# Statistics Questions

1. Jan 6, 2004

### Moose352

It seems to me that a lot the concepts in statistics are rather arbitrary and don't seem be mathematically derived. For example, how is the equation for standard deviation derived? The textbook says that the standard deviation is the mean of all of the deviations of the values in the sample and since all the deviations add up to zero, the values are sqaured to get rid of the negative. I understand that, but why doesn't it just take the absolute value? Why is the square-root taken only after everything has been summed? Furthermore, why is it divided by (n-1) and not n?

Also, can anyone explain the proof for Chebychev's rule?

Thanks very much.

2. Jan 6, 2004

### repugno

Hello Moose,

The standard deviation formula can be derived, my Maths teacher showed me. Unfortunately I am unable to derive it so I will not be much help there. The reason we divide by n-1 sometimes is to give as a most accurate or unbiased estimate for sample data. There is also proof for that, which I am also unable to do. Hope this helped.

Regards,

Daniel

3. Jan 6, 2004

### Moose352

Thanks repugno. It's good to know that there is a proof, but I will not be convinced until i see it.

4. Jan 6, 2004

### repugno

Lol .. tried to give you some Mathematical proof, seems that I can't get the Latex code right. You're on your own now. :D

Last edited: Jan 6, 2004
5. Jan 9, 2004

### Moose352

Ah! Please try again. I can't find any other proof. I think the real problem is I haven't yet found a concept (of course, granted that I haven't learnt much) that the current definition of SD exclusively works for.

6. Jan 9, 2004

### NateTG

A large amount of statistics is based on the notion of normal distributions.

For normal distributions it is possible to, for example, show that a certain fraction of the results are within a standard deviation of the peak.

7. Jan 9, 2004

### Moose352

I completely understand. But why does it have to be based on that specific definition standard distribution. Can not those fractions be recalculated based on another definition of the standard deviation?

8. Jan 9, 2004