Variance represents how spread out the data are. It is the average of the squared differences from the mean.
The distances from the mean are calculated by subtracting each x from the mean. These distances are squared and then averaged to arrive at the variance.
Because the differences are squared, the result is in squared units - for example, if the measurements are "miles," then the variance is "miles^2". Therefore, the variance value does not intuitively describe the data. To overcome this, the square-root of the variance is taken. The square-root of variance is called standard deviation.
Here is an example data set:
miles driven (x): 43, 70, 27, 36
n = 4
mean = 44 miles
differences
43 - 44 = -1
70 - 44 = 26
27 -44 = -17
36 - 44 = -8
differences^2
(-1)^2 = 1
(26)^2 = 676
(-17)^2 = 289
(-8)^2 = 64
The average of the differences^2:
(1+676+289+64)/4 = 257.5
The variance is:
257.5 miles^2
