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-bar = 10, CV = 30 Step 1: Find SD of x. CV = sigmax/x-bar x 100 30 = sigmax/10 x 100 sigmax = 3 Step 2: Find Var(x). text{Var}(x) = 3^2 = 9 Step 3: Find Var(30 - 2x). text{Var}(30 - 2x) = (-2)^2 text{Var}(x) = 4 x 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.

Central Tendency & DispersionMTP 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

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

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.

Ready to Master Central Tendency & Dispersion?

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

Start Practicing — It's Free

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