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Bryn

which form of standard deviation

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can someone give me a explernation of when to use the form

 

[math]\sigma^2 = \frac{\sum(x-\mu)^2}{n}[/math]

 

and when to use

 

[math]s^2 = \frac{\sum(x-\bar{x})^2}{n-1}[/math]

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Well, it really doesn't make that much of a difference to which one you use. But anyways, here is the explanation:

 

The first form that you have mentioned needs to be used when you are going to take the standard deviation OF THE WHOLE population.

 

The second one is when you take a sample of a population ie. only some of the population

 

{edit}

 

Got them the wrong way round :)

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No you didn't.

 

The n form is the population standard deviation, the n - 1 form is the sample standard deviation. That's why the top one uses Mu, denoting the population mean, and the bottom one uses XBar, denoting the sample mean.

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You didn't understand, the edit WAS the correction that I had made! I put it the other way round, after the edit, it was correct.

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the n-1 is for sample of a population, this is because, since you are estimating a statistic, u want it be unbiased,

 

which is E(s^2)=sigma^2

 

s^2 is called the unbiased esimator of the population variance.

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oh wow! It is too complex for me to comprehend :)))) !!!!

 

I'm only at GCSE level for crying out loud! I kind of get the idea of what it is trying to say, but, can't really understand how they get to that answer.

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oh sorry, if u do maths a levels especially the stats modules then u will understand it. you don need to know this now

 

I had the same problem when doing GCSE cos the course isnt really exact on which formula ur meant to use. Its better to ask you teacher.

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Well, i did, and that's why i know which formula to use. I needed it for the stats project for my coursework. I am planning to do maths A level since I want to go into chemical engineering

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why dont u go to the exam boards website,

if its AQA http://www.aqa.org.uk/qual/gcse.html and select which maths ur doing, and then view the specifications.

 

and for edexcel

 

http://www.edexcel.org.uk/qualifications/QualificationSubject.aspx?id=50009

 

the specs should have everything u need in there. there are should also be some past papers with answers, so if u look at them u should get an idea of which form to use

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Well, thanx for the link, but all the coursework has been finished and all. I have actually sat the non-calculator paper before yesterday!

 

 

{Edit}

 

Just noticed I have 1111 posts!

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You didn't understand, the edit WAS the correction that I had made! I put it the other way round, after the edit, it was correct.

Sorry. Reading your post as it stands, there is no way of knowing that.

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