Math 1 · Unit 12 · Lesson 4 · part 3 of 4
What an outlier does
What does an outlier do to each statistic?
What an outlier does
What does an outlier do to each statistic? The Washington High girls' basketball team has nine players, measured in inches: 70, 64, 67, 66, 65, 63, 67, 67, 68. The mean is about 66.3 inches and the median is 67. A new player who is 6 feet 2 inches tall, 74 inches, joins the team. Add her and watch.
| statistic | nine players | with the 74 | changed? |
|---|---|---|---|
| mean | 66.3 | 67.1 | up |
| σ | 2.0 | 3.0 | up, by half again |
| median | 67 | 67 | the same |
| IQR | 3 | 3 | the same |
With ten players, Q1 = 65 and Q3 = 68, so the IQR is 3 and the upper fence is 68 + 4.5 = 72.5. The new player, at 74, is past it: an outlier. She pulled the mean up and made the standard deviation half again as big, but the median and the IQR did not move. So the median is the better description of a typical player on this team.
The same thing happens with the class periods from Lesson 2. The eleven schools have σ ≈ 7.8 minutes. Add Cherry Lane's 100 minute period, which is past the upper fence of 90: the mean rises from about 58.2 to 61.7, the standard deviation nearly doubles to about 13.7, and the median (60) and the IQR (15) do not change at all.