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-bar x 100 40 = sigmax/10 x 100 sigmax = 40 x 10/100 = 4 Step 2: Find variance of x. text{Var}(x) = sigmax^2 = 16 Step 3: Find variance of y = 30 - 2x. Using the property: text{Var}(a + bx) = b^2 text{Var}(x) (the constant a does not affect variance). Here a = 30, b = -2: text{Var}(30 - 2x) = (-2)^2 text{Var}(x) = 4 x 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.

Central Tendency & DispersionPYQ 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

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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.

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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?