Measures of Central Tendency and DispersionMCQPYQ Nov. 19Question 3123 of 473
All Questions

Origin is shifted by 5\displaystyle 5, what will happen

Options

ASD will increase by 5\displaystyle 5
BQD will increase by 5\displaystyle 5
CMD will increase by 5\displaystyle 5
DThere will be no change in SD
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Correct Answer

✅ Option d — There will be no change in SD

All Options:

  • ASD will increase by 5\displaystyle 5
  • BQD will increase by 5\displaystyle 5
  • CMD will increase by 5\displaystyle 5
  • DThere will be no change in SD

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Detailed Solution & Explanation

A shift of origin occurs when a constant is added to or subtracted from every observation in a dataset. Measures of dispersion (such as Standard Deviation, Mean Deviation, and Quartile Deviation) are completely independent of change of origin. Therefore, if the origin is shifted by 5\displaystyle 5, there will be no change in the value of the standard deviation. 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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