Half of the People on this political forum are below average...

Half the people on this political forum are below average compared to the other half of people on this political forum.

That is...

...If the people on this political forum are normally distributed-

According to the Central Limit Theorem, in a normal distribution, the mean median and mode are all the same thing

The only requirement, there has to be a sample size of at least n = 30

 

Since you are the observer and the observed, and you sit outside the average by wide margin, should you regard yourself as an outlier?

 

I should also warn you that if you compare half the posters to the other half and there is an uneven number of posters, you could end up with half a person. This thread could get shut down for promoting mathematical violence.

 

Half the people on this forum like a cold glass of chocolate milk with their scones. The other half are crazy.

 

So that's in reference to what exactly?

Maybe hieght?

 

Mathematically I suppose, but with a big assumption and no context other than who the subjects are ... so implications are unclear.

 

You forgot that some might sit exactly on the median so they are neither above nor below average.

 

The joke is you can say that about any population.

Half of the hockey players in the NHL are below average compared to the other half of the hockey players in the NHL.

Half of Physicists are below average compared to the other half of Physicists.

 

Good Point

 

That could be said about any group in reference to itself.

 

There really isn't a way to make this meaningful.

You could say this about any population.

You could say it about Nobel Laureates.

 

How about if I were to say...

Half the people on this political forum are above average compared to the other half of people on this political forum

 

For any collection of people, you can apply a test, sort the scores, find the midpoint in the scores and there you have it - half above and half below.

 

As the say, the average human has one breast and one testicle.

 

lol the mode confounds things a bit.

 

True, but it doesn't make the comparison meaningful in any way. The problem isn't in which definition of average is used.

 

True. My joke works because in a normal distribution, according to the central limit theorem, the mean and median are the same.

The median is the central value.

 

That has nothing to do with why it fails.

It fails because there is always a midpoint. Plus, it doesn't even say anything about the distribution of scores.

 

Half the people here are below median.

 

Not me - I is purrrfect!

 

Again, that is a totally meaningless statement.

 

It's factually accurate by the very definition of median. Average is not necessarily evenly divided.

 

True.

On the other hand, your "evenly divided" idea IS getting to new information.

One can look at how closely measured results are clustered around the average (how alike people are) or whether one side of the average is spread out more than the other, or whether the spreading of the results of people on this board compare to the spreading of the general population in America.

But, that takes more than just calculating an average.

 

The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution. Where the variables are independent and identically distributed random variables with the same arbitrary distribution, zero mean, and variance �2 and � is their mean scaled by �

The normal distribution with density �(�) (mean � and standard deviation 0}">�>0) has the following properties:

· It is symmetric around the point �=�, which is at the same time the mode, the median and the mean of the distribution.[18]

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest.

In a normal distribution the mean (Average) and the Median (the middle value) are the same thing

 

And that's why the OP is factual, but meaningless.

It doesn't say anything about the population.