Anscombe's Quartet

In 1973, British statistician Francis Anscombe published a four-page paper in *The American Statistician* titled "Graphs in Statistical Analysis." He did something very simple but very striking. He constructed four datasets, each with: identical means (all 9.0), identical variances, identical correlation coefficients (0.816), and identical regression lines (y = 3 + 0.5x).

Looking at the numbers alone, all four datasets are "identical."

But when he plotted them — four completely different patterns. The first is a normal linear distribution. The second is a graceful curve with an obviously poor linear fit. The third has a single outlier that completely distorts the entire line. The fourth is nearly vertical — all points clustered together, with a single outlier determining the regression line.

Anscombe's point: **If you only look at summary statistics (mean, standard deviation), you'd think all four datasets tell the same story. But the graphs reveal they tell four completely different stories.**

This paper later became a classic in statistics education, changing how countless analysts approach data. Tukey's *Exploratory Data Analysis*, published in 1977, took this principle to its extreme — plot first, then examine the numbers.

Your 4.5 rating is Anscombe's mean. It compresses the story of five dimensions into a single number. Without examining the dimensional distribution, you have no idea where your 3.2 is hiding.