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Six Sigma Histogram: Examples & Tutorial

Instructor: Dr. Douglas Hawks

Douglas has two master's degrees (MPA & MBA) and is currently working on his PhD in Higher Education Administration.

Six Sigma methodology contains powerful tools for use in quality improvement initiatives. The histogram is one of the most frequently used tools. This lesson discusses how it fits in the project and provides examples for its proper use.

Histograms vs. Bar Charts

A histogram is a visual charting tool used to measure the frequency of values, classified into groups called bins. You may see a histogram and think that it looks like a bar chart, but there is one important difference. Bar charts are used to represent and compare categorical variables. Histograms are used to represent and compare distributions of quantitative variables.

For example, if you wanted to create a visual representation of the make of vehicles in a parking lot, you could use a bar chart. Each bar or column on a bar chart represent a type of vehicle, such as Ford, Chevy, Toyota, etc. A bar chart is appropriate because the Ford category isn't statistically related to the Chevy category.

However, if you want to chart the frequency of values that are on a continuous scale, such as the daily high temperatures in your town for a year, you would use a histogram. Each bar or column is a bin, or interval, representing quantitative values, such as 0-20 degrees, 20-40 degrees, etc.

What a Histogram Looks Like

As mentioned earlier, a histogram looks a lot like a bar chart. Along the bottom, there are labels associated with each bin. Along the side axis, there is some sort of measurement, in whatever units the data is being measured. Here is an example of what a histogram looks like.


Histogram: 100 Twenty Ounce Soda Bottles
Histogram: 100 Twenty Ounce Soda Bottles


Notice that along the bottom, there are labels for each bin. In this chart, those measurements are fluid ounces. Along the side, we have a count of how many bottles, tested during our quality assurance tests, fell into each bin.

On the other hand, a bar chart is based on values that aren't numerically continuous. Each bar might be a distinct category, numeric or not. In the example below, the groups show the number of people in a group that have a favorite state for winter skiing. So, unlike a histogram that charts continuous data, a bar chart is categorical.


Favorite States for Skiing
Favorite States for Skiing


How to Use a Histogram

In Six Sigma, every analytical tool has a unique purpose. A histogram has the purpose of being a graphical representation of a specific quality metric. Let's use our earlier histogram as an example.

Imagine you are the manager at a bottling center for a soda company. At your location, your automated assembly line fills 20-ounce soda bottles. Ideally, each bottle of soda should have exactly 20 ounces of soda, but as with most production processes, the variance, or degree of difference from unit to unit, is something you need to measure and control.

Based on the machines and process you use, the company and quality assurance standards say that if a bottle has 19.9 - 20.1 ounces of soda, it is an acceptable bottle. The one-tenth of an ounce below and above 20 is known as the tolerance limit, and defines how much variance is acceptable before a bottle of soda is considered a defect, or a unit outside the tolerance limits.

Each hour, you have a quality assurance manager select 100 random bottles of soda and measure exactly how much soda is in each bottle. The goal of this exercise is to ensure all bottles are within the tolerance limits, and if not, to share the results with management and the production specialists to see if there is a failure somewhere in the process. If we look at the histogram again, we can see how much soda was in each of those 100 bottles.


Histogram: 100 Twenty Ounce Soda Bottles
Histogram: 100 Twenty Ounce Soda Bottles


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