math guys: how does one figure out a standard deviation

[Lawrence of Arabia]

anything else you have to say to me before I go to bed?

[KrazyHorse]

No, that about sums it up.

[KrazyHorse]

I need to remind myself to bump this tomorrow so that people with a clue (other than myself and Kuci) can enjoy it.

[Jon Miller]

Hey, I read it...

I was going to post to, but I thought you did your normal good job (not in your first post) so didn't.

Jon Miller

[KrazyHorse]

Sorry. Didn't mean to cut you out of that.

[snoopy369]

Us econ folks don't need to learn statistics this well ... and if you're becoming an economist and not a math/stat person, it's probably because you don't enjoy the math this much

That said, Standard Deviation doesn't approach zero ever [unless it is of a set of identical items] iirc. It's not supposed to be a measure of the total variance of the set's mean from the true mean, but rather a predictor of how far from the mean any given single item in the set is likely to be.

Lawrence, if you actually know statistics, you are probably confusing this with something else.

[SpencerH]

I just love these math threads.

[self biased]

what if i'm only looking for certain values? for example, what if i'm looking for a 3+ on a d6 on 15 dice? odds say that ten of those fifteen will be a three or better. dropping some dice now i get: 2, 3, 1, 1, 2, 2, 1, 4, 6, 2, 4, 6, 6, 6, and 1. more than half my values are less than my target of 3+.

is there any way of shortcutting this? more often than not, we're looking for 3+ or 4+ on anywhere from four to thirty-six dice.

[Kuciwalker]

Originally posted by KrazyHorse
They spoil the kids at Hopkins. We're combination graders, tutors and assistant professors.

Same here.

I don't know some of my professors, either...

[Kuciwalker]

Originally posted by snoopy369
Us econ folks don't need to learn statistics this well

The mistake here is elementary.

That said, Standard Deviation doesn't approach zero ever [unless it is of a set of identical items] iirc. It's not supposed to be a measure of the total variance of the set's mean from the true mean, but rather a predictor of how far from the mean any given single item in the set is likely to be.

So close, and yet so far. The standard deviation of the set's mean does approach zero.

[Kuciwalker]

Originally posted by self biased
what if i'm only looking for certain values? for example, what if i'm looking for a 3+ on a d6 on 15 dice? odds say that ten of those fifteen will be a three or better. dropping some dice now i get: 2, 3, 1, 1, 2, 2, 1, 4, 6, 2, 4, 6, 6, 6, and 1. more than half my values are less than my target of 3+.

is there any way of shortcutting this? more often than not, we're looking for 3+ or 4+ on anywhere from four to thirty-six dice.

15 choose 10 divided by 2^15 for 10 4+'s. You'll need a calculator.

In general, if you're making n rolls and you want to know the probability of getting k of some result (with a probability p of getting that result on any single roll, e.g. p=1/2 for a 4+), use the formula (n choose k) * p^k * (1-p)^k.

edit: (n choose k) = n! / ((n-k)! * k!), where ! = factorial.

[Kuciwalker]

Also, if you're making n rolls with a probability p of success then your average number of successful rolls will be n*p and the standard deviation will be sqrt(n*p*(1-p)).

[snoopy369]

Originally posted by Kuciwalker

That said, Standard Deviation doesn't approach zero ever [unless it is of a set of identical items] iirc. It's not supposed to be a measure of the total variance of the set's mean from the true mean, but rather a predictor of how far from the mean any given single item in the set is likely to be.

So close, and yet so far. The standard deviation of the set's mean does approach zero.

Yes, that would be the variance of the set's mean from the true mean... the standard deviation itself does not approach zero [unless the set is identical items].

[Kuciwalker]

Um. You still don't quite get it.

The mean of a set of n items is a random variable. It has a variance which is an inherent property of that variable (and is decreasing in n). Any individual sample is also a random variable, with a variance that is an inherent property of that variable. If you don't know the variance already you can estimate it by taking a large number of samples and calculating the sample variance, which will approach the true variance as you take more samples.

[self biased]

kuci: i'll digest your post after i've had some sleep.
All: thanks for the help and/or backbiting.