Central Tendency & DispersionMTP Dec 22 - Series IQuestion 3190 of 473
All Questions

If all observations in a distribution are increased by 6, then the variance of the series will be ____

Options

AIncreased
BDecreased
CUnchanged
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — Unchanged

All Options:

  • AIncreased
  • BDecreased
  • CUnchanged
  • DNone of these

Detailed Solution & Explanation

**Concept:** Variance (like SD) is independent of change of origin. **Proof:** If xi′=xi+6\displaystyle x_i' = x_i + 6, then xˉ′=xˉ+6\displaystyle \bar{x}' = \bar{x} + 6. xi′−xˉ′=(xi+6)−(xˉ+6)=xi−xˉx_i' - \bar{x}' = (x_i + 6) - (\bar{x} + 6) = x_i - \bar{x} σnew2=∑(xi′−xˉ′)2n=∑(xi−xˉ)2n=σold2\sigma^2_{new} = \frac{\sum(x_i' - \bar{x}')^2}{n} = \frac{\sum(x_i - \bar{x})^2}{n} = \sigma^2_{old} **Variance remains unchanged.** Hence, **Option C** 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