I've heard this statement many times now in reference to people expressing views on their own performance in some skill. Some scientist/public intellectual will reference the fact that most people think they're "above average" in some endeavour(like driving a car or w/e), and then state that this is impossible.

I don't see why that would be impossible. Doesn't that really depend on what kinds of numbers you assign to the skill in question?

Consider if the set of all people with some skill were 10 people. And the skill we assign a "level" that can be anything between 1 and 10. Say, how far they can jump or something, in meters.

If nine people have a skill of 9, and one person has a skill of 1. The average is then 8.2

So nine out of those ten people have a skill above average. So in fact, it is possible for most people to be above average. Provided the below-average people are exceedingly unskilled.

Of course one might argue it isn't realistic to have a distribution like that (and please forget that nobody can jump nine meters). In reality performance in whatever category probably follows a gaussian distribution. But it's not IMPOSSIBLE for most people to be above average.

But what if all 10 of them believed they were above average?

median

Sloppy speech. It's impossible for over half of of a sample to be over the median by definition. As you say, it's very possible for over half of something to be above average, given a very one-sided distribution.


ETA: I've been ninja'd by minininja. Fitting.

1. Average is not a mathematical term. The correct terms are (arithmetic) mean or median. However, most people would understand average as being the same as the arithmetic mean. So your point still stands.

2. I think that "impossible" is just being used as a shortcut for "so remotely unlikely to be about indistinguishable from impossible".
The type of distribution you give as an example is not likely to come up especially in larger populations.

3. You don't need a large difference: Theoretically you could have like 999 999 people scoring 10 and one scoring 9.9. The 999 999 people would all be "above average" (the arithmetic mean being 9.9999999).

It appears the concept of "average" isn't all that useful.

Corneel wrote:1. Average is not a mathematical term. The correct terms are (arithmetic) mean or median. However, most people would understand average as being the same as the arithmetic mean. So your point still stands.

I didn't even think that far. The German word for average is also the word for mean. Funny.

The_Metatron wrote:It appears the concept of "average" isn't all that useful.

Mathematically? No.
Sociologically: we use it all the time, consciously or unconsciously, to evaluate/judge other people by (is someone tall or short, fat or slim) and it works well enough for simple things (like describing things to someone). Of course it might go haywire if people's frameworks of reference (including averages) are too different (someone who's short to a Dutchman might be about average height to an Italian).

Mazille wrote:

Corneel wrote:1. Average is not a mathematical term. The correct terms are (arithmetic) mean or median. However, most people would understand average as being the same as the arithmetic mean. So your point still stands.

I didn't even think that far. The German word for average is also the word for mean. Funny.

In Dutch it is middled (gemiddeld)

The_Metatron wrote:It appears the concept of "average" isn't all that useful.

Yeah, as a word, it's pretty average.

Mediocre.

In a large population, the distribution would almost certainly be a normal distribution. So then roughly half would be above average.

where all the women are strong, all the men are good looking, and all the children are above average.

The stat always comes up that most people in the UK consider themselves above average drivers. And I've gotta say, if you're including the whole world in that, then I'd have to agree with them. I got driven home by a taxi driver entirely in second gear yesterday.

I'm With Stupid wrote:The stat always comes up that most people in the UK consider themselves above average drivers. And I've gotta say, if you're including the whole world in that, then I'd have to agree with them. I got driven home by a taxi driver entirely in second gear yesterday.

I'd think that it's not a sufficiently well defined question as there are lots of differing and even contradictory metrics when it comes to measuring your quality as a driver. For instance, Lewis Hamilton is clearly an above average driver in terms of speed, but quite possibly a below average driver in terms of accident rate.

So, even taxi drivers in the developing world are likely to consider themselves above average, just because they'll skew their comparisons around metrics that would favour them.

There is no link between level of skill and level of caution.

Hence many men think they are above average due to their perception of ability, with little regard for their concept of acceptable risk, and many women think they are above average due to their concept of acceptable risk, with little regard for their perception of ability.

Insurance companies will take a woman who cannot parallel park over a man who is prepared to parallel park with a handbrake turn any day.

#everydaysexism

minininja wrote:#everydaysexism

Qualified stereotyping, if you like. There are women-only car insurance companies for a reason, it's not just a marketing ploy.

It's been illegal in the EU to differentiate insurance premiums purely on the basis of gender since 2012. All else being equal, you'd pay the same.

Men still tend to pay more though, because they have other identifiable risk factors such as the cars they drive, the jobs they work in, and the number of penalty points they've picked up.