16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

- Aug 6th 2007, 04:23 AMprincess_anna57Find the variance and standard deviation of this set of data?
16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

- Aug 6th 2007, 05:00 AMtopsquark
$\displaystyle \sigma ^2 = \frac{1}{N} \sum_{n = 1}^N (\bar{x} - x_n)^2$ <-- variance

where $\displaystyle \bar{x} = \frac{1}{N} \sum_{n = 1}^Nx_n$

and

$\displaystyle \sigma = \sqrt{\frac{1}{N} \sum_{n = 1}^N (\bar{x} - x_n)^2}$ <-- standard deviation

Depending on the kind of statistic you are trying to work with the $\displaystyle \frac{1}{N}$ might be a $\displaystyle \frac{1}{N - 1}$. You'll have to check your text or your notes to make sure.

So the first thing to is to calculate the average, $\displaystyle \bar{x}$, then use that to find the variance.

-Dan - Aug 6th 2007, 05:20 AMprincess_anna57
The mean is 26.73. Now what do I do? ^_^

It's 1/N by the way. - Aug 6th 2007, 05:47 AMtopsquark
- Aug 6th 2007, 05:58 AMprincess_anna57
Cool beans. How about the standard deviation?

- Aug 6th 2007, 06:19 AMtopsquark
Take a look at the symbol I used for the variance, $\displaystyle \sigma ^2$. (This may not be a Universal notation, but it is standard in the two books I own.)

So to get the standard deviation $\displaystyle \sigma$ from the variance, just take the square root.

-Dan