What is difference of the shape of the distribution of sample mean ( x ) and the shape of the distribution of x?

Answer 1

Matheus,

The sampling distribution is usually a normal or a t as long as the sample size is large enough. You can check this out with Excel. Take a large (200) number of random samples from say x∼U(0,1) of size say 10

Compute the average for each sample then make a histogram of the averages and you will see that the shape is approx. normal. This is easy to do in Excel.

Regards

Jim