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