Glossary

Anscombe's quartet: same statistics, different data

Anscombe's quartet is four data sets with nearly identical means, variances, correlations and regression lines that look completely different when plotted. The data, the statistics, what each plot reveals and what it means for dashboards.

Su He Reviewed by Emma Collins Also called Anscombe quartet Last updated Nov 5, 2026 Glossary

Quick answer

Anscombe's quartet is a set of four data sets, published by Francis Anscombe in 1973, that share nearly identical means, variances, correlation and linear regression line but have very different distributions, demonstrating the importance of plotting data.

What is Anscombe's quartet?

Anscombe's quartet is a set of four small data sets, each with eleven (x, y) points, that have nearly identical summary statistics but look completely different when plotted. The statistician Francis Anscombe published it in 1973 to show that you should always graph data before trusting its summary numbers.

The four data sets

Set I x	Set I y	Set II x	Set II y	Set III x	Set III y	Set IV x	Set IV y
10	8.04	10	9.14	10	7.46	8	6.58
8	6.95	8	8.14	8	6.77	8	5.76
13	7.58	13	8.74	13	12.74	8	7.71
9	8.81	9	8.77	9	7.11	8	8.84
11	8.33	11	9.26	11	7.81	8	8.47
14	9.96	14	8.10	14	8.84	8	7.04
6	7.24	6	6.13	6	6.08	8	5.25
4	4.26	4	3.10	4	5.39	19	12.50
12	10.84	12	9.13	12	8.15	8	5.56
7	4.82	7	7.26	7	6.42	8	7.91
5	5.68	5	4.74	5	5.73	8	6.89

The identical statistics

We recomputed the summaries for all four sets:

Statistic	Set I	Set II	Set III	Set IV
Mean of x	9	9	9	9
Variance of x	11.00	11.00	11.00	11.00
Mean of y	7.50	7.50	7.50	7.50
Variance of y	4.13	4.13	4.12	4.12
Correlation of x and y	0.816	0.816	0.816	0.817
Linear regression line	y = 3.00 + 0.500x	same	same	same
R²	0.67	0.67	0.67	0.67

Anyone reading only this table would conclude the four data sets describe the same relationship.

What the plots reveal

Set I is what the statistics suggest: a noisy linear relationship.
Set II is a clean curve. A straight line is the wrong model; a quadratic fits almost perfectly.
Set III is a perfect straight line except for one outlier, which drags the slope and lowers the correlation from nearly 1.
Set IV has no relationship at all: ten points share the same x, and a single extreme point creates the entire correlation.

A scatter plot of each set takes seconds and makes all four stories obvious.

Why it matters for analytics

Dashboards are built on summary statistics: averages, rates, correlations and trend lines. Anscombe's lesson applies directly:

Two campaigns with the same average conversion rate can behave very differently: one steady every day, the other driven by a single viral day.
A correlation between time on site and purchases can come from one heavy buyer rather than a general pattern, the Set IV problem. See correlation vs causation.
A trend line through a seasonal series fits a straight line to a curve, the Set II problem.
One bot spike or tracking bug can move an average the way Set III's outlier moves the slope; see outliers in data.

Practical habits:

Look at the distribution, or the daily series, before reporting an average.
Plot two variables against each other before quoting their correlation.
Check whether one point or one day drives the result by recomputing without it.
Prefer medians and percentiles when a few values dominate; see mean vs median.

The Datasaurus Dozen

In 2017, Justin Matejka and George Fitzmaurice at Autodesk Research extended the idea with the Datasaurus Dozen: thirteen data sets, including one shaped like a dinosaur, that share the same means, standard deviations and correlation to two decimal places. They generated them by nudging points while holding the statistics fixed, showing that almost any shape can hide behind the same numbers.

Sources

Anscombe, F. J. (1973). Graphs in statistical analysis. The American Statistician, 27(1).
Matejka, J. and Fitzmaurice, G. (2017). Same stats, different graphs. Autodesk Research.
Wikipedia. Anscombe's quartet.

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Su He

Data Analyst

Explores traffic sources, conversion funnels, and retention, using clear metric definitions and concrete examples to explain what the numbers mean.

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What is the point of Anscombe's quartet?

To show that summary statistics can hide very different patterns, so data should be visualized before conclusions are drawn.

What statistics are the same in Anscombe's quartet?

The mean and variance of x and y, the correlation between them (about 0.816) and the regression line y = 3 + 0.5x, with R² about 0.67.

What is the Datasaurus Dozen?

A 2017 extension by Autodesk Research: thirteen data sets, one shaped like a dinosaur, with the same summary statistics to two decimals.

How does Anscombe's quartet apply to business analytics?

Averages, correlations and trend lines on dashboards can be driven by one outlier, a curve or a single day. Plot the data before trusting the number.

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