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 Originally Posted by seven-deuce
Thanks for responding, feel free to wave the white flag any time.
Nevar!
Originally Posted by seven-deuce
So the variance is always a squared number due to the calculation you perform to obtain it. And cm^2 implies area, like the area of a square is x cm^2.
Yes.
Originally Posted by seven-deuce
Is the area the variance is referring to the area of the bell curve?
No. Every probability distribution has an associated Cumulative Distribution function, which is the integral of the prob. dist.
An integral gives the area under the curve (of whatever function it integrates).
Originally Posted by seven-deuce
So the larger the area the wider the dispersion of the data around its mean? The higher the variance figure is the more dispersed the data is about its mean, and the lower the variance figure is the tighter data is clumped around the mean?
Yes and yes (and yes).
Nit picking: Variance is a value, or scalar. A figure is a 2D object (a form is a 3D object).
Originally Posted by seven-deuce
Only when you square root the variance in order to get the standard deviation you're removing the square and hence converting it back into its original units mm, years or whatever it happened to be?
And are they "the same" because they're the same information expressed in a different "format" for lack of a better word.
Yes.
Originally Posted by seven-deuce
If my assumption about the area was correct, then variance is the area the data points cover around the mean, and the std deviation is, well I dunno what it is yet.
In your example, the only reason it's an "area" is because the data was in length units, and length units, squared, is an area.
Don't put too much weight on my use of the word area as pertains to variance.
If we were measuring the surface area of the dogs (why? STFU and measure dem bitches!), then the variance would be in mm^4... and we'd want to take the square root so that it was in mm^2, like the areas we measured in the data set.
It's about the apples-to-apples comparison.
Not only do the units match, but the value is directly cooperative with our mean.
So, if our mean value is 20 with a stdev of 5, then that's easy to immediately read off:
That's 20 +/- 5 @ ~68% CI and 20 +/- 10 @ ~95% CI
Originally Posted by seven-deuce
A good portion of that could be pure garbage, but I know how to calculate the variance and std deviation now, and basically understand what they indicate. The larger the variance is, the larger the std deviation will be. The smaller the variance, the smaller the std deviation. And large variance = a flatter curve, while small variance produces a steeper curve?
Not much garbage, and it was my use of the word "area" that started it. Other than that, yes, yes, yes -
*ugh*
- since we're using cooperative distributions.
There are distributions with no well-defined mean or variance, but thankfully they do not concern us in poker.
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