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.

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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