Re: Dice
Re: Dice
- Subject: Re: Dice
- From: Graff <email@hidden>
- Date: Tue, 26 Oct 2004 14:28:20 -0400
On Oct 26, 2004, at 1:48 PM, Emmanuel wrote:
At 12:46 PM -0400 10/26/04, Graff wrote:
I just ran it 1000 times and got the following distribution:
1 161
2 167
3 173
4 170
5 169
6 160
std deviation = 5.16
So no, it doesn't seem to be perfect but it's probably good enough
for most applications.
Out of curiosity, what would the std deviation be if the random was
perfect?
A perfectly even distribution would be for every value to show up the
same number of times. In that case the std deviation would be 0.
The standard deviation means that 68.3% of the values were plus or
minus so much of the mean of the data set. If you double the standard
deviation then 95.4% of the data will be within that deviation, if you
triple it then 99.7% will fit within that.
Thus, for the numbers I gave:
68.3% of the data will fit within 161.5 - 171.9 (166.7 ± 5.16)
95.4% of the data will fit within 156.4 - 177.0 (166.7 ±10.32)
99.7% of the data will fit within 151.2 - 182.2 (166.7 ±15.48)
To calculate standard deviation you first get the mean of your data
set. You then calculate the deviation of each element from the mean
and square it. You sum up these squared deviations and divide them by
the number of items in your data set. Finally you take the square root
of this number.
So if your numbers are {161, 167, 173, 170, 169, 160}
n = 6
sum = 1000
mean = sum / n = 1000 / 6 = 166.7 (approximately)
deviations are:
(161 - 166.7)^2 = (-5.7)^2 = 32.5
(167 - 166.7)^2 = ( 0.3)^2 = 0.1
(173 - 166.7)^2 = ( 6.3)^2 = 39.7
(170 - 166.7)^2 = ( 3.3)^2 = 10.9
(169 - 166.7)^2 = ( 2.3)^2 = 5.3
(160 - 166.7)^2 = (-6.7)^2 = 28.1
sum of deviations = 116.6
standard deviation = square root (116.6 / 5)
( I used 5 here instead of 6 because it gives you a better standard
deviation to use n -1 instead of n)
standard deviation = square root (23.3)
standard deviation = 4.8 (approximately)
Rounding errors account for different value here, I calculated the
previous standard deviation in Excel because I'm lazy. :)
You can read more about standard deviation here:
<http://www.med.umkc.edu/tlwbiostats/variability.html>
- Ken
_______________________________________________
Do not post admin requests to the list. They will be ignored.
Applescript-users mailing list (email@hidden)
Help/Unsubscribe/Update your Subscription:
This email sent to email@hidden
| References: | |
| | >Re:Dice (From: Kevin <email@hidden>) |
| | >Re: Dice (From: Adrian Milliner <email@hidden>) |
| | >Re: Dice (From: Robert Poland <email@hidden>) |
| | >Re: Dice (From: Graff <email@hidden>) |
| | >Re: Dice (From: Emmanuel <email@hidden>) |