Measures of Central Tendency and DispersionMCQMTP June 24 Series IQuestion 3206 of 473
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Suppose a population A has 100\displaystyle 100 observations 101,102,103,...,200\displaystyle 101, 102, 103, ..., 200 and another population B has 100\displaystyle 100 observations 151,152,153,...,250\displaystyle 151, 152, 153, ..., 250. If VA\displaystyle V_A and VB\displaystyle V_B represents the variance of the two populations respectively, then VA/VB\displaystyle V_A / V_B ______.

Options

A94\displaystyle \frac{9}{4}
B1\displaystyle 1
C49\displaystyle \frac{4}{9}
D23\displaystyle \frac{2}{3}
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Correct Answer

✅ Option b — 1\displaystyle 1

All Options:

  • A94\displaystyle \frac{9}{4}
  • B1\displaystyle 1
  • C49\displaystyle \frac{4}{9}
  • D23\displaystyle \frac{2}{3}

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Detailed Solution & Explanation

**Key Observation:** - Population A: 101, 102, ..., 200 — These are 100 consecutive integers. - Population B: 151, 152, ..., 250 — These are also 100 consecutive integers. Population B is obtained by adding 50 to each element of Population A: bi=ai+50b_i = a_i + 50 **Effect on Variance:** Adding a constant to every observation does NOT change the variance. Variance is independent of change of origin. VA=VBV_A = V_B **Therefore:** VAVB=1\frac{V_A}{V_B} = 1 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

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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