Flaw of Averages (2002) | Hacker News Reader

Flaw of Averages (2002)

hbr.org

40 pointstchalla17 comments

My favorite flaw of averages isn't even mentioned in this article. It's the aggregation of averages across covariates. The more covariates (higher dimensions) your problem has, the less likely the population will exist "in the average".

This was explored in a famous study of Air Force pilots and when measuring across 10 different dimensions, found that 0 pilots were "average" across all 10.

https://www.thestar.com/news/insight/2016/01/16/when-us-air-...

>There was no such thing as an average pilot. If you’ve designed a cockpit to fit the average pilot, you’ve actually designed it to fit no one.

edit: wrong link

You had the wrong link in your clipboard ;)

It's probably this one?

https://www.thestar.com/news/insight/2016/01/16/when-us-air-...

(PS: this is my favourite pet theory why UX is such a trainwreck these days, UIs are designed for an "average user" that doesn't exist, driven by "telemetry averages")

User interfaces should be designed for the users you will have in the long run. In industry and commerce these will be expert users.

I spent a large chunk of my life writing software to design transformers. The UIs broke all of the naive 'rules' about UI design and were crammed full of information, buttons, boxes, entry fields, pull down lists, etc.

For the users they were designed for they were very productive. For a casual or first time user they were impossible to use. But we had no casual users, only experts who were in a hurry and would not tolerate having to wade through multiple screens to perform some small what-if exercise. It was like an airliner cockpit, everything as close to hand as possible and only the rarely used items on other pages.

A frequent request was to enlarge the window so that more could be fitted in at once, it was much rarer to be asked to move something off the main window.

You linked to the OP by mistake. Please share the article you were referring to!

One of my favorite quotes from The Hitchhiker's Guide to the Galaxy:

"Population: None. Although you might see people from time to time, they are most likely products of your imagination. Simple mathematics tells us that the population of the Universe must be zero. Why? Well given that the volume of the universe is infinite there must be an infinite number of worlds. But not all of them are populated; therefore only a finite number are. Any finite number divided by infinity is zero, therefore the average population of the Universe is zero, and so the total population must be zero."

> But not all of them are populated; therefore only a finite number are.

Isn't this a leap in logic? Not all subsets of an infinite set are finite.

Douglas Adams wasn't writing a treatise on mathematics...

He was not, but the usage of the quote in this context implies some relevance to mathematical averaging and it's flaws. If the reasoning is not sound, neither is the usefulness in this context.

How do you mean that not all subsets of an infinite set are finite, or in what cases would this be so?

Ex: {n ∈ R ∣ n is odd}

The set of prime integers is a strict subset of the set of integers, and yet both are infinite (they have the same cardinality even--that is, they are the same size, in one sense of 'size').

Take all the even numbers. That's a subset of all whole numbers. Is it a finite set? Clearly not. Both are infinite; the population of even numbers is 50%. Sometimes infinity/infinity = 0.5.

The universe isn't infinite either. But neither of those is the major error with his reasoning.

Any average is a reduction of dimensionality.

Strange that people never see it that way. I wonder if they don’t worry about it in other everyday contexts (e.g. floor plans)?

The example is not great. I wouldn't blame the use of averages there, but rather not realizing that when the cost of excess/spoil is not symmetrical the optimal answer in terms of minimizing average cost is not going to be the forecasted value regardless of how it was obtained.

Well, you don't necessarily want to optimize expected return alone, since you also care about the probability of ruin. Which is why Monte Carlo's are great, you get everything for free without having to think very hard. (All particle physicists are trained to reach for a toy MC before thinking about anything :) ).

that's why you should use guesstimate! https://www.getguesstimate.com/

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