For a given data, the standard deviation is 20.If 3 is added to each observation , what is the new variance of the resulting observations?a)20b)23c)17d)60Correct answer is option 'A'. Can you explain this answer?

Question

Answer

When 3 is added to each observation, then mean is

also increased by 3....now, deviation = x - mean ....(where, x is the value of observation)when we calculate the devi

Answer

Keep remember my friend that variance won't change even a fixed added to every observation

But it's mean will by Xtimes of it

Answer

Given information:
- Standard deviation of the given data = 20

Objective:
- To find the new variance of the resulting observations when 3 is added to each observation.

Formulae:
- Variance = (Standard Deviation)^2

Calculation:
Step 1:
- We are given that the standard deviation of the given data is 20. Let's assume the given data has n observations.

Step 2:
- We know that the standard deviation is calculated as the square root of the variance. Therefore, the variance can be calculated by squaring the standard deviation.
- Variance = (Standard Deviation)^2 = (20)^2 = 400

Step 3:
- Now, we need to find the new variance of the resulting observations when 3 is added to each observation.
- Let's consider a single observation from the given data as x.
- After adding 3 to this observation, the new observation will be (x + 3).
- Since we have n observations in the given data, the new resulting observations will be (x1 + 3), (x2 + 3), ..., (xn + 3).

Step 4:
- To find the new variance, we need to calculate the new standard deviation first.
- The new standard deviation can be calculated using the formula:
New Standard Deviation = Standard Deviation of the resulting observations = Standard Deviation of the given data = 20

Step 5:
- Finally, we can find the new variance by squaring the new standard deviation.
- New Variance = (New Standard Deviation)^2 = (20)^2 = 400

Conclusion:
- The new variance of the resulting observations, when 3 is added to each observation, is 400.

Similar JEE Doubts

For a given data, the variance is 15. If each observation is multiplied by 2, what is the new variance of the resulting observations?

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is

The variance of 20 observations is 5. If each observation is multiplied by 2 then the new variance of the resulting observations, is

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is: [JEE M 2015]

Select the correct alternative in each of the following. Indicate your choice by the appropriate letter only.Let S be the standard deviation of n observations. Each of the n observations is multiplied by a constant c. Then the standard deviation of the resulting number is (1980)

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Mathematics (Maths) for JEE Main & Advanced

Chemistry for JEE Main & Advanced

Chapter-wise Tests for JEE Main & Advanced

Top Courses for JEE

Top Courses for JEE

Suggested Free Tests

Related Content

JEE Courses

Mock Test Series

Past Year Papers

Additional Courses

Company