Question

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?

Answer 1

Answer:

20

Step-by-step explanation:

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Answer 2

Answer:

20

Step-by-step explanation:

Concept= Standard Deviation and Variance

Given= Standard Deviation and Constant to add

To find= Resulting Variance

Explanation=

We have been given the standard deviation of the data and the constant which is added afterwards.

The standard Deviation is 20.

Now it is said that 3 is added to each observation and find new variance.

Initially each one of us will calculate the value and then deduce the answer but, there is a very nice and useful theorem.

It States that: When a constant is added or subtracted to the each observation the standard deviation and variance of the data does not change it remains the same.

According to the theorem, if 3 is added to each observation the variance and standard deviation does not change. It remains same.

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