The arithmetic mean and coefficient of variation of data set x are respectively 10 and 30. The variance of 30-2x is

Option d: 36. Solution: Given: x = 10 , CV = 30 Step 1: Find SD of x . CV = sigmax/x × 100 30 = sigmax/10 × 100 sigmax = 3 Step 2: Find Var( x ). Var(x) = 32 = 9 Step 3: Find Var( 30 - 2x ). Var(30 - 2x) = (-2)2 × Var(x) = 4 × 9 = 36 Hence, Option D is the correct answer.

The arithmetic mean and coefficient of variation of data set $x$ are respectively 10 and 30. The variance of $30-2x$ is

The correct answer is Option d: 36. **Given:** $\bar{x} = 10$, CV = 30 **Step 1: Find SD of $x$.** $$CV = \frac{\sigma_x}{\bar{x}} \times 100$$ $$30 = \frac{\sigma_x}{10} \times 100$$ $$\sigma_x = 3$$ **Step 2: Find Var($x$).** $$\text{Var}(x) = 3^2 = 9$$ **Step 3: Find Var($30 - 2x$).** $$\text{Var}(30 - 2x) = (-2)^2 \cdot \text{Var}(x) = 4 \times 9 = 36$$ Hence, **Option D** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 22 - Series IQuestion 3191 of 473

All Questions

The arithmetic mean and coefficient of variation of data set $\displaystyle x$ are respectively 10 and 30. The variance of $\displaystyle 30-2x$ is

Options

A28

B32

C34

D36

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Correct Answer

✅ Option d — 36

All Options:

Detailed Solution & Explanation

**Given:**

\displaystyle \bar{x} = 10

, CV = 30 **Step 1: Find SD of

\displaystyle x

.**

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

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

\sigma_x = 3

**Step 2: Find Var(

\displaystyle x

).**

\text{Var}(x) = 3^2 = 9

**Step 3: Find Var(

\displaystyle 30 - 2x

).**

\text{Var}(30 - 2x) = (-2)^2 \cdot \text{Var}(x) = 4 \times 9 = 36

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

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

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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The arithmetic mean and coefficient of variation of data set x\displaystyle xx are respectively 10 and 30. The variance of 30−2x\displaystyle 30-2x30−2x is