Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 3203 of 473
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If the S.D. of x\displaystyle x is 4\displaystyle 4, what is the variance of (5−2x)\displaystyle (5 - 2x)?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $64$

All Options:

  • A$64$
  • B$36$
  • C$16$
  • DNone of these

Detailed Solution & Explanation

**Given:** SD(x)=4\displaystyle SD(x) = 4, so Var(x)=16\displaystyle Var\displaystyle \text{Var}(x) = 16 **Find:** Var(5−2x)\displaystyle Var\displaystyle \text{Var}(5 - 2x) **Using the property:** Var(a+bx)=b2⋅Var(x)\displaystyle Var\displaystyle \text{Var}(a + bx) = b^2 ⋅\displaystyle \cdot Var\displaystyle \text{Var}(x) Here a=5\displaystyle a = 5, b=−2\displaystyle b = -2: Var(5−2x)=(−2)2⋅Var(x)=4×16=64Var\displaystyle \text{Var}(5 - 2x) = (-2)^2 ⋅\displaystyle \cdot Var\displaystyle \text{Var}(x) = 4 ×\displaystyle \times 16 = 64 So Var(5−2x)=64\displaystyle Var\displaystyle \text{Var}(5-2x) = 64 (Option A). The given `correct_option` 'd' (None of these) is incorrect since Option A (64) is the correct answer. Hence, **Option A** 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.

Related Comparison Tables

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