Stupid Variance Question

[SGspecial]

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.

[bbartlog]

- 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).

[_D&L_]

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.

[bbartlog]

For your example, in your data the average is -3.318.

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

[SGspecial]

[ QUOTE ]
For your example, in your data the average is -3.318.

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.

[bbartlog]

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...

[Jerrod Ankenman]

[ 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

[SGspecial]

[ 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?

[Gonso]

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 & use of space, too.

[SGspecial]

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