Test scores: 10, 12, 11, 13, 14. Step 1: Before the outlier: mean = 60 / 5 = 12; median = 12; mode: none. Step 2: Now a score of 60 is added (a perfect paper from a much harder test got mixed in). New data: 10, 11, 12, 13, 14, 60. Step 3: New mean = 120 / 6 = 20 - the mean leapt from 12 to 20, even though five of the six scores are 14 or less. The outlier pulled the mean up. Step 4: New median: the two middle values are 12 and 13, so the median is 12.5 - it barely moved. Mode: still none. Model both ways: the number line with five points clustered at 10-14 and one point far away at 60, AND a before/after table (mean 12 -> 20; median 12 -> 12.5; mode none -> none). Say it plainly: the mean feels every value, so it chases the outlier. The median only feels positions, so it stays with the pack.

Points per game: 3, 4, 5, 4, 6. Then a 40-point game is added. Find the mean, median and mode before and after. -> Before: mean 4.4, median 4, mode 4. After (3, 4, 4, 5, 6, 40): mean about 10.3, median 4.5, mode 4. The mean changed by far the most.