President Martin was crowing about the incoming class of first-year students at Brand X University. “Last year the mean SAT score for first-year students was 1260,” he began, “and this year it’s risen to 1270! I think we can all be proud of that!” Although the scores from one year to the next are indeed different, why should no one get too excited?

President Martin forgot to mention that the median in the first group was 1200, and the mode in the second group was1300.

Although there is a numerical difference between 1260 and 1270, there is unlikely to be a statistically significant difference between those two results; both groups are performing pretty much the same on the SAT.

The standard deviations in both distributions were identical, and that’s what counts; inferential statistics compare one standard deviation to another.

President Martin forgot to describe the standard deviation; the formula “mean minus standard deviation” is what’s needed to compute inferential statistics.