Measures of Central Tendency and DispersionMCQMTP May 19 Series IIQuestion 3155 of 473
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If the profits of a company remain 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:** Standard Deviation measures the variability of data from the mean. **Analysis:** If profits remain the same for all 10 months, then all observations are equal (say, each = P\displaystyle P). - Mean xˉ=P\displaystyle \bar{x} = P - Each deviation (xi−xˉ)=P−P=0\displaystyle (x_i - \bar{x}) = P - P = 0 - σ2=∑(xi−xˉ)2n=0\displaystyle \sigma^2 = \frac{\sum(x_i - \bar{x})^2}{n} = 0 - σ=0\displaystyle \sigma = 0 **Key Facts:** - SD is always **non-negative** (σ≥0\displaystyle \sigma \geq 0) - SD can NEVER be negative - When all values are identical, SD = 0 The given `correct_option` is 'b' (Negative), which is **wrong**. SD cannot be negative. The correct answer is **Zero** (Option C). 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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