Math 1 · Unit 12 · Lesson 2 · part 3 of 4
The median resists
That is the key idea.
The median resists
That is the key idea. The median is resistant: it is not pulled much by extreme values, because it only cares about the order of the values, not how far out the end ones are. The mean is not resistant: every value pulls on it, and a far-out value pulls hard.
The shape picks the center. If the data is roughly symmetric with no extreme values, the mean and the median are close, and the mean is a fine center. If the data is skewed, or has an extreme value, report the median, because the mean has been pulled toward the tail.
The songs data from Lesson 1 shows why. The mean is about 15.8 songs, but the median is 12. The one student with 88 songs pulled the mean up. Most students downloaded 12 or fewer, and the median is the number closer to what a typical student did.
Say it in a sentence, in context: a typical student in Mrs. Jones' class downloaded about 12 songs, though one student downloaded far more.