Anscombe’s quartet

Anscombe's quartet is a group of datasets that have the same mean, standard deviation, and regression line, but which are qualitatively different. Named after the English statistician Frank Anscombe, it's a powerful illustration of the drawback of relying solely on basic descriptive statistics to summarise data.

The data in all of the graphs in the quartet are virtually indentical when using standard descriptive methods, like mean, sample variance, and linear regression. The graphs reveal the truth.

The same data graphed

Anscombe's quartet is often used to illustrate the importance of looking at a set of data graphically before starting to analyze according to a particular type of relationship, and the inadequacy of basic statistic properties for describing realistic datasets. Looking at your data before analysing it is something that Anscombe was passionate about:

Most kinds of statistical calculation rest on assumptions about the behaviour of the data. Those assumptions may be false, and then the calculations may be misleading. We ought always to try to check whether the assumptions are reasonably correct; and if they are wrong we ought to be able to perceive in what ways they are wrong. Graphs are very valuable for these purposes. Frank Anscombe, Graphs in Statistical Analysis (1973)