Statistics are not enough¶

Averages, spreads and correlations are useful summaries. But very different data can produce exactly the same summary numbers. The only safe habit is to look at the data as well.

Anscombe's quartet¶

In 1973 the statistician Francis Anscombe created four small datasets. Each has eleven points. Look at their summary statistics:

If you only read this table, you would say the four datasets are the same. Now look at them:

The Datasaurus Dozen¶

In 2017, researchers Justin Matejka and George Fitzmaurice took the idea further. Starting from a dinosaur drawing made of data points (originally created by Alberto Cairo), they nudged points step by step into new shapes while keeping the summary statistics nearly identical, to about two decimal places.

Every one of these thirteen datasets has:

• mean of x ≈ 54.3 and mean of y ≈ 47.8
• standard deviation of x ≈ 16.8 and of y ≈ 26.9
• correlation between x and y between −0.06 and −0.07

A report that said "x and y are essentially unrelated, centred around 54 and 48" would be technically correct for all of them, including the dinosaur.

What this means at work¶

You will rarely meet a dinosaur in a sales report. But you will meet the same problems in everyday forms:

• An average hides two very different groups. Average delivery time looks fine, because most deliveries are fast while a few customers wait weeks.
• One outlier drives the trend. A single huge order makes a quiet month look like growth.
• A relationship is curved, not straight. Discounts raise sales up to a point, then only cut profit.

Try it yourself¶

import pandas as pd
import matplotlib.pyplot as plt

d = pd.DataFrame({
    "x": [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],
    "y": [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74],
})
print(d.mean())
print("Correlation:", d["x"].corr(d["y"]))
d.plot(kind="scatter", x="x", y="y", title="Anscombe dataset II")
plt.show()