---
title: The same summary, four different pictures
description: Anscombe's quartet is a reminder to look at the data.
styles: [scientific]
title_image:
  src: https://images.unsplash.com/photo-1611692381152-c77b3e8f0afb?crop=entropy&cs=tinysrgb&fit=max&fm=jpg&ixid=M3wxMTE0NDQ4fDB8MXxzZWFyY2h8MXx8eWVsbG93c3RvbmUlMjBob3QlMjBzcHJpbmclMjBhZXJpYWx8ZW58MHwwfHx8MTc5NDI0NzI5MXww&ixlib=rb-4.1.0&q=80&w=1080
  alt: "Aerial view of a Yellowstone hot spring"
  caption: "A Yellowstone hot spring seen from above, near Old Faithful."
  fit: cover
  width: 1080
  height: 432
  credit:
    author: "Gary Yost"
    author_url: https://unsplash.com/@gyostimages?utm_source=daniel-ai-skills&utm_medium=referral
    source: Unsplash
    source_url: https://unsplash.com/photos/brown-sand-near-body-of-water-during-daytime-7Azj1ufiOgA?utm_source=daniel-ai-skills&utm_medium=referral
---

Four datasets can share summary statistics and still tell very different stories. Each panel uses the observations published in Anscombe's quartet.

```chart
type: scatter
title: A summary cannot show you the shape
data: { csv: data/anscombe.csv }
encoding: { x: x, y: y, facet: set }
annotations:
  - { kind: text, at: { x: 8, y: 13 }, text: 'y = 3.00 + 0.500x' }
axes:
  x: { label: x }
  y: { label: y }
```

*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.

```chart
type: scatter
title: Longer eruptions accompany longer waits
data: { csv: data/old-faithful.csv }
encoding: { x: waiting_min, y: eruption_min }
axes:
  x: { label: Waiting time, unit: min }
  y: { label: Eruption duration, unit: min }
```

*Source: Old Faithful geyser data, [R datasets package](https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/faithful.html); see Azzalini and Bowman (1990) and Härdle (1991).*