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Comment by axaxs | Hacker News Reader

I'm impressed with how honest people are. Most answers were in the 40 to 60 percent range, which is about where it should be mathematically of course.

Two big outliers I saw was that apparently everyone thinks they have more common sense than average, and also more polite than average.

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> Most answers were in the 40 to 60 percent range, which is about where it should be mathematically of course.

Not necessarily. For instance there's:

> 77% of participants think they give less to homeless people than average.

Say most people give $0 to homeless people, but 30% of people give some. In that case 77% giving less than average may be correct.

Depends on the average. In your example the median gives $0; the mean gives 'less than half of some'; the mode gives $0.

I know people learn this in middle school, but I've never seen an actual scholarly work call the median or mode "the average"--and I think I'd find it slightly misleading if they did.

"Typical", "likely", (etc) are all fine, but to me, "average" strongly implies "mean."

That precision of language is not the way most people would use that word, eg "a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values" - https://www.merriam-webster.com/dictionary/average

"be conservative in what you do, be liberal in what you accept from others" - Robustness principle

It's good to be precise when communicating, but in most contexts you shouldn't expect it from others.

I understand that some sources say that one can use "average" to mean something other than the mean.

My claim, as an actual working[0] scientist who encounters those words a lot, is that nobody really does, outside of "Well, actually the average can be the median or mode too...."-type statements.

I'd put describing the mode as "the average" on par with giving someone a tomato and zucchini salad while describing it as "mixed berries." Not technically wrong but....

[0] Well, slacking scientist at the moment, but...

For the record I was assuming that "average" meant mean in my original comment.

Scholarly works will pretty much never call the mean "the average" without clarifying what they mean either.

As for the implication, a statement along the lines of "the average person" will almost always be interpreted as median, not mean. For example, Jeff Bezos lives in Medina, WA, a remarkably anagrammatic suburb for this demonstration. You can probably understand why saying "the average person in Medina has a net worth of $65,000,000" is both somewhat misleading and remarkably unhelpful for pretty much any purpose you'd want that information.

People use "mean" and "average" in way that suggest they're the same, but one certainly doesn't have to say "average (herein defined as the mean)" because that's the overwhelmingly dominant meaning anyway.

Two random examples from other tabs I had open: https://direct.mit.edu/neco/article/16/3/477/6879/Mean-Insta... or https://www.cell.com/neuron/fulltext/S0896-6273(13)00798-8 Mean and average are clearly the same thing, but only via context.

In fact, I'd say that "averagING" (as a verb) almost has to be the mean; I'd find it deceptive if it were mode-finding.

You're right that people often conflate the mean and median, but I think that's more to do with underestimating the very, very long tails of some distributions.

You're replying to a perfectly clear demonstration that people often mean the median when they say average, and completely ignoring it.

What was the point of that?

That it's rarely deliberate.

I certainly agree that people mix them up. If you ask someone to quickly estimate the average/mean of something, you are likely to get some other location measure, like the median or mode. Some of this might be a heuristic: it's easier to mentally estimate the middle/most common item than it is to keep a running sum, and for many distributions, you get a similar answer. Some of it might be due to fogginess over the definitions. And, of course, these other summary statistics are often closer to what people regard as a `typical' value, especially if there's a long tail, so it

On the other hand, suppose we had some data like this

    X=[2, 2, 2, 4, 4, 8, 16]

If I asked you what the average of X was, the answer I'm expecting is "5.4", or perhaps "the median is 4", "the mode is 2", etc. I would be surprised if you just answered "2" or "4", and once I figured out what you did, I would find it annoyingly pedantic.

I've worked with a lot of different people from different backgrounds, and I don't think anyone has ever used (unadorned) average to mean something other than the mean. Perhaps your experience is different.

Ah.

Alright, this is rooted in a confusion between the normal use in statistics and the normal use in human speech.

Absolutely, average-without-qualifications means the mean, if we're going to be handed a list of actual numbers and expected to produce another number from them.

But especially for highly right-tailed distributions, when people talk about the average, they mean something more like the median, if there's a significant difference.

I would find it annoyingly pedantic if someone said the average net worth in Jeff Bezos' municipality was 60mm, if the median was closer to 0.75mm. If I was handing someone an Excel spreadsheet of tax returns, I would of course tell them that we needed the median. Or the mean but in this circumstance I wouldn't use the word 'average' because of the wide skew. If I did anyway, yeah I would probably get the mean back.

That's how average works in statistics, but not in common speech.

Whatever 'scholarly work' does or doesn't do, journalists certainly interchange them; sometimes leaving a hint like the implied distinction between 'the average <trait>' (mean) and 'the average person's <trait>' (median; sometimes mode for physical discrete things). Also, though, that can just be sloppy and have no intentional implication, misleading depending on the reader.

"Almost all of us have an above average number of legs."

Maybe. Body brokers are companies that own cadavers and sell them for medical research. The people who own these and similar companies have large numbers of legs and probably raise the average number of legs more than the few people who have one or fewer legs.

If we were betting on average leg ownership in the US I'd bet on slightly more than 2.

Your argument doesn't make sense.

Those legs came from people which had at most two of them. They don't manufacture legs or whatever.

That raises an interesting philosophical question, do you have to be alive to retain ownership?

I would say no, but in this case I think only "attached legs" should count.

But those people are dead. So if you count up all the live legs, which will be slightly less than 2*live people, and then add in the dead legs, this may be somewhat more than 2*live people. And since the humor in GP comment is attributing the "having" of the legs to the owners of the cadavers, the denominator remains 'live people'. Thus the average number of legs to "have" is greater than 2.

Why do you count dead legs, but choose not to count the bodies they're attached to?

Or if you chop them ... does the rest of the body cease to exist?

And if some of this chopping happens. Is it more likely that the legs or body is destroyed? I would guess that more of the bodies are stored than the legs... But now if we extend to organs, heads and brains... How do we calculate those? Like do we need complete sets, or something less? Or is sufficient mass enough to count as one unit.

Because the dead person they were attached to doesn't answer polls, nor own much of anything.

But I suppose a live person can also own a bunch of torsos. The statement however only pertained to legs.

Yes, the legs come from people who had at most two but the people who own the body brokers now have those legs. For simplicity let's say person X is the sole owner of a body broker that sells cadavers to medical schools. If a school calls up X they may ask how many legs he has, and may give an answer like "I have 100 legs" (plus the approximately 2 legs X is likely not willing to sell).

On subjective qualitative questions, the average should probably be above 50% because everybody has different scales and are probably following their own scale better than average. eg. If you believe good driving means following traffic laws, you probably follow traffic laws better than average. If you believe good driving means low lap time on a race track, you might have a better lap time than average.

It says "average" not "median" so it's not necessary for the result to be 50/50 even if everyone was perfectly honest.

When it comes to personality traits/skills, average has to refer to the median. I can't think of a qualitative way to do it otherwise.

You can sort the results by agreement percent to see which questions are most and least skewed. Interestingly one of the most precisely balanced is "50% of participants think they are better looking than average."

77% think they are smarter than average.

That's part of the Lake Woebegone effect.

For me it's different, I think I'm smarter than average 77% of the time.

I believe in this. Smarts are more like a distribution curve, even in a single individual.

There are areas I am in the 1 percentile, I think I can say without exaggeration. Those areas I seem to have insights in without effort, coupled with thousands of hours of focus.

But I experience a high cost of many things I do very very badly compared to almost EVERY SINGLE PERSON I know.

I am not alone in this assessment of myself. Friends & family all agree.

My many areas of remarkable incompetence, besides occasionally causing me great shame, make it very clear to me that everyone I know or meet has something to offer, at least to me!

There's so many facets to intelligence. There's a lot of areas that I'm more competent than most in and I learn very quickly. Then there's things like math where I have plenty of education, but the simplest real-world applications throw me for a loop. Add in frequent blonde moments and I can go from looking like the smartest person in the room to the stupidest in no time.

My definition of dumb is people who don't agree with me. So it's safe to say I'm basically Einstein ;-)

Smarter at what? Smarter at the things you are good at of course and there are lots of people who are not good at the things you are good at, so you consider yourself smarter than average.

If you asked people if they were smarter at everything than average what would they answer?

It could well be true that 77% of people are smarter than average if intelligence is a heavily skewed distribution.

Most people think they are better drivers than average.

Right, but some of us know we are. :)

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