Question

the mean of 10 observations is 10. All the observations are increased by 10%. The mean of increased observations will be: a. 10 b. 11 c. 1.1 d. 6

Answer 1

Answer:

Explanation:

Conclusion first: mean will increase by 10% and variance will increase by 10%^2.

Personally I can never memorize those complex formulas and theorem. For any mathematical and statistical question, I just need to know the logic and then write it out which is already a very good proof for many equations.

Back to this question: suppose you have 2 observations A and B.

Mean_Initial = (A+B)/2

Mean_New = (1.1*A+1.1*B)/2 = 1.1*(A+B)/2 = 1.1*Mean_Initial

Variance_Initial = (A-Mean_Initial)^2 + (B-Mean_Initial)^2

Variance_New = (1.1*A-1.1*Mean_Initial)^2+(1.1*B-1.1*Mean_Initial)^2 = 1.1^2*Variance_Initial

Starting from this simple example, you can make it more abstract which is something called general method.

You can expend your sample size into a large one until infinity. They all follow the same procedures and you will get the same conclusion