STATISTICS: How is standard deviation of the sampling distribution of the sample mean different from standard deviation of sample or standard deviation of the population?

Question

debbieg · Answer

Do you mean DESCRIBE how/why it's different? Or the actual difference in the formulas? (Which I'm assuming you have or can look up.)

anonymous · Answer

describe how its different

debbieg · Answer

OK... think about this. It's sort of a "thought experiment" (although you COULD actually DO it).

Using a random number generator or table, randomly select  10 numbers between 1-10. Compute the standard deviation.

Now, selection a sample of 10 numbers and compute the mean. do it again. and again. Do that 10 times, so you have 10 different samples and you have 10 different means. Now, compute the standard deviation OF THOSE 10 MEANS. Do you think it will have HIGHER or LOWER variance than your first answer, which was the st dev for ONE random sample?

Remember, in the first case you are talking about the variance of the observations in one sample of 10 elements.

In the second case, you are talking about the variance of the MEANS of 10 SAMPLES.