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Hamlet: "Do you see yonder cloud that's almost in the shape of a camel?"

Polonius: "By th'Mass and 'tis, like a camel indeed."

Hamlet: "Methinks it is a weasel."

Polonius: "It is backed like a weasel."

Hamlet: "Or a whale."

Polonius: "Very like a whale."

I'm convinced that statistics, like software, attracts well meaning yet proud nerds.

Bear with me here, because I'm one of them. Yes, I am a card carrying member of the, "Keeps an Edward Tufte book on their coffee table to look smart," club.

The gotcha

Let's start by accepting that there's no shortage of submissions or discussion on Hacker News about statistical errors.

Here's an example that I plucked out of the ether:

Ask HN: Anyone else seeing people averaging percentiles?

September 14, 2021.

I work at a middling SV company, and I see people taking averages of percentiles (or, even crazier, percentiles of percentiles) every day - that is, each server computes its own "50%/90%/95% latency" of all requests, sends it to a central time-series database, and the Grafana console averages them all to show a "nice" graph. They are used for everything from alerts to launch decisions. It's driving me crazy because that makes no sense: you can't average percentiles, you will get bogus numbers that randomly jumps up and down based on aggregation (how many servers you have, which tag sets you use, and so on). And I'm apparently the only one who is seriously bothered. Everyone else is somewhere between "Eh, that's the best data we have." and "What do you mean the numbers are wrong?" Is this normal?

Here's one from ten plus years ago:

Liked it better when it was called "Programmers Need To Learn Statistics...

Dec 11, 2013.

Liked it better when it was called "Programmers Need To Learn Statistics Or I Will Kill Them All" http://zedshaw.com/essays/programmer_stats.html, but still kind of wrong.

Perhaps something with less hauteur:

Averages Can Be Misleading: Try a Percentile

And here's one that was shared just today:

The mean means nothing: data visualization to debug a latency problem

There's a theme here, and the theme is a simple gotcha: a distribution of numbers has been summarised into a single, misleading, number.

The joy behind the gotcha

I personally relish seeing that insight reposted, or reread, in one form or another every year or so. It's a joy watching a programmer get their quantitative wings.

I enjoy it so much, because statistics, like software, has so much room for clever thinking. You know, the "no, it's not that simple." The "um, actually." The puzzle. There's a joy to it.

But also like software, wielding that knowledge in a way that is empathetic, compassionate, and helpful is hard. You have to resist the urge to be a smart asshole. Turns out for nerds, it's not always so easy. It's a learned skill.

But it can be done, I believe that. And it's so fun to do it.

You be smart, you can be kind, and you can also nerd out over statistics.

The world behind the joy

I also believe that statistics, more than software, comes up more often in conversation with people. To quote an equal-parts loved and hated high school teacher of mine:

Maths... is everywhere. It's in the air, it's in your hair. It's in the walls.

Don't believe me?

The theme of, "look at the distribution, not the data point," is everywhere:

⭐ Economics. Average full-time income in Australia, where I live? AU$1400/week. Median? AU$1200/week.

⭐ Biology. famously, Stephen Jay Gould was diagnosed with cancer and told the median mortality of eight months after discovery. He lived for 20 more years.

⭐ Ergonomics. US Air Force cockpits were designed around body measurements of the 'average' pilot. But no single pilot fit those dimensions. This contributed to many unexpected incidents and accidents, suspicion of simply poor piloting, but ended up with throwing out the average, and replacing it with the simple adjustable seat. Pilot performance soared.

⭐ Finance. Billionare Howard Marks likes to quote the simple example of the 6 foot-tall man who drowned crossing the river that was 5 feet tall on average. Okay, this one's more of a pithy aphorism, but I invite you to read the linked memo of his for investors. I think you'll find some insight there.

⭐ Social media. It's straightforward to look up that a relatively small proportion of YouTubers, or Twitch streamers, receive the majority of views. The mean is high, the median is low. Both of these numbers obscure how viewership accumulates.

Takeaway

Thinking in distributions, and being open to "seeing" the shape in the cloud of data, instead of a single point, can totally change the way you see the world around you. And once you see things in that way, you can start exploring them in that way as well. And that opens up whole new worlds, too.

I want to write more about statistical thinking. In the meantime, click these: