

  • AStandard deviation increased by 7\displaystyle 7
  • BMean deviation increased by 7\displaystyle 7
  • CNot affected at all
  • DQuartile deviation increased by 7\displaystyle 7.

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Detailed Solution & Explanation

Measures of dispersion (such as Standard Deviation, Mean Deviation, Quartile Deviation, and Range) are independent of change of origin. This means that if a constant is added to or subtracted from every observation in a dataset, the value of these measures of dispersion remains completely unaffected. Therefore, increasing every observation by 7\displaystyle 7 will not affect the dispersion measures. 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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