Measures of Central Tendency and DispersionMCQMTP Nov 21Question 3180 of 473
All Questions

Find the variance of 3x+2\displaystyle 3x+2 if standard deviation of x\displaystyle x is 4

Options

A9
B160
C16
D144
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Correct Answer

✅ Option d — 144

All Options:

  • A9
  • B160
  • C16
  • D144

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Detailed Solution & Explanation

**Given:** SD(x)=4\displaystyle SD(x) = 4, so Var(x)=42=16\displaystyle \text{Var}(x) = 4^2 = 16 **Find:** Var(3x+2)\displaystyle \text{Var}(3x + 2) **Using the property:** Var(a+bx)=b2⋅Var(x)\displaystyle \text{Var}(a + bx) = b^2 \cdot \text{Var}(x) Here a=2\displaystyle a = 2, b=3\displaystyle b = 3: Var(3x+2)=(3)2⋅Var(x)=9×16=144\text{Var}(3x + 2) = (3)^2 \cdot \text{Var}(x) = 9 \times 16 = 144 So Variance = **144** (Option D). The given `correct_option` 'c' (16) is incorrect — that's just Var(x)\displaystyle \text{Var}(x), not Var(3x+2)\displaystyle \text{Var}(3x+2). Hence, **Option D** 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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