Math Says Yes

Concept

Averages Mislead

The mean adds everything up and divides, so a few extreme values can drag it far from the typical case. In skewed data the median — the middle value — better represents what is normal. Ask about the shape of the data, not just its average.

Lessons

A lopsided distribution with one average line hiding the shape.

Averages Hide the Shape

A single number cannot capture a lopsided distribution.

Four small scatterplots with similar summary lines but different shapes.

Summaries Need Pictures

Means, variances, correlations, and regression lines can match while the underlying data tell completely different stories.

Related Facts

Bars rising from short to tall, a pointer on the middle bar and a dashed line sitting high above most of them.

Mean vs median: which average should you use?

The mean shares the total equally. The median finds the middle case. In skewed data, those can tell very different stories.

Four mini scatterplots showing different shapes under the same summary line.

Anscombe's quartet has the same statistics and different stories

Four datasets can share almost the same mean, variance, correlation, and regression line, yet look completely different when plotted.

Many short figures and a few very tall ones, with a dashed average line sitting above most of them.

Most people earn less than the average wage

In a lopsided economy, a handful of huge incomes pull the 'average' above what a typical person actually makes.