Varying variances

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, \sigma^2, s^2 and the sample variance. So what is what?

\sigma^2 is our population variance. I like to teach my students that this is the TRUE value that no one knows, unless question states it.

s^2 is our unbiased estimate of population variance. One thing I constantly stress to students is that, s^2\ne \sigma^2. It is extremely important to identify that they are very different things. s^2 is an ESTIMATE of \sigma^2. And we get s^2 from the sample variance, which is the variance of the sample you collect.

I hope this helps to clarify their differences.

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