Variance

variance   =   (standard deviation)2   =  

The units of the variance are the square of the units of the original values. For example, if the values are weights, the standard deviation might be 6 kg, but the variance would be 36 square kg. Since its units are easier to interpret, standard deviations are more easily understood measures of spread, but variances are important in advanced statistics. (An important collection of methods for analysing relationships between variables is called analysis of variance.)

Degrees of freedom (optional)

The divisor (n − 1) in the formula for the sample standard deviation is called its degrees of freedom. This is the number of 'independent pieces of information' that contribute to it.

Sample of size n = 1
With only a single value, there is no information about the spread of values, so there are 0 degrees of freedom.
Sample of size n = 2
With two values, x1 and x2, there is only a single piece of information about the spread — the difference between the values, x1 − x2 — and there is one degree of freedom.
Sample of size n
In general, there is one less 'piece of information about the spread' in the sample than the number of data points because the sample mean, , is one piece of information that does not give any information about the spread of the data. There are therefore (n − 1) degrees of freedom.