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Comment by tomp | Hacker News Reader

No, the most appropriate "average" number is the median - the number that is at exactly 50% of the population. At least, that's what most people think about when they hear "average".

For example, most people intuitively perceive the fact that "the majority of drivers consider themselves above average" as human stupidity, however mathematically it makes perfect sense if average == arithmetic mean.

If you are not convinced, consider Bill Gates walking into a room full of college students - suddenly, almost everybody becomes below-average wealthy (if average == mean).

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The median can be just as misleading as the mean, if the outliers matter. Properly played, roulette can have a positive median profit for the player, but the mean will always converge on a loss.

The vast majority of people have an above average number of legs.

The median has its problems too. If you only look at the median page load time, you won't even be aware of huge problems like 40% of your visitors with slow internet connections not being able to load your page at all. If huge effects don't move users across the median, the median won't reflect those effects at all.

To me, it's not clear that there is a "most appropriate" number. All mappings of a distribution into a number will throw information away - the trick is to pick a number that keeps the information you want. And that seems to depend on the context.

most people intuitively perceive the fact that "the majority of drivers consider themselves above average" as human stupidity

I intuitively perceive it as good drivers being clustered together near the top, with a few outstanding lousy drivers near the bottom.

If you are not convinced, consider Bill Gates walking into a room full of college students - suddenly, almost everybody becomes below-average wealthy (if average == mean).

That's true in my country even if Bill Gates doesn't walk in. Hell, perhaps it's true even in the US.

I meant "below room-average wealthy", i.e. taking only the people in the room into the account.

I like 90th percentile as the "one number" to choose. Mean is misleading, and median (50th percentile) is too low to capture what most of your users are experiencing.

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