If the variance of random variable ' x ' is 17, then what is variance of y = 2x+5 ?

Option c: 68. Solution: Given: Var(x) = 17 Find: Var(y) where y = 2x + 5 Key Property of Variance: For a linear transformation y = a + bx : Var(y) = b2 × Var(x) The additive constant a does NOT affect variance. Step 1: Identify b = 2 (the multiplier of x ). Step 2: Apply the formula. Var(2x + 5) = (2)2 × Var(x) = 4 × 17 = 68 Hence, Option C is the correct answer.

If the variance of random variable '$x$' is 17, then what is variance of $y = 2x+5$?

The correct answer is Option c: $68$. **Given:** $\text{Var}(x) = 17$ **Find:** $\text{Var}(y)$ where $y = 2x + 5$ **Key Property of Variance:** For a linear transformation $y = a + bx$: $$\text{Var}(y) = b^2 \cdot \text{Var}(x)$$ The additive constant $a$ does NOT affect variance. **Step 1:** Identify $b = 2$ (the multiplier of $x$). **Step 2:** Apply the formula. $$\text{Var}(2x + 5) = (2)^2 \cdot \text{Var}(x) = 4 \times 17 = 68$$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Dec 22Question 3139 of 473

All Questions

If the variance of random variable ' $\displaystyle x$ ' is 17, then what is variance of $\displaystyle y = 2x+5$ ?

Options

\displaystyle 34

\displaystyle 39

\displaystyle 68

\displaystyle 78

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Correct Answer

✅ Option c — $\displaystyle 68$

All Options:

A $\displaystyle 34$
B $\displaystyle 39$
C $\displaystyle 68$
D $\displaystyle 78$

Detailed Solution & Explanation

**Given:**

\displaystyle \text{Var}(x) = 17

**Find:**

\displaystyle \text{Var}(y)

where

\displaystyle y = 2x + 5

**Key Property of Variance:** For a linear transformation

\displaystyle y = a + bx

\text{Var}(y) = b^2 \cdot \text{Var}(x)

The additive constant

\displaystyle a

does NOT affect variance. **Step 1:** Identify

\displaystyle b = 2

(the multiplier of

\displaystyle x

). **Step 2:** Apply the formula.

\text{Var}(2x + 5) = (2)^2 \cdot \text{Var}(x) = 4 \times 17 = 68

Hence, **Option C** 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 variance of random variable 'x\displaystyle xx' is 17, then what is variance of y=2x+5\displaystyle y = 2x+5y=2x+5?