Central Tendency & DispersionMTP Nov 21Question 3178 of 473
All Questions

If all the observations are decreased by 4, find the relation between new SD and old SD.

Options

ANew SD = Old SD/2
BNew SD = Old SD - 2
CNew SD = Old SD - 4
DRemains unchanged
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — Remains unchanged

All Options:

  • ANew SD = Old SD/2
  • BNew SD = Old SD - 2
  • CNew SD = Old SD - 4
  • DRemains unchanged

Detailed Solution & Explanation

**Concept:** SD is independent of change of origin. Subtracting a constant from all observations does NOT change the SD. **Proof:** If xi′=xi−4\displaystyle x_i' = x_i - 4, then xˉ′=xˉ−4\displaystyle \bar{x}' = \bar{x} - 4. xi′−xˉ′=(xi−4)−(xˉ−4)=xi−xˉx_i' - \bar{x}' = (x_i - 4) - (\bar{x} - 4) = x_i - \bar{x} Deviations unchanged ⇒\displaystyle \Rightarrow Variance unchanged ⇒\displaystyle \Rightarrow SD unchanged. **New SD = Old SD** (Remains unchanged). The given `correct_option` 'b' (New SD = Old SD - 2) is incorrect. 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