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Main => General Board => Topic started by: Coxx16 on January 18, 2010, 09:01:09 PM

Title: Standard Deviation Question...
Post by: Coxx16 on January 18, 2010, 09:01:09 PM
 I have seen a few posts about not ever seeing 6 standard deviations. I do not quite understand why 6 standard deviations in roulette.
Title: Re: Standard Deviation Question...
Post by: Marven on January 19, 2010, 12:57:44 AM
Because (when applied to a significant sample size) it's an extremely rare event.

Here you can see the normal distribution of random outcomes in terms of standard deviations (horizontal axis):

(https://www.vlsroulette.com/proxy.php?request=nolinks%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2F8%2F8c%2FStandard_deviation_diagram.svg%2F500px-Standard_deviation_diagram.svg.png&hash=3f3e4764a4b08e67cb09b419f722c4f7a3d47513)

34.1% fall between 0 and 1σ (standard deviations)
13.6% fall between 1 and 2σ
and so on.
Title: Re: Standard Deviation Question...
Post by: TierPlayer on January 19, 2010, 01:27:49 AM
I recall only using up to 4 std.devs when programming statistical apps.
In wikipaedia you will find  this table:

1   0.682689492137
2   0.954499736104
3   0.997300203937
4   0.999936657516
5   0.999999426697
6   0.999999998027

68% of values (see line 1 of the table) will be within 1 std.dev. away from the mean.
The "usual" 4 std.devs. will cover the 99.99% of cases (ie. only 1 in 10,000 will be outside this range)
With 6 std.devs.  the range is so wide that only 1 in 1 billion random values will fall outside.