AM and Coefficient of variation of x is 10 and 40. What is the variance 30-2x ?

Option a: 64. Solution: Given: AM of x = 10, CV of x = 40 Step 1: Find SD of x . CV = sigmax/x × 100 40 = sigmax/10 × 100 sigmax = 40 × 10/100 = 4 Step 2: Find variance of x . Var(x) = sigmax2 = 16 Step 3: Find variance of y = 30 - 2x . Using the property: Var(a + bx) = b2 × Var(x) (the constant a does not affect variance). Here a = 30 , b = -2 : Var(30 - 2x) = (-2)2 × Var(x) = 4 × 16 = 64 Hence, Option A is the correct answer.

AM and Coefficient of variation of $x$ is 10 and 40. What is the variance $30-2x$?

The correct answer is Option a: $64$. **Given:** AM of $x$ = 10, CV of $x$ = 40 **Step 1: Find SD of $x$.** $$CV = \frac{\sigma_x}{\bar{x}} \times 100$$ $$40 = \frac{\sigma_x}{10} \times 100$$ $$\sigma_x = \frac{40 \times 10}{100} = 4$$ **Step 2: Find variance of $x$.** $$\text{Var}(x) = \sigma_x^2 = 16$$ **Step 3: Find variance of $y = 30 - 2x$.** Using the property: $\text{Var}(a + bx) = b^2 \cdot \text{Var}(x)$ (the constant $a$ does not affect variance). Here $a = 30$, $b = -2$: $$\text{Var}(30 - 2x) = (-2)^2 \cdot \text{Var}(x) = 4 \times 16 = 64$$ Hence, **Option A** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ June 22Question 3134 of 473

All Questions

AM and Coefficient of variation of $\displaystyle x$ is 10 and 40. What is the variance $\displaystyle 30-2x$ ?

Options

\displaystyle 64

\displaystyle 56

\displaystyle 49

\displaystyle 81

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

Correct Answer

✅ Option a — $\displaystyle 64$

All Options:

A $\displaystyle 64$
B $\displaystyle 56$
C $\displaystyle 49$
D $\displaystyle 81$

Detailed Solution & Explanation

**Given:** AM of

\displaystyle x

= 10, CV of

\displaystyle x

= 40 **Step 1: Find SD of

\displaystyle x

.**

CV = \frac{\sigma_x}{\bar{x}} \times 100

40 = \frac{\sigma_x}{10} \times 100

\sigma_x = \frac{40 \times 10}{100} = 4

**Step 2: Find variance of

\displaystyle x

.**

\text{Var}(x) = \sigma_x^2 = 16

**Step 3: Find variance of

\displaystyle y = 30 - 2x

.** Using the property:

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

(the constant

\displaystyle a

does not affect variance). Here

\displaystyle a = 30

\displaystyle b = -2

\text{Var}(30 - 2x) = (-2)^2 \cdot \text{Var}(x) = 4 \times 16 = 64

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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AM and Coefficient of variation of x\displaystyle xx is 10 and 40. What is the variance 30−2x\displaystyle 30-2x30−2x?