Illinois high school football teams scored slightly fewer points this year in the first week of the season, compared to last year.
| 2013 | 2014 | |
| Total points scored | 13,618 | 13,022 |
| Teams playing games | 571 | 574 |
| Mean points scored | 23.85 | 22.69 |
| Standard deviation | 16.25 | 15.95 |
| Median points scored | 22.0 | 21.0 |
We performed a t test for the null hypothesis that the mean number of points scored by each team in Week 1 of the 2014 season was equal to that statistic in the 2013 season:
In our analysis, t is less than the critical value of the Student’s t distribution, even all the way at the α=0.1 significance level, and the null hypothesis cannot be rejected. The means are not significantly different, although Illinois teams in Week 1 of the 2014 season scored, on average, 1.16 fewer points than in 2013.
Why is it reasonable to expect the median to be lower than the mean? See Common Core math standard HSS.ID.A.2-3 for more information.