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
|
= |
 |
|
| 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
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.
