Standard Deviation

The standard deviation is usually used instead of the variance. It is simply the square root of the variance:

The statistic is represented by 's'. The corresponding process parameter is called 'σ ' ('sigma').

The reason that the standard deviation is usually preferred is because it is in the same units as the original data, not 'square units'.

The figure shows a number of points, and a circle of one standard deviation radius. The size of the circle is independent of the scale or the dimensions used. I can estimate the size of the standard deviation just by looking at the points, without any dimensions or calculation:

I cannot do the same thing with the variance. The radius of the circle depends on the dimensions used. To give a practical example, compare the two calculations below. They use exactly the same values, but one is measured in centimeter units and the other in millimeters:

Calculation	Units	Values					Variance	Standard Deviation
1	cm	1	3	6	4	2	3.70	1.92
2	mm	10	30	60	40	20	370	19.2

The standard deviation in millimeters is ten times the standard deviation in centimeters, it remains in scale. However the variance is 100 times as large, it is not to scale.

	The times taken to repair equipment breakdowns, in hours, over the past week were as follows: 5 4 3 2 5 5 What was the standard deviation of the repair time?