definition of variance  and standard deviation in statistics
In statistics, the standard deviation is a very common measure of dispersion. Standard deviation measures how spread out the values in a data set are around the mean. More precisely, it is a measure of the average distance between the values of the data in the set and the mean.
First, calculate the deviations of each data point from the mean, and square the result of each: The variance is the mean of these values: and the population standard deviation is equal to the square root of the variance: This formula is valid only if the eight values with which we began form the complete population.