Standard deviation is a statistical concept. Standard deviation tells us how far the data in a data set deviate from the norm or average – how homogeneous or how heterogeneous the data are.

The standard deviation is usually given together with the average score in a data set so that we can get a complete picture of how the scores are distributed.

If we compare the average scores and standard deviations of two classes, we can see that even if the average score in both classes is the same, this does not necessarily mean that students in both classes have the same levels of ability.

Look at the two graphs below. Each graph shows the distribution of test scores of 6th grade classes in two different towns, Town A and Town B. Both classes wrote the same test. In each town, the average score on the test was 87, but:

The standard deviation for Town A is large - this means that in Town A, there was a very large range of scores on the test.

The standard deviation for Town B is small - this means that many students got similar scores and so there was a small range of scores in Town B.

What do the above description and graph tell us about standard deviations?

Sort the following sentences into 2 categories:

sentences that tell us what a small standard deviation means sentences that tell us what a large standard deviation means