AKA The
Normal distribution.
The statistical distribution. Its
importance flows from the fact that :
- Any sum of Normal distributed variables is itself a Normal distributed variable
- Sums of variables that, individually, are not Normal distributed tend to become Normal distributed (asymptotically)
You won't find many
stochastic variables on this
planet that are not Gaussian of
nature.
Examples
- The number of single girls in a bar (when measuring eg. every day at noon in the same bar
- The number of cars passing a point on the highway (go ahead: Spend an hour a day - a 1000 days in a row and see the nice distribution curve smoothing more and more until it is perfectly Gaussian
- The height of Japanese people
- The number of bytes/links/images on a homepage (this one would be easy to check
Let Z be a Gaussian distributed stochastic variable with mean=0 and standard deviation=1.
Interesting values of Z follow:
- Prob(|Z|>=1) <= 0.3173105
- Prob(|Z|>=1.96) <= 0.0499957
- Prob(|Z|>=3.29055) <= 0.0010000
For the not so much into
mathematics reader:
The small list shows that the probability of
finding a value in the
data set that is more than 3.29055 times higher than the
standard deviation is 1 in a thousand.
So - if all cars on the highway are doing 50 plus/minus 10, only one car in a thousand will do more/less than 50+10*3.29055 which is about 83.
(Or to use the first
entry in the list: The
chance that there are more
single girls in a bar than normally is 31.7%/2= 15.8% - go push your luck!)
Well folks - that's all for now.
Thanks for letting me use this place as a test stage for my
thesis, where I'm actually
discussing small
uninteresting matters like this (
focusing a little less on single girls, though)
And to ariels - yes - you're absolutely right. You'd also never find a car going faster than the speed of light, even though it SHOULD happen de temps en temps if the velocities were truly Gaussian distributed. Forgive my engineer-geekish way of looking at things (eg. 0.98 is not close to 1, it IS 1)