Measures of Central Tendency and DispersionMCQMTP Apr 21Question 3173 of 473
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If the profits of a company remains the same for the last ten months, then the standard deviation of profits for these ten months would be ?

Options

APositive
BNegative
CZero
DA or C
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Correct Answer

✅ Option c — Zero

All Options:

  • APositive
  • BNegative
  • CZero
  • DA or C

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Detailed Solution & Explanation

**Concept:** SD measures variability. If all values are identical, there is no variability. **Analysis:** If profits are the same P\displaystyle P for all 10 months: - Mean = P\displaystyle P - Each deviation = P−P=0\displaystyle P - P = 0 - σ2=0\displaystyle \sigma^2 = 0, σ=0\displaystyle \sigma = 0 SD is always ≥0\displaystyle \geq 0. So: - It CANNOT be negative (Option B is wrong). - It CAN be positive only if there is variability. - It is ZERO when all values are equal. - Option D (A or C) includes the possibility of being positive, which is wrong here since profits are exactly the same. The correct answer is **Zero** (Option C). The given `correct_option` 'd' (A or C) is misleading — the only correct answer is C (Zero). 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.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

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