Basic QA Statistics Series(Part 5)- Basic Histogram

REFLECTION: FOR STUDENTS: When that graph pops up showing you data in histogram, pay closer attention to everything the graph is conveying, because effective conveyance of data is the future

FOR ACADEMICS: Teach your students how to use visual data graphics, and correct them when they slip up. From teachers to the boardroom, being able to construct a histogram for a presentation is a vital skill for information conveyance.

FOR PROFESSIONALS/PRACTITIONERS: Excel and Minitab do the job, but always remember the underlying theory behind the graphs for when the software goes down, or you need to do it quickly without a computer.

Foundation

As Promised from the last post from this series, we will now delve a little bit into histograms. The primary purpose of a histogram is to provide a straightforward graphic representation of the distribution of data. I’m sure everyone has heard the term “a picture speaks a thousand words.” To demonstrate this, I will show you three histograms and think you will see before you read any caption which histogram looks like useful data. Sample data should appear pretty much like a bell curve to be declared “normal.”

When the “Tail” is to the left the data is left skewed- and look at that clear outlier bin

A histogram with an almost perfectly normal distribution

When the “Tail” is to the left the data is right skewed

The histogram is a quick communication of the state of the data.  When you see the strong left or right skew, you must investigate the outliers and determine why you have so many.

Constructing a Histogram from your Data

To construct a histogram from a continuous variable, you need to determine the amount of data to be used. If you were researching problems with a production line, Cost would be your horizontal, split into bins, with the recommended number of bins equal to √n (n being the number of samples), and the bins having set boundaries. Fifty data points should be your minimum. Each bin will separate the data into classes based upon frequency, but the histogram will not show you the raw data, only represent the frequency distribution. I would suggest familiarizing yourself with your company’s statistical software so that everyone uniformly performs the analysis. Having the statistical guidelines per the software will save you in some auditing situations. Minitab, Excel, and many others provide straightforward access to histogram construction. (Kubiak, 2017) Most software equalize the width of the bars, but the way I have seen the width determined by hand most often is:

• Determine # of Bars to use based upon the sample size
  • Sample size of 100 or less: 7-10 Bars
  • Sample size of 100-200: 11-15 Bars
  • Sample size of 201 or more: 13-20 Bars
• Choose # of Bars to use
• Width(W) = Overall Range of Data (R) / # of Bars(B)
  • W=R/B. 
  • Keep adding W to the previous bar to find the lower edge of the next bar, starting from 0

(Tague, 2005)

Conclusion

Histograms are kind of like a way to count your data frequency of occurrence within set boundaries, and then show graphically how your data is distributed. Always remember that if a histogram is constructed with too many or too few bins, it can be manipulated misleadingly. Always check the numbers yourself! This tool is one of the Seven Basic Quality Tools and meant to be used to help flag issues like outliers or non-normal data. It is not something that can solve a problem on its own, but a tool that enables you to understand what the data is telling you. The next post we cover will talk about another visual stat tool- the box and whisker diagram (for any cat lovers 😊).

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Bibliography

Kubiak, T. a. (2017). The Certified Six Sigma Black Belt Handbook Third Edition. Milwaukee: ASQ Quality Press.

Tague, N. R. (2005). The Quality Tool Box. Milwaukee: Quality Press.