# What insights can be derived from the SD of these data?

I'm a non-Math major. I need help interpreting my students' scores. The following are the post-test scores of two groups. Group A: 26 32 31 30 36 29 28 29 36 30 36 29 36 38 34 31; Group B: 33 29 37 27 34 28 36 39 32 40 38 36 50 40 32

I computed the mean and standard deviations of the scores and got the following. For Group A: Mean = 31.94; SD = 3.59; for Group B: Mean = 35.44; SD = 5.63. The mean and SD of the two groups' pre-test scores were: Group A: Mean = 17.06, SD =6.29; Group B: Mean = 18.19, SD = 6.39.

I noticed that the mean scores of both groups increased in the post-test while their SD decreased. However, although Group B has a higher mean post-test score, the SD score of Group B is higher than Group A's. What insights can be derived from this? How should I discuss when I present the data?

• The differences in standard deviations is not significant, if you apply ANOVA using the sampling distribution of sample variance. For instance, applying Eq 10 from here would render the standard deviation of the standard deviation for 16 observations as $\approx 0.7$ SD.