To estimate the mean we add the 50 values together and then
divide by 50. Or we could put them into 5 groups of 10, take the mean of each
group and then average the 5 groups. This is equivalent to changing the
integration time from 0.1 s to 1 s. But we find that the two means are
the same, even though the standard deviations are different. So perhaps the standard
deviation is telling us something about how the intensity is varying rather than
telling us how good the mean is. We can determine the confidence in the real mean m from

We can determine the confidence in the real mean m from where *t*[1-a/2;*n*-1]
are the percentage points of Student’s *t* distribution.