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Sigma – Standard Deviation

Sigma, or Standard Deviation, (Std. Dev.), is used in combination with X Bar to describe the "Normal Distribution". It is denoted by several symbols depending on the kind of sample and/or if it is calculated using the formula below, or estimated using the d2 factor, also below among other factors.

To find six sigma, calculate sigma, multiply by 6, and add or subtract the result to the calculated mean.

Sigma, (Standard Deviation), Formula

 = Sigma,or Standard Deviation (Std. Dev.) Formula

n or (n – 1)
  • Get the average, (X Bar), of the given observations, (subgroups), using random stratified sampling.
  • Calculate the differences between each value and X Bar.
  • Square the differences, total them, and divide by the number of samples. The ‘E’ looking sign is the sign for sum.
  • Extract the square root

n = Total Number of Samples
Note: If (n) < 32, then subtract 1. (n – 1) This is the degrees of freedom

To estimate Sigma, used in some formulas, you calculate R Bar and divide by d2 from the factor table below.

d2 Factor Table
n d2
2 1.128
3 1.693
4 2.059
5 2.326

Sigma, (Standard Deviation), Estimate Formula

 =  R Bar


And at only $150.00, (USD), our software can get you going quickly. It only calculates sigma using the square root method. See the ZeroRejects feature page for more details. We also have sigma lookup table software. See the free one and the commercial one for more details.

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Last Updated: Saturday, 10-Jun-06 15:50:57 PDT