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

Ah well, it was a joke. It wasn't meant to be taken seriously but it made me think, and it made me think hard and thinking hard is a good thing especially when it comes to Math.

Math is hard to debate but look what we did here.

We debated Math!

 

PF is rather like the children from Lake Woe-be-gone - way above average.

 

I don't believe we debated math. The issue was with how it was applied to the real world.

 

I'm not sure height would work but Height is a good example of calculating the standard deviation of a population.

The standard deviation equation is a very good example of Applied Mathematics.

 

Half the people in the world are below average compared to the other half of people in the world.

 

Not Really.

 

More math that means absolutely nothing to the real world.

 

Well WillReadmore if you want math that means something in the, quote, "real world" How about the math used to derive the standard deviation of a population. I'm sure you already know standard deviation is the average amount the variables in your population are from the mean.

OK, I will show you how standard deviation is calculated.

A normal distribution is a lot like a number line in algebra with variables to the left of zero being negative and numbers to the right of zero being positive, except in a normal distribution the 0 in the number line is replaced by the average of the variables in your study,

The numbers to the left of your average are still negative.

But there's a problem.

Let's say you're calculating the height of a population.

For one thing, there is no negative height, but more importantly the negative variables to the left of the mean will cancel out the positive values to the right of the mean, distorting not only your variables but also the standard deviation of height in your population

So, what can you do in this circumstance.

You square all the values in your population, even the positive numbers to the right of the mean.

Two negative numbers multiplied by each other creates a positive number.

You've calculated out the negative numbers, so that's taken care of. But you just multiplied your variables by each other distorting their distance from the mean.

So what do you do???

You take the square root of all the variables which gives you an accurate representation of your variables distance from the mean.

Then you simply count all the variables in your population and use that number to divide the variables you squared and determined the square roots for which gives you the standard deviation, the average distance all the variables in your study are from the mean

 

Now you are changing the subject.

Remember that I pointed out there are ways that math CAN be used to tell you something meaningful about a population. In fact, it can show a LOT about a population.

Also, recording height as a difference from the mean is preposterous. Until you've collected the data, you don't know what the mean is. So, how can you use the mean in the way you propose?

 

Really?

 

Standard Deviation is lost on you but don't worry you're not the only one.

Tell liberals the standard deviation of women's intelligence is less than the standard deviation of men's intelligence and watch them freak out and they don't even know what standard deviation is

 

My Asperger's Syndrome means that I have Emotional Quotient far below average. Thus, I can not fit into Society.

My IQ is average -- thus I am nether a fool nor a genius.

 

To calculate an average add all the values of the variables together then divide that value by the number of variables you added.

And standard deviation is the average amount the variables in your study are from the mean.

Take IQ scores. The average IQ is 100 and the standard deviation on IQ tests is 15. Using the central limit theorem, you know 68% of the variables will be within one standard deviation of the mean. Therefore, 68% of your variables will be between an IQ of 85 and an IQ of 115.

And 95% of your variables will be within two standard deviations of the mean. Therefore, 95% of the variables in your study will be between an IQ of 70 and an IQ of 130.

And 97.7% of the variables will be within 3 standard deviations of the mean.

 

This has various problems, starting with the issues surrounding various attempts to create tests of "IQ" that might be considered meaningful in some way.

You can't guess the standard deviation of tests given to some population.

 

Often in Statistics, a sample standard deviation is calculated when variables used to calculate the population standard deviation are unknown.

 

That's why it's a good joke.

 

The standard deviation indicates the extent of randomness of individuals about their common average. The deviations are the distances from each data value to the average. Positive deviations represent above-average individuals, and negative deviations indicate below-average individuals.

It's like a number line in Algebra. Except instead of 0 being the median value, the average is the median value.

 

Well on this site half are funnier than the other half.

 

Half the people on this political forum have below average funnyness compared to the other half of people on this political forum who have above average funnyness.*

 

You're going to have to explain that one.

 

This is true regardless of the population. It's true for the Supreme Court justices. It's true for every other group imaginable.

The problem is that it is a totally meaningless statement.

 

No, its a gross misunderstanding.

Lake Woebegone tales made a joke about it, but that joke tied together issues of society, the feelings of parenthood and common understanding in a way that was actually funny - and universally recognized as being so.

 

Well a good sense of humor is a sign of intelligence.

 

It's hard to explain only with text without equations but:

Whenever you wish to generalize beyond the immediate data set to some larger population (either real or hypothetical), be sure to use the sample standard deviation



Both formulas add up the squared deviations, divide, and then take the square root to undo the initial squaring of the individual deviations. For the sample standard deviation, you divide by n − 1 because the deviations are computed using the somewhat uncertain sample average instead of the exact population mean.

The variance is the square of the standard deviation. It provides the same information as the standard deviation but is more difficult to interpret because its unit of measurement is the square of the original data units (such as dollars squared, squared miles per squared gallon, or squared kilograms, whatever these things are).

Many equations in inferential statistics use the sample standard deviation.

 

You switched your argument. Your argument was that AVERAGE says something meaningful.

I'm glad you are making progress.