Anscombe's quartet
In 1973 F. J. Anscombe published four datasets with almost identical summaries and sharply different shapes. Plotting each set shows what a mean, variance or fitted equation can conceal.
A summary cannot show you the shape
This chart cannot be displayed here: it needs JavaScript and WebGL.
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 |
The same chart in each style
Source
---
title: "Anscombe's quartet"
styles: [scientific]
---
```chart
{
"annotations": [
{
"at": {
"x": 8,
"y": 13
},
"kind": "text",
"text": "y = 3.00 + 0.500x"
}
],
"axes": {
"x": {
"label": "x"
},
"y": {
"label": "y"
}
},
"data": {
"csv": "data.csv"
},
"encoding": {
"facet": "set",
"x": "x",
"y": "y"
},
"title": "A summary cannot show you the shape",
"type": "scatter"
}
```
Data and credits
Complete report and provenance · Rich Markdown source · CSV observations.