Quick question about finding standard deviation

[rock.freak667]

[SOLVED] Quick question about finding standard deviation

Now I know that $$\sigma=\sqrt{var(x)}$$

which simplifies to this expression : $$\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(x-\overline{x})^2}$$ can someone show me how they got such an expression?

and in chemistry I have to use a standard deviation calculation to get out a problem. Now normally I would use the above equation but my notes tell me to use this equation:

$$\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x-\overline{x})^2}$$


Which one is correct to use? and can someone tell me if this is correct $$c_v =\frac{\sigma}{\overline{x}}$$ where $$c_v$$ is the coefficient of variation

 

[mathman]

The definition of the st. dev. depends on whether or not the mean is the true mean or the average of the experimental data. For the true mean use 1/N, for the experimental average use 1/(N-1). If you take the average of the variance with the experimental mean and compare it to the average of the variance with the true mean, you will see they are equal.

 

[rock.freak667]

Oh I see now,thank you