Math Says Yes

Concept

Summary Statistics

Summary statistics compress a dataset into numbers such as the mean, variance, correlation, or regression line. They are useful, but they can hide shape, outliers, clusters, and curved relationships that a graph would reveal immediately.

Lessons

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

A wide scattered dot cloud on the left and a tight error bar around a single point on the right.

Standard error vs standard deviation: spread vs precision

Standard deviation describes spread among individual values. Standard error describes uncertainty in an estimate such as the mean.

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.