Suppose we cover a chessboard with 32 dominoes so that each domino covers two squares. What is the likelihood that there will be an even number of dominoes in each of the two orientations (horizontal and vertical)?

In fact this will always be the case. Consider the 32 squares in the odd-numbered horizontal rows. Each horizontal domino on the board covers either two of these squares or none of them. And each vertical domino covers exactly one of these squares. So the horizontal dominoes cover an even number of these squares (call it n), and the number of squares remaining in this group (32 – n) must also be even. This latter number is also equal to the number of vertical dominoes, so both quantities are even.

(By Vyacheslav Proizvolov.)

The first “true cat,” Proailurus, or “Leman’s Dawn Cat,” appeared about 30 million years ago. But from 25 to 18.5 million years ago, strangely few catlike fossils are found in North America. Biologist Luke Hunter writes:

Following the appearance of the dawn cat, there is little in the fossil record for 10 million years to suggest that cats would prosper. In fact, although Proailurus persisted for at least 14 million years, there are so few felid fossils towards the end of the dawn cat’s reign that paleontologists refer to this as the ‘cat gap’. The turning point for cats came about with the appearance of a new genus of felids, Pseudaelurus.

The gap may be due to changes in climate and habitat, the rise of competing doglike species, an unsustainable “hypercarnivorous” dietary specialization, or some other factor. Modern cats descended from Pseudaelurus.

Three male offspring, aged 9–14 years, of one of the authors were observed to experience visual problems profound enough to imply functional blindness. The visual deficit was evident on almost every occasion when any one of the children of this physician went to the refrigerator and opened the door. The acute visual problem encountered was noted to be part of a consistent behaviour pattern, wherein a few seconds after the fridge door was opened a cry would be heard from the affected child of ‘Mum, where’s the milk?’

— Andrew J. Macnab and Mary Bennett, “Refrigerator Blindness: Selective Loss of Visual Acuity in Association With a Common Foraging Behaviour,” Canadian Medical Association Journal, Dec. 6, 2005

Suppose that there’s no correlation between talent and attractiveness in the general population (left). A person who studies only celebrities might infer that the two traits are negatively correlated — that attractive people tend to lack talent and talented people tend to lack attractiveness (right). But this is deceiving: People who are neither attractive nor talented don’t typically become celebrities, and that large group of people aren’t represented in the sample. Celebrities tend to have one trait or the other but (unsurprisingly) rarely both.

The phenomenon was studied by Mayo Clinic statistician Joseph Berkson; this example is by CMG Lee.

In June 2006, Iowa paralegal Jane Wiggins looked out the window of her Cedar Rapids office and saw a cloud unlike any she’d seen before. “It looked like Armageddon,” she told the Associated Press. “The shadows of the clouds, the lights and the darks, and the greenish-yellow backdrop. They seemed to change.”

Wiggins sent a photo to the Cloud Appreciation Society, a weather-watching group founded by Gavin Pretor-Pinney, author of The Cloudspotter’s Guide. Other sightings were registered around the world (this one appeared over Tallinn, Estonia), and eventually Pretor-Pinney nominated it as an entirely new type.

The 2017 edition of the World Meteorological Organisation’s International Cloud Atlas included asperitas in a supplementary feature. The name is Latin for “roughen” or “agitate” — “not necessarily gentle or steady, but quite violent-looking, turbulent, almost twisted in its appearance,” Pretor-Pinney said.

It’s not new, really — such clouds have always been up there — but it’s the first formation added to the atlas since 1951. “We like to believe that just about everything that can be seen has been,” Society executive director Paul Hardaker said. “But you do get caught once in a while with the odd, new, interesting thing.”

Yale statistician Frank Anscombe devised this demonstration in 1973. Here are four datasets, each with 11 (x,y) points:

I		II		III		IV
x	y	x	y	x	y	x	y
10.0	8.04	10.0	9.14	10.0	7.46	8.0	6.58
8.0	6.95	8.0	8.14	8.0	6.77	8.0	5.76
13.0	7.58	13.0	8.74	13.0	12.74	8.0	7.71
9.0	8.81	9.0	8.77	9.0	7.11	8.0	8.84
11.0	8.33	11.0	9.26	11.0	7.81	8.0	8.47
14.0	9.96	14.0	8.10	14.0	8.84	8.0	7.04
6.0	7.24	6.0	6.13	6.0	6.08	8.0	5.25
4.0	4.26	4.0	3.10	4.0	5.39	19.0	12.50
12.0	10.84	12.0	9.13	12.0	8.15	8.0	5.56
7.0	4.82	7.0	7.26	7.0	6.42	8.0	7.91
5.0	5.68	5.0	4.74	5.0	5.73	8.0	6.89

Each set produces the same summary statistics (mean, standard deviation, and correlation). But their graphs are strikingly different:

The lesson, Anscombe said, is to “make both calculations and graphs. Both sorts of output should be studied; each will contribute to understanding.”

Justin Matejka and George Fitzmaurice created a similar collection in 2017: the Datasaurus Dozen.

(Thanks, Rick.)

09/05/2021 UPDATE: Here’s an animation of the Datasaurus Dozen. (Thanks, Eric.)