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OK, it is funny.

The I Am Ready To Settle Down Now Burger:

Yeasty!
UkraineIsTotallyFucked says

The I Am Ready Too Settle Down Now Burger:

Ironically, he is showing stupidity by confusing mean (average) with median.

HeadSet says

Ironically, he is showing stupidity by confusing mean (average) with median.

How?

UkraineIsTotallyFucked says

HeadSet says

Ironically, he is showing stupidity by confusing mean (average) with median.

How?

The 'mean' is the midpoint at which fifty percent of data points are above and fifty percent below. The data points can be weighted, however, so that the 'average' can be some value at variance with the mean. The 'average' value, for instance, might be at the data points that are forty percent below and sixty percent above due to weighting, or some other point.

People use them interchangeably but they are not the same thing. He should have said 'mean' rather than 'average'.

UkraineIsTotallyFucked says

HeadSet says

Ironically, he is showing stupidity by confusing mean (average) with median.

How?

Mean (average) is summing up n numbers and dividing by n. The average is rarely the middle point. The point in a group of numbers where half are below and half are above called the median.

HeadSet says

Mean (average) is summing up n numbers and dividing by n. The average is rarely the middle point. The point in a group of numbers where half are below and half are above called the median.
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So?

You can derive a number from an average and apply a median to that, too. It's deriving a median
from a subset of numbers, so what?

UkraineIsTotallyFucked says

You can derive a number from an average and apply a mean to that,

?? "Mean" and "average" are synonymous.

HeadSet says

UkraineIsTotallyFucked says

HeadSet says

Ironically, he is showing stupidity by confusing mean (average) with median.

How?

Mean (average) is summing up n numbers and dividing by n. The average is rarely the middle point. The point in a group of numbers where half are below and half are above called the median.

Standardized tests like the SAT and the Stanford-Binet IQ test are taken by millions of people. As such, the law of large numbers applies; namely, the distribution of the standardized distribution of scores (score - mean)/(std. deviation of score) converges to a normal distribution with mean 0 and standard deviation of 1. A normal distribution is symmetric about its mean; i.e., mean=median.

In this case, Carlin is right, although to @Headset's point, it might be coincidental if Carlin is unaware of the law of large numbers and how standardized test scores are distributed.

Disclosure: Statistician by training.

stereotomy says

Standardized tests like the SAT and the Stanford-Binet IQ test are taken by millions of people. As such, the law of large numbers applies

Good point. I did not think that IQ would fit a normal distribution, but I looked it up and you are correct. I suspect that is because, as you said, the large n and also because of the relatively small number of possible scores (about 200?).

HeadSet says

stereotomy says

Standardized tests like the SAT and the Stanford-Binet IQ test are taken by millions of people. As such, the law of large numbers applies

Good point. I did not think that IQ would fit a normal distribution, but I looked it up and you are correct. I suspect that is because, as you said, the large n and also because of the relatively small number of possible scores (about 200?).

It applies generally, even to discrete distributions (like the Poisson distribution which has as its basis the counting numbers 0,1,2, . . . ). As long as N is sufficiently large, any distribution of the mean of a sample from a population/source distribution will converge to a normal distribution. IIRC this is the weak law of large numbers. There is a strong law of large numbers as well.

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stereotomy says

any distribution of the mean of a sample from a population/source distribution will converge to a normal distribution.

I presume you are referring to taking a sample distribution of sample means, and that would plot out as normal regardless of the actual distribution of the original data. I used to do that trick in order to force a normal so that I could use normal tools, and not have to work with Poisson, Chi, and the like. Funny how you mentioned Poisson, because that is what I assumed the IQ distro would look like before looking it up. But then, my experience has been with thousands or less of data points (traffic, call center, academics), and I rarely saw anything that came out as a normal distribution. Long ago, but now that I think about it, the whole point of those other distributions was to extract data when one did not have the money or time to collect enough data points to generate a Normal distribution naturally.

@Headset,

I think we're talking about the same thing. If you take a very large sample from a distribution and calculate the mean, then do it again and again, you'll get a highly symmetric normal distribution for the means. If you take multiple smaller samples and compute the mean, you'll get a distribution of the means that is almost normal, but not quite.

You might be talking about the Strong Law of Large Numbers - almost sure convergence, as opposed to the Weak Law - convergence in probability.

If you have messy data, you can use bootstrap, jackknife or other resampling techniques to simulate larger samples. Generally, to get the "easy" solution where you can run inference on a normal distribution, you need either 1) a distribution which is approximately normal, in which case you can get by with a smaller sample size (think binomial with p=0.5) or 2) a very large sample size for distributions which are highly skewed or otherwise ill-behaved (Cauchy).

Anything I said before does NOT apply to most other statistics. If you need upper or lower quantiles of the distribution, then you'll have to probably use empirical quantiles (rank-ordering the values in your sample) as opposed to using normally distributed quantiles. Quantiles are almost always necessary for inferential statistics (proving a hypothesis) as opposed to descriptive statistics (describing the distribution). With cheap computing, Nonparametric Statistics is almost as good nowdays.

Interesting historical fact - R. A. Fisher (one of the titans in the field) ended up exploring parametric statistics because it was too hard to calculate nonparametric statistics by hand, at least in the late 1800's / early 1900's. He thought parametrics were an excellent approximation to real, nonparametric statistics.

Just for those who can't tell, that's a John Deere cotton picker.

stereotomy says

He thought parametrics were an excellent approximation to real, nonparametric statistics.

That reminds me of a funny incident.
Right after I got my MS I saw a one of the professors in a local bar. He was a big loud blond Polish guy with PhD. I sat on the stool next to him and told him about one of his journal articles I read. He beamed a bit and sipped his beer, but then I told him "You used non-perimetric statistics on ordinal data." His eyes got wide as he went into thought and set down his beer. Then he turned to me and said "I did not." Then I borrowed a pen from the babe bartender and wrote out on a napkin what I was referring to. He then countered with his own napkin scribbles, and we went back and forth for quite a while, where his strategy was to go off into complex tangents to obscure his blatant mistake. His loud personality garnered attention and couple of tipsy guys gathered behind him cheering him on, and I had a couple of supporters get behind me. I eventually conceded (although I was right) so he could save face. His team cheered and one of the guys behind me said "You really lets us down, man." That was the most fun I ever had in a bar.

stereotomy says

Just for those who can't tell, that's a John Deere cotton picker.

Still could use a slave to drive it.

Back in my day, women would work three jobs to have their boobs augmented...

Ceffer says

People use them interchangeably but they are not the same thing. He should have said 'mean' rather than 'average'.

Actually, he might have meant the mode of intelligent people, which doesn't know and doesn't give a fuck what average really means.

Had Carlin said, "Think about how stupid the median person is..." It wouldn't have been as funny.

In these difficult times, where our national identity is under threat, we must stop feeling guilty about who we are. We are not “kafir,” we are not guilty. Like other peoples, Germans have the right to remain who they are. Germans must not become French, nor Dutch, nor Americans, nor Turks. They should remain Germans. When the Turkish Prime Minister Erdogan visited your country in 2008, he told the Turks living here that they had to remain Turks. He literally said that “assimilation is a crime against humanity.” Erdogan would have been right if he had been addressing the Turks in Turkey. However, Germany is the land of the Germans. Hence, the Germans have a right to demand that those who come to live in Germany assimilate; they have the right – no they have a duty to their children – to demand that newcomers respect the German identity of the German nation and Germany’s right to preserve its identity. - Geert Wilders, Speech in Berlin on October 2, 2010

Ceffer says

gabbar says

Nina Turner is a Democratic politician from Cleveland, Ohio area

LOL! Ghetto pathogen philosophy: grow up with Mama beating it into your thick hide and skull that robbing Whitey is honorable. Then, puzzle when the doors clang shut on you in prison. Moral imbeciles with a Soros pay stub are still moral imbeciles.

This is the part that seems to be changing…less lockey uppy.

LOL! "Fruity Pebbles of Rockefeller Poison, in toxic Amazon Frog colors with pedo cartoons!"

They love their ritual humiliations and processed food slaps to the face to the Idiopolous.

Any allocation to anything called 'homeless' or virtue signaling as such is a laundering scheme.

Actually, this makes for good Islamic propaganda. "Would you rather have women in Hijab and related modest dress, or have your daughters devolve into this sick Western degeneracy?"