How to Calculate 3 Sigma

by Mackenzie Maxwell - Updated November 14, 2018
Gaussian (bell) curve

Although some business owners may be wary of using statistics, these equations can help you understand your company better. For example, understanding the three-sigma rule of thumb can help you make specific calculations or generally identify outliers in your business. However, you must learn to use it correctly for this equation to be effective.

What is 3 Sigma?

Three sigma is a calculation that comes from statistics. Researchers and statisticians use this calculation to identify outliers in data and adjust their findings accordingly. They do this because even well-controlled environments can yield results for which a study doesn't account.

For example, consider a prescription medication trial. If most patients on the new medicine saw improvements within a certain range, but one patient had an incredible change in their condition, it's likely that something else influenced this patient, not the drug in the study.

3 Sigma in Business

In business, you can apply the three-sigma principle to your analysis. For example, you may want to see how much your store makes on a given Friday. If you use three sigma, you may find that Black Friday is far outside the normal range. You may then decide to remove that Friday from your calculations when you determine how much the average Friday nets at your store.

You can also use three sigma to determine if your quality control is on target. If you determine how many defects your manufacturing company has per million units, you can decide if one batch is particularly faulty or if it falls within the appropriate range.

Generally, a three-sigma rule of thumb means 66,800 defects per million products. Some companies strive for six sigma, which is 3.4 defective parts per million.

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Terms You Should Know

Before you can accurately calculate three sigma, you have to understand what some of the terms mean. First is "sigma." In mathematics, this word often refers to the average or mean of a set of data.

A standard deviation is a unit that measures how much a data point strays from the mean. Three sigma then determines which data points fall within three standard deviations of the sigma in either direction, positive or negative.

You can use an "x bar" or an "r chart" to display the results of the calculations. These graphs help you further decide if the data you have is reliable.

Make Your Calculations

Once you understand the purpose of the exercise and what the terms mean, you can get out your calculator. First, discover the mean of your data points. To do this, simply add up each number in the set and divide by the number of data points you have.

For example, assume the data set is 1.1, 2.4, 3.6, 4.2, 5.3, 5.5, 6.7, 7.8, 8.3 and 9.6. Adding up these numbers gives you 54.5. Since you have ten data points, divide the total by ten and the mean is 5.45.

Next, you need to find the variance for your data. To do this, subtract the mean from the first data point. Then, square that number. Write down the square you get, then repeat this method for each data point. Finally, add the squares and divide that sum by the number of data points. This variance is the average distance between the points and the mean.

Using the previous example, you would first do 1.1 - 5.45 = -4.35; squared, this is 18.9225. If you repeat this, add the sums and divide by ten, you find the variance is 6.5665. If you want, you can use an online variance calculator to do this part for you.

To find the standard deviation, calculate the square root of the variance. For the example, the square root of 6.5665 is 2.56 when rounded. You can use online calculators or even the one on your smartphone to find this.

Finally, it's time to find the three sigma above the mean. Multiply three by the standard deviation, then add the mean. So, (3x2.56) + 5.45 = 13.13. This is the high end of the normal range.

To find the low end, multiply the standard deviation by three and then subtract the mean. (3x2.56) - 5.45 = 2.23. Any data that is lower than 2.3 or higher than 13.13 is outside the normal range. For this example, 1.1 is an anomaly.

About the Author

Mackenzie Maxwell is a small business owner. She has two businesses, including a martial arts gym in Texas. Prior to building her own, Mackenzie worked with small businesses and organizations to create effective marketing - from churches to insurance companies. She enjoys helping businesses with the startup spirit grow. Mackenzie has been writing in this field for six years and shows no signs of slowing.

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