Hiya, I'm getting confused with standard deviations and more!

I'm stuck with question 13 on this link, where on earth did that formula come from and when do I use it? - https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FAQA%2FAS-Paper-2%2FMA%2FJune%202020%20MA.pdf

and also 13C on this link - https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FAQA%2FAS-Paper-2%2FMA%2FJune%202019%20MA.pdf I really don't get why they divide by a number one less than the samples given?

I'm stuck with question 13 on this link, where on earth did that formula come from and when do I use it? - https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FAQA%2FAS-Paper-2%2FMA%2FJune%202020%20MA.pdf

and also 13C on this link - https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FAQA%2FAS-Paper-2%2FMA%2FJune%202019%20MA.pdf I really don't get why they divide by a number one less than the samples given?

Original post by mitostudent

Hiya, I'm getting confused with standard deviations and more!

I'm stuck with question 13 on this link, where on earth did that formula come from and when do I use it? - https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FAQA%2FAS-Paper-2%2FMA%2FJune%202020%20MA.pdf

and also 13C on this link - https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FAQA%2FAS-Paper-2%2FMA%2FJune%202019%20MA.pdf I really don't get why they divide by a number one less than the samples given?

I'm stuck with question 13 on this link, where on earth did that formula come from and when do I use it? - https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FAQA%2FAS-Paper-2%2FMA%2FJune%202020%20MA.pdf

and also 13C on this link - https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FPapers%2FAQA%2FAS-Paper-2%2FMA%2FJune%202019%20MA.pdf I really don't get why they divide by a number one less than the samples given?

that variance equals npq or np(1-p)?

Note: None of the following is examinable, but for satisfying curiosity... I think.

For the first one, basically what mqb says. If you want to know the derivation of it, see here. P.S. my favorite is to use something called moment generating function (mgf).

(EDIT: Whoops I've linked to expectation instead of variance, but the techniques are effectively the same, noting all we want to find are E[X] and E[X^2].)

For the second question, The sampled variance is indeed dividing by one less than than the number of samples - that's the formula. I don't know how much you need to know for exam sake, but it's something to do with (un)biased estimators for the variance, and how dividing by one less is actually the unbiased one. Sorry I can't help you more - I'm just pulling off my statistics knowledge eons ago.

But the upshot for exam, I'd assume, is to just remember by heart; or if you happen to have a formula sheet, use it.

For the first one, basically what mqb says. If you want to know the derivation of it, see here. P.S. my favorite is to use something called moment generating function (mgf).

(EDIT: Whoops I've linked to expectation instead of variance, but the techniques are effectively the same, noting all we want to find are E[X] and E[X^2].)

For the second question, The sampled variance is indeed dividing by one less than than the number of samples - that's the formula. I don't know how much you need to know for exam sake, but it's something to do with (un)biased estimators for the variance, and how dividing by one less is actually the unbiased one. Sorry I can't help you more - I'm just pulling off my statistics knowledge eons ago.

But the upshot for exam, I'd assume, is to just remember by heart; or if you happen to have a formula sheet, use it.

(edited 1 month ago)

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