The standard deviation is a little more work to calculate than the mean, but it is still fairly straight forward. First you have to calculate two other values. Deviation is the distance of each measurement away from the mean. If the mean were 10, and a measurement were 8, the deviation would be 2. So, variance is a measure of the variability of measurements around the mean.
Standard deviation is simply the square root of the variance.
It s kind of like correcting for having squared the deviations. Now we are able to use this information to ask whether the difference in two distributions is likely to have come about by chance or because the values from which they are taken really are different. One test that can be used is called the Student s t-test, and essentially looks at how different both the mean and the variance of two populations are, and then allows you to determine the probability that these two distributions come from the same data. The t statistic is the difference of the two means divided by the square root of the sum of the variance of each sample divided by its sample size.