Anscombe's quartet
Four datasets that share a mean, a variance, a correlation and a regression line, and look nothing like each other. Drawn here, with every statistic computed from the numbers rather than repeated.
Why this exists
Francis Anscombe published these four datasets in 1973 to make one argument: that summary statistics are not a substitute for looking at your data, and that a computer which only prints numbers is helping you less than you think.
All four have the same mean x, the same mean y, the same variance, the same correlation and the same fitted line to two decimal places. Set I is a linear relationship with scatter. Set II is a clean curve with no noise at all. Set III is a perfect straight line with one outlier dragging the fit. Set IV is ten points at a single x and one point elsewhere deciding the entire slope.
Every one of those is a different problem and the numbers describe none of them.
Set IV is the one worth staring at
Ten of its eleven points share the same x. A regression line needs variation in x to have a slope at all, so the whole slope rests on the single point at x = 19. Remove that point and there is no line to compute — not a worse line, no line.
The summary statistics do not hint at this. The R² is 0.67, the same as the others.
One thing every retelling gets slightly wrong
The correlations are almost always quoted as “0.816 to three decimal places”, as though identical. Computed from the published data they are 0.81642, 0.81624, 0.81629 and 0.81652 — agreeing with each other to about three parts in ten thousand, which is far more than enough for the argument, but set IV rounds to 0.817.
It changes nothing about Anscombe's point. It is included because this site's habit is to compute the numbers rather than repeat them, and when you do, that is what comes out.
Anscombe, F. J. (1973). “Graphs in Statistical Analysis.” The American Statistician 27(1): 17–21.