One of the confusing thing that many JC2s stumble upon is that variances in A-levels. This is partly attributed to the lack of understanding and introduction of the concept. By hypothesis testing, students should be exposed to three types of variances, 
, 
and the sample variance. So what is what?
is our population variance. I like to teach my students that this is the TRUE value that no one knows, unless question states it.
is our unbiased estimate of population variance. One thing I constantly stress to students is that, 
. It is extremely important to identify that they are very different things. is an ESTIMATE of . And we get from the sample variance, which is the variance of the sample you collect.
I hope this helps to clarify their differences.
