Three different answers to “what is a typical value?” — and they disagree more often than you would think. Add one billionaire to the room and watch only one of them survive.
Click the chart to add a value there. Each bar is a count of data points.
Three measures of "typical" — and knowing which one someone quoted you matters enormously.
All three are measures of central tendency — attempts to summarise a whole dataset with one number. They answer subtly different questions, and on skewed data they can be wildly far apart.
On a perfectly symmetric distribution all three land in the same place. Load Symmetric and see the three markers stack up.
Press Add a billionaire. One extreme value arrives and the mean lurches toward it, while the median barely twitches and the mode does not move at all.
This is why median household income is reported rather than mean. The mean answers "what if the total were shared equally?" — a real question, but not the same as "what does a typical household earn?". Whenever someone quotes an "average", the first thing worth asking is which one.
The relationship between the three is a reliable fingerprint of shape:
The mean is always pulled toward the tail, because it is the only one of the three that uses the actual magnitude of every value.
In practice this is a data-cleaning decision: filling missing values with the mean is standard for symmetric numeric columns, with the median for skewed ones, and with the mode for categories.
The mean is the balance point and uses every value — which makes it precise but fragile. The median is the middle and shrugs off outliers. The mode is the most common and is the only option for categories. Skewed data pulls them apart, and "average" without qualification is an ambiguous word.
Three different answers to “what is a typical value?” — and they disagree more often than you would think. Add one billionaire to the room and watch only one of them survive.