Two Plus Two Newer Archives Stupid Variance Question
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#1
02-08-2007, 11:36 AM
 SGspecial Senior Member Join Date: Aug 2006 Location: Doctor Razz Posts: 1,209
Stupid Variance Question

I know there are no stupid questions, but this one should be absurdly easy to answer for someone who knows statistical analysis. I want to compute the variance of a population of EV samples, many of which have the same value. For example, I have 1000 samples: 412 of them are -2, 307 of them are -4, 211 of them are -6, and 70 of them are 0 (zero). What's the easiest way to compute the variance of this population?

p.s. Jerrod and Bill, if you're out there, just let me know if this is already in your book and I'll go out and buy it. Well, the 2nd edition anyway.
#2
02-08-2007, 02:09 PM
 bbartlog Senior Member Join Date: Nov 2006 Posts: 882
Re: Stupid Variance Question

- find the average value of your samples
- sum up the squares of all the differences between each sample and the average
- divide this sum by the number of samples less 1 (so 999 in your example)

If you don't want to do it by hand, Excel (and presumably its OpenOffice equivalent) has a nice variance calculation function (VAR).
#3
02-08-2007, 02:12 PM
 _D&L_ Senior Member Join Date: May 2006 Posts: 128
Re: Stupid Variance Question

Take the mean of your sample. (add them up, then divide by number of observations)

For each data point, subtract the data point from the mean, and square the result. (say mean is 5 and data point is 8, you subtract, you get -3, then you square it, so you get 9).

Then for each result from the previous step, add them up, and then divide by the number of data points less 1.

Variance is simply the average of the square of the distance of each data point from its mean.
#4
02-08-2007, 02:16 PM
 bbartlog Senior Member Join Date: Nov 2006 Posts: 882
Re: Stupid Variance Question

412 * (2 - 3.318)^2 = 715.7
307 * (4 - 3.318)^2 = 142.8
211 * (6 - 3.318)^2 = 1517.7
70 * (0 - 3.318)^2 = 770.6

(715.7 + 142.8 + 1517.7 + 770.6) / 999 = 3.15
#5
02-08-2007, 03:23 PM
 SGspecial Senior Member Join Date: Aug 2006 Location: Doctor Razz Posts: 1,209
Re: Stupid Variance Question

[ QUOTE ]

412 * (2 - 3.318)^2 = 715.7
307 * (4 - 3.318)^2 = 142.8
211 * (6 - 3.318)^2 = 1517.7
70 * (0 - 3.318)^2 = 770.6

(715.7 + 142.8 + 1517.7 + 770.6) / 999 = 3.15

[/ QUOTE ]

ok, thanks. Not quite as short a short cut as I was hoping for, but it's not too hard to make a couple extra tables in excel to do it this way.
#6
02-08-2007, 03:50 PM
 bbartlog Senior Member Join Date: Nov 2006 Posts: 882
Re: Stupid Variance Question

If you have Excel, use VAR. Check it up in the documentation. Shouldn't be necessary to create entire tables, the function operates on a range...
#7
02-08-2007, 04:10 PM
 Jerrod Ankenman Senior Member Join Date: Jun 2004 Location: Avon, CT Posts: 187
Re: Stupid Variance Question

[ QUOTE ]
I know there are no stupid questions, but this one should be absurdly easy to answer for someone who knows statistical analysis. I want to compute the variance of a population of EV samples, many of which have the same value. For example, I have 1000 samples: 412 of them are -2, 307 of them are -4, 211 of them are -6, and 70 of them are 0 (zero). What's the easiest way to compute the variance of this population?

p.s. Jerrod and Bill, if you're out there, just let me know if this is already in your book and I'll go out and buy it. Well, the 2nd edition anyway.

[/ QUOTE ]

There is no second edition of our book, as it's only been out for a couple months. This kind of topic is covered just briefly, but other posters here have given you a better answer than our book would.

You should still read it anyway. [img]/images/graemlins/smile.gif[/img]

jerrod
#8
02-08-2007, 04:23 PM
 SGspecial Senior Member Join Date: Aug 2006 Location: Doctor Razz Posts: 1,209
Re: Stupid Variance Question

[ QUOTE ]
[ QUOTE ]

p.s. Jerrod and Bill, if you're out there, just let me know if this is already in your book and I'll go out and buy it. Well, the 2nd edition anyway.

[/ QUOTE ]

There is no second edition of our book, as it's only been out for a couple months. This kind of topic is covered just briefly, but other posters here have given you a better answer than our book would.

You should still read it anyway. [img]/images/graemlins/smile.gif[/img]

jerrod

[/ QUOTE ]

Ah I figured if I left out cookies for you or Bill, one of you would see this and reply! [img]/images/graemlins/wink.gif[/img] I am very curious to read your book, despite all the errata to it posted here (hence the reference to the presumed 2nd edition). One of the things I hope to find discussed there is the "cost" of variance, or how it affects your decisions and therefore your net EV. As it happens I'm also wading into the poker author pool myself, and wanted to see if you or Bill had any pearls of wisdom to lend me on the subject?
#9
02-10-2007, 05:59 AM
 Gonso Senior Member Join Date: Apr 2006 Location: seat zero Posts: 3,265
Re: Stupid Variance Question

The errata is not THAT bad. There's a lot of content in the book, bound to be some mistakes.

I like the small text &amp; use of space, too.
#10
02-10-2007, 12:50 PM
 SGspecial Senior Member Join Date: Aug 2006 Location: Doctor Razz Posts: 1,209
Re: Stupid Variance Question

That's cool. I was just teasing them anyway [img]/images/graemlins/tongue.gif[/img]

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