Common Core: S-ID.3
Problem 1 of 45s12-001
A histogram of the commute times of 200 workers has a tall peak at short times and a long tail stretching right toward a few very long trips. How does the mean compare with the median?
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Solution walkthrough1:53
- Skew is named for the side of the long tail. This tail stretches right, so the times are skewed right.
- The median is the middle value. Of these trips it is the th, minutes, with trips on each side.
- The mean adds every time: minutes. The long trips in the tail pull it to the right.
- The mean, , is greater than the median, . A right tail pulls the mean above the median.
- Traps: mean below median is the left-tail pattern, equal needs a symmetric shape, and the shape alone is enough.