More on Mean and Median
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Statistics & Probability
Summary
Mean and median behave differently when a data set includes symmetry or outliers. On ACT questions, you can often compare them without calculating by checking whether the list is evenly spaced, symmetrical, or pulled in one direction by extreme values.
- Outliers are numbers far from the center of a list, and they affect the mean strongly while leaving the median unchanged.
- The mean equals the median when numbers are evenly spaced, such as consecutive integers or consecutive multiples of the same number.
- The mean also equals the median when a list is perfectly symmetrical, because values balance evenly around the middle number.
- When a list is asymmetrical, especially with outliers on one side, the mean gets pulled toward those outliers while the median stays in place.
- On ACT problems, comparing mean and median often does not require full computation; identifying whether high or low outliers were added is usually enough.
- In the sample test-score problem, adding one score above 81 and one much lower score keeps the median at 81 but lowers the mean, because the low outlier pulls the average down.
Chapters
00:00
Outliers and Their Effect on Mean vs. Median
00:21
When Mean and Median Are Equal
02:20
ACT Strategy: Compare Mean and Median Without Full Calculation
02:41
Practice Problem with Test Scores