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:
What was the
standard deviation of the repair
time?

