Variance and standard deviation

The variance is the mean of the squared deviations from the mean of every value.

The standard deviation is the square root of the variance.

When the data is grouped, the mid-interval value of the group can be used as the x-value for that group to obtain estimated values of the mean and standard deviation.

When a constant is added to every item in a set of data, the mean also increases by b but the standard deviation is unchanged.

If each value in a data set is multiplied by a, then the mean and standard deviation are also multiplied by a.