The same summary, four different pictures
Anscombe's quartet is a reminder to look at the data.
Four datasets can share summary statistics and still tell very different stories. Each panel uses the observations published in Anscombe’s quartet.
A summary cannot show you the shape
This chart cannot be displayed here: it needs JavaScript and WebGL.
Source: F. J. Anscombe, “Graphs in Statistical Analysis”, The American Statistician (1973), via the R datasets package.
Almost the same summary
The published observations are rounded, so the fitted values differ slightly. The means and x variance agree at the precision below; the small differences in y variance and correlation remain visible. Each rounded fitted relationship is y = 3.00 + 0.500x. The annotation repeats that shared rounded fit in each panel; it is not an extra set of observations.
| Statistic | Set I | Set II | Set III | Set IV |
|---|---|---|---|---|
| Mean x | 9.00 | 9.00 | 9.00 | 9.00 |
| Sample variance x | 11.0 | 11.0 | 11.0 | 11.0 |
| Mean y | 7.50 | 7.50 | 7.50 | 7.50 |
| Sample variance y | 4.13 | 4.13 | 4.12 | 4.12 |
| Correlation r | 0.816 | 0.816 | 0.816 | 0.817 |
A second distribution
Old Faithful’s waiting times and eruptions form two clusters. The observations are pairs, not a time series.
Longer eruptions accompany longer waits
This chart cannot be displayed here: it needs JavaScript and WebGL.
Source: Old Faithful geyser data, R datasets package; see Azzalini and Bowman (1990) and Härdle (1991).