Two numbers both answer to the name “average”, and most of the time they agree closely enough that nobody asks which one was used. Drag a single value away from the crowd and they stop agreeing. The mean follows the runaway point, a fixed fraction of the way for every step it takes; the median does not move at all. Every dot, marker, curve and number below is computed live from the values currently on screen.
The data
Where each statistic goes as you drag
Mean vs mediandrag the gold point
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Mean—
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Mean − median—
Send the point somewhere — tap to jump
The mean is the balance point. Line the values up on a plank and it is the spot where the plank tips level, because the distances above it and below it cancel exactly. It therefore feels how far every value sits, and a value dragged twice as far pulls twice as hard. The median is the middle address. It only counts how many values lie on each side, never how far away they are, so a point at the edge of town and a point on the next continent are the same single vote. That one difference explains everything else on this page.
Two things people say that are not quite right. First, “right-skewed means the mean is above the median” is a dependable rule of thumb, not a theorem — distributions exist whose long tail runs right while the mean still sits below the median. Read it off the picture rather than deducing it. Second, the median is not automatically the better number. The mean is the one that multiplies: mean income × number of households recovers the total money on the street, and no median can do that. Use the median when you want a typical case, the mean when you want a total, and report both whenever they disagree — the size of the gap is itself a finding.