Central Tendency & DispersionMTP Apr 21Question 3176 of 473
All Questions

The Standard Deviation of a variable x\displaystyle x is known to be 10. The Standard deviation of 50+5x\displaystyle 50+5x

Options

A50
B100
C10
D500
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — 50

All Options:

  • A50
  • B100
  • C10
  • D500

Detailed Solution & Explanation

**Given:** SD(x)=10\displaystyle SD(x) = 10 **Find:** SD(50+5x)\displaystyle SD(50 + 5x) **Using the property:** SD(a+bx)=∣b∣⋅SD(x)\displaystyle SD(a + bx) = |b| \cdot SD(x) Here a=50\displaystyle a = 50, b=5\displaystyle b = 5: SD(50+5x)=∣5∣×SD(x)=5×10=50SD(50 + 5x) = |5| \times SD(x) = 5 \times 10 = 50 So the SD = **50** (Option A). The given `correct_option` 'c' (10) is incorrect — the constant 50 doesn't affect SD, but the multiplier 5 does. Hence, **Option A** 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