Standard deviation can be used to make important extrapolations from past data. As a measure of volatility, standard deviation measures the tendency of data to be spread out. When looking at the historic returns of a mutual fund, standard deviation can be used to measure the variation of expected return that has taken place in the past giving a sense of range of performance that can be expected given different probabilities of return for the future. It is also used to measure the risk of a security. The smaller the standard deviation, the tighter the probability distribution, and the lower the risk associated with the security.
Standard deviation is calculated by first calculating the mean of a group of data points.
There is a minimum number of data points that are necessary to calculate the standard deviation properly. The mean is then subtracted from each element of the data group. Each of the differences is then squared and then summed together. The sum of all the squared differences is then divided by the number of data points minus one. The square root of that end figure is then determined and is called the standard deviation.