Question

If each item of the sample data or observation is decreased by 50%, then the variance will?

Answer 1

Question :- If each item of the sample data or observation is decreased by 50%, then the variance will ?

Solution :-

First, lets understand if any number is decreased by 50% .

Ex:- 10 is decreased by 50% .

Solve :- 50% of 10 is = 50 * 10/100 = 5 .

So, 10 is decreased by 5.

That, means new value is 10 - 5 = 5 which is equal to half of initial value .

Conclusion :- if any number is decreased by 50% , the number becomes half of itself. Or, the number is divide by 2.

concept :-

• If we add or subtract the same number from every item in the data, the variance doesn't change.
• If we multiply or divide every item in the data by the same number, the variance will change.

As we have seen , decreased by 50% cause each item is divide by 2.

Therefore, if each item of the sample data is divide by 2 , then the the variance will change .