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.

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