Central Tendency & DispersionMTP Dec 2023 Series IIQuestion 3202 of 473
All Questions

If the same amount is added or subtracted from all the of the individual series then the standard deviation and variance both shall be ______.

Options

AChanged
BUnchanged
CSame
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — Unchanged

All Options:

  • AChanged
  • BUnchanged
  • CSame
  • DNone of these

Detailed Solution & Explanation

**Concept:** Both SD and Variance are measures of spread/dispersion around the mean. They measure how far data points deviate from the mean. **When a constant is added/subtracted from all observations:** - Each observation shifts by the same constant c\displaystyle c - The mean also shifts by c\displaystyle c - The deviation of each observation from the mean (xi−xˉ)\displaystyle (x_i - \bar{x}) remains **unchanged** - Therefore, Variance =∑(xi−xˉ)2n\displaystyle = \frac{\sum(x_i - \bar{x})^2}{n} remains **unchanged** - And SD =Variance\displaystyle = \sqrt{\text{Variance}} also remains **unchanged** **Both SD and Variance remain Unchanged.** Hence, **Option B** 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