If the S.D. of x is 4 , what is the variance of (5 - 2x) ?

Option a: 64. Solution: Given: SD(x) = 4 , so Var(x) = 16 Find: Var(5 - 2x) Using the property: Var(a + bx) = b2 × Var(x) Here a = 5 , b = -2 : Var(5 - 2x) = (-2)2 × Var(x) = 4 × 16 = 64 So Var(5-2x) = 64 (Option A). The given correctoption 'd' (None of these) is incorrect since Option A (64) is the correct answer. Hence, Option A is the correct answer.

If the S.D. of $x$ is $4$, what is the variance of $(5 - 2x)$?

The correct answer is Option a: $64$. **Given:** $SD(x) = 4$, so $\text{Var}(x) = 16$ **Find:** $\text{Var}(5 - 2x)$ **Using the property:** $\text{Var}(a + bx) = b^2 \cdot \text{Var}(x)$ Here $a = 5$, $b = -2$: $$\text{Var}(5 - 2x) = (-2)^2 \cdot \text{Var}(x) = 4 \times 16 = 64$$ So $\text{Var}(5-2x) = 64$ (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.

Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 3203 of 473

All Questions

If the S.D. of $\displaystyle x$ is $\displaystyle 4$ , what is the variance of $\displaystyle (5 - 2x)$ ?

Options

\displaystyle 64

\displaystyle 36

\displaystyle 16

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle 64$

All Options:

A $\displaystyle 64$
B $\displaystyle 36$
C $\displaystyle 16$
DNone of these

Detailed Solution & Explanation

**Given:**

\displaystyle SD(x) = 4

, so

\displaystyle \text{Var}(x) = 16

**Find:**

\displaystyle \text{Var}(5 - 2x)

**Using the property:**

\displaystyle \text{Var}(a + bx) = b^2 \cdot \text{Var}(x)

Here

\displaystyle a = 5

\displaystyle b = -2

\text{Var}(5 - 2x) = (-2)^2 \cdot \text{Var}(x) = 4 \times 16 = 64

\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.

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If the S.D. of x\displaystyle xx is 4\displaystyle 44, what is the variance of (5−2x)\displaystyle (5 - 2x)(5−2x)?