From a sample population lets say 1000 numbers, I know the standard deviation SD. I take the size of the groups n=100 and fill the groups randomly with those 1000 numbers. I find out the average of those groups: a0,a1,…,a10
I want to find out (or approximate) a new standard deviation taking now as a sample the averages of those groups of 100 numbers: a0,a1,…,a10
The data I know at the start is the standard deviation of the whole population of 1000 numbers, and the size 100 of those groups. I need to find out the new standard deviation of the sample a0,a1,…,a10 without knowing ai values
I have tried dividing the standard deviation of the full population by sqrt(n) and I get close, is there a more precises way?