# How to estimate sample mean/variance from another, smaller sample?

Let's say I record some variable from Sample 1 of size = 10 and find that mean = 10 and variance = 5. If I then took Sample 2 of size = 100, before actually recording the variable, what could I say about Sample 2 based on Sample 1?

I'd intuitively want to say that Sample 2 has mean = 10 and variance = 5 with some confidence intervals. It seems to me that I'd be making a statement where I extrapolate Sample 1 -> Population, and then Population -> Sample 2.

Is there a term for this kind of sample-to-sample extrapolation? How would I do it?

• If your two samples follow the same distribution, or come from the same population, it is not an extrapolation. just a normal statistical inference. If the random variable follows normal distribution, what you can say about sample 2 based on the sample 1 is that about 95 of 100 cases will be between 5 and 15. (mean +/- t*sd). – user158565 Nov 18 '18 at 5:38