Average is median

Stormtroper

This is a quote with a fairly high score over someone asking something hardly obvious. No, bash.org not the only place I've seen people assuming half of anything has to be above/below average and vice versa.

I'm mostly posting this because I haven't gotten the chance to write the "most humans have an above average number of legs" retort.

Related: When people interpret "Average" in a mathematical sense as "common".

DYRE

Median isn't the only possible way of determining an average, but it's one of them.



And if you're using that way to determine an average, most humans certainly would have an average amount of legs.

ClockworkUniverse

^Incorrect. Some humans have one leg or zero, so the average is 1.99somethingsomething.

DYRE

Right, but I mean if you take the median, it should be two.  Unless there are an incredibly large number of people with fewer than two legs.

The mean will be less than two though, of course.

Unless there are a lot of 3-legged people...

ClockworkUniverse

Ah. I see. This is why vague, confusing grammar constructions like "that way" shouldn't exist.

Stormtroper

Arithmetic mean all the way, baby.

DYRE

Nah.  That's just one way to take an average.  And it really doesn't make sense a lot of the time.

Like, well, with humans and legs.  2 legs/human is a much more sensible answer than ~1.999999 legs/human or whatever.

When you're trying to find the "average" of some data, you should generally use whatever method results in the answer that makes the most sense, unless you have some other reason to choose one method over another.

Stormtroper

Alright, alright, the legs thing is out.

The rest of it still bugs me.

Longfellow

I always used "average" to mean the mean, never the median or any other measure of the "middle" of a distribution.

DonZabu

They always referred to the mean as "the average" in elementary school. It never even occurred to me that people might call the median "the average".

Central Avenue

^ Same here.

DYRE

Still, you do have all these different ways of calculating the average of a set of data.

Arithmetic mean is the most common one, of course, but others have their applications too, and they aren't any less of an "average" even if they aren't the most commonly used method.

Longfellow

Well, we're just talking words here. I have always understood "average" to be another word for "arithmetic mean," which is probably a redundant usage that leaves a gaping hole in my vocabulary for "the middle of a distribution as measured in any way", but I'm just telling you how I learned the language.

Central Avenue

^ Exactly. In elementary school I was taught that "average" and "mean" meant the same thing.

ClockworkUniverse

I too thought "average" meant "mean" and all of the other things were just related.

Nyktos

"Average", in common usage, refers (in the context of numbers) to the arithmetic mean. However, in mathematics it can refer to any measure of central tendency.

I'm actually quite surprised people don't know this: in all of my math classes from like grade 7 onward they drilled that into our heads whenever averages were relevant.

Longfellow

Never knew that. Guess my math classes were deficient on the terminology.

In the context of the OP, of course, "average" is used in the layman's (mathematical) sense.

glennmagusharvey

I always knew average, mean, and arithmetic mean to be the same thing.

I wondered why they had to specify "arithmetic" until I discovered the geometric mean years later.

DYRE

And there's also the harmonic mean... apparently!