Question

the mean of 10 observations is 10.all the observations are increased by 10percent the mean of increase observations will be​

Answer 1

Answer:

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.

Answer 2

Given : The mean of 10 observations is 10.

All the observations are increased by 10%.

To Find : What is the mean of increased observations?​

Solution:

Note :

Mean of observations  is increased by k if each observation is increased by k

Mean of observations  is decreased by k if each observation is decreased by k

Mean of observations  is multiplied by k if each observation is multiplied by k

Mean of observations  is divided by k if each observation is divided by k

All the observations are increased by 10%

Let say Earlier observation was a

Then observation after 10 % increase is  a + (10/100)a  

= 1.1a

Hence Each observation is multiplied by 1.1

Mean of observations  is multiplied by k if each observation is multiplied by k

Here k = 1.1

old mean = 10  

Hence Mean of  increased observations = 1.1 * 10

=> Mean of  increased observations =  11

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