# Sigma

It is the greek letter that represents S.

In mathematics, the uppercase sigma is denoted by Σ, and the lowercase sigma is denoted by σ.

Σ = summation of values

For example, if you have 5 data points (15, 22, 27, 28, 31), then the Σ of these values would be 15+22+27+28+31 = 123

σ = standard deviation of values

To calculate standard deviation, you first calculate the average of the data values, then subtract each data value from the average. Next, you square the differences from the average and add them up (summation). This converts the standard deviation into a variance, which is the squared value of the standard deviation. Next, you divide by one less than the sample size (n-1). Finally, you take the square root of the final number to undo the squared values, and convert the number from a variance back into a standard deviation.

The standard deviation of the 5 data points above equates to 6.27.

Learn more about the standard deviation and see an example calculation

Sigma is most known for the improvement methodology, Six Sigma.

### Additional Resources

- Control Charts: A Basic Component of Six Sigma– creativesafetysupply.com
- Implementing Six Sigma– hiplogic.com
- Six Sigma Principles– blog.5stoday.com
- An Overview on Six Sigma Technique– blog.creativesafetysupply.com
- Why Six Sigma Root Cause Analysis is a Great Tool– kaizen-news.com
- Design For Six Sigma (DFSS)– iecieeechallenge.org
- If You Were Stuck On An Island With Only 3 Six Sigma Tools…– lean-news.com
- 5 Things You should Know about Six Sigma Belts– 5snews.com
- Lean Six Sigma Can Improve Environmental Performance– creativesafetypublishing.com