If the variance of random variable ' x ' is 18 , then what is variance of y = 2x + 5 ?

Option d: 72. Solution: Given: Var(x) = 18 Find: Var(y) where y = 2x + 5 Using the property: Var(a + bx) = b2 × Var(x) Here a = 5 , b = 2 : Var(2x + 5) = (2)2 × 18 = 4 × 18 = 72 So Var(y) = 72 (Option D). The given correctoption 'b' (39) is incorrect. Hence, Option D is the correct answer.

If the variance of random variable '$x$' is $18$, then what is variance of $y = 2x + 5$?

The correct answer is Option d: $72$. **Given:** $\text{Var}(x) = 18$ **Find:** $\text{Var}(y)$ where $y = 2x + 5$ **Using the property:** $\text{Var}(a + bx) = b^2 \cdot \text{Var}(x)$ Here $a = 5$, $b = 2$: $$\text{Var}(2x + 5) = (2)^2 \times 18 = 4 \times 18 = 72$$ So $\text{Var}(y) = 72$ (Option D). The given `correct_option` 'b' (39) is incorrect. Hence, **Option D** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 3197 of 473

All Questions

If the variance of random variable ' $\displaystyle x$ ' is $\displaystyle 18$ , then what is variance of $\displaystyle y = 2x + 5$ ?

Options

\displaystyle 34

\displaystyle 39

\displaystyle 68

\displaystyle 72

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

Correct Answer

✅ Option d — $\displaystyle 72$

All Options:

A $\displaystyle 34$
B $\displaystyle 39$
C $\displaystyle 68$
D $\displaystyle 72$

Detailed Solution & Explanation

**Given:**

\displaystyle \text{Var}(x) = 18

**Find:**

\displaystyle \text{Var}(y)

where

\displaystyle y = 2x + 5

**Using the property:**

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

Here

\displaystyle a = 5

\displaystyle b = 2

\text{Var}(2x + 5) = (2)^2 \times 18 = 4 \times 18 = 72

\displaystyle \text{Var}(y) = 72

(Option D). The given `correct_option` 'b' (39) is incorrect. 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

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

Mean vs Median vs Mode: Measures of Central Tendency Fiscal Policy vs Monetary Policy: CA Foundation Economics

Ready to Master Measures of Central Tendency and Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

If the variance of random variable 'x\displaystyle xx' is 18\displaystyle 1818, then what is variance of y=2x+5\displaystyle y = 2x + 5y=2x+5?