Measures of Central Tendency and DispersionMCQMTP Sep 24 Series IQuestion 3214 of 473
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If the same amount is added or subtracted from all the of an individual series then the standard deviation and variance both shall be

Options

AChanged
BUnchanged
CSame
DNone of these
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Correct Answer

✅ Option b — Unchanged

All Options:

  • AChanged
  • BUnchanged
  • CSame
  • DNone of these

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Detailed Solution & Explanation

**Concept:** Adding or subtracting a constant from all observations changes the **origin** of the data but does NOT change the spread. **Proof:** If xi′=xi±c\displaystyle x_i' = x_i \pm c, then xˉ′=xˉ±c\displaystyle \bar{x}' = \bar{x} \pm c. - Deviation: xi′−xˉ′=(xi±c)−(xˉ±c)=xi−xˉ\displaystyle x_i' - \bar{x}' = (x_i \pm c) - (\bar{x} \pm c) = x_i - \bar{x} (unchanged) - Variance: σ′2=∑(xi−xˉ)2n=σ2\displaystyle \sigma'^2 = \frac{\sum(x_i - \bar{x})^2}{n} = \sigma^2 (unchanged) - SD: σ′=σ\displaystyle \sigma' = \sigma (unchanged) **Both SD and Variance remain Unchanged.** Hence, **Option B** 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.

Variance

A measure of dispersion equal to the average of the squared deviations of each data point from the mean. Formula: σ² = Σ(xᵢ − x̄)² / n. Standard Deviation = √Variance.

Related Comparison Tables

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