# Quick question about finding standard deviation

Homework Helper

## Main Question or Discussion Point

[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

## Answers and Replies

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mathman
Science Advisor
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.

Homework Helper
Oh I see now,thank you