Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 3202 of 473
All Questions

If the same amount is added or subtracted from all the of the 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:** Both SD and Variance are measures of spread/dispersion around the mean. They measure how far data points deviate from the mean. **When a constant is added/subtracted from all observations:** - Each observation shifts by the same constant c\displaystyle c - The mean also shifts by c\displaystyle c - The deviation of each observation from the mean (xi−xˉ)\displaystyle (x_i - \bar{x}) remains **unchanged** - Therefore, Variance =∑(xi−xˉ)2n\displaystyle = \frac{\sum(x_i - \bar{x})^2}{n} remains **unchanged** - And SD =Variance\displaystyle = \sqrt{\text{Variance}} also remains **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.

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