Central Tendency & DispersionMTP Nov 21Question 3180 of 473
All Questions

Find the variance of 3x+2\displaystyle 3x+2 if standard deviation of x\displaystyle x is 4

Options

A9
B160
C16
D144
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — 144

All Options:

  • A9
  • B160
  • C16
  • D144

Detailed Solution & Explanation

**Given:** SD(x)=4\displaystyle SD(x) = 4, so Var(x)=42=16\displaystyle \text{Var}(x) = 4^2 = 16 **Find:** Var(3x+2)\displaystyle \text{Var}(3x + 2) **Using the property:** Var(a+bx)=b2⋅Var(x)\displaystyle \text{Var}(a + bx) = b^2 \cdot \text{Var}(x) Here a=2\displaystyle a = 2, b=3\displaystyle b = 3: Var(3x+2)=(3)2⋅Var(x)=9×16=144\text{Var}(3x + 2) = (3)^2 \cdot \text{Var}(x) = 9 \times 16 = 144 So Variance = **144** (Option D). The given `correct_option` 'c' (16) is incorrect — that's just Var(x)\displaystyle \text{Var}(x), not Var(3x+2)\displaystyle \text{Var}(3x+2). Hence, **Option D** is the correct answer.

More Questions from Central Tendency & Dispersion

If the range of 28,22,40,20,15,50\displaystyle 28, 22, 40, 20, 15, 50 is

If the S.D. of the 1st\displaystyle 1^{st} n\displaystyle n natural numbers is 30\displaystyle \sqrt{30} then the value of n\displaystyle n is

If the variance of 5,7,9\displaystyle 5, 7, 9 and 11\displaystyle 11 is 4\displaystyle 4, then the coefficient of variation is:

A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is

If Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of two numbers are 6.50 and 6 respectively, then the two numbers are

Which of the following is not a method of dispersion?

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