small sample size - right math

[jazzwillbe]

Hello All,
I have a very basic question. I hope to get some help from here. What would be the right tool to use for small sample sizes.

For example:

A material is tested for yield stress. 3 samples tested got the following results

Sample 1: 120 MPa
Sample 2: 132 MPa
Sample 3: 125 MPa

How can I use this data to confidently arrive at a yield stress for the material.

Thanks
J

[kazec]

I don't see any reason why you should not use the arithmetic mean.

If you know the distribution of the measurement, you may wish to use the estimator constructed based on that specific distribution. But first I don't think it's easy to get the distribution. Second, even so, your sample size is small (=3) while the optimality of maximum likelihood estimator is in the asymptotic sense and is only suboptimal for your case.

So a way that is both easy and efficient is the arithmetic mean!