Histograms: A Valuable Tool for Quality Evaluation

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Histograms A Valuable Tool for Quality
Evaluation

• By Perry Katz

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Overview

• What is a Histogram?
• What are some possible uses for a Histogram?
• Where did the Histogram come from?
• How do Histograms work?
• A real world example.
• An exercise.

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What is a Histogram?

• A Histogram is a variation of a bar chart in
  which data values are grouped together and put
  into different classes.
• This grouping allows you see how frequently data
  in each class occur in the data set.

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What is a Histogram (cont.)

• Higher bars represent more data values in a
  class.
• Lower bars represent fewer data values in a
  class.
• On the next slide is an example of what a
  Histogram looks like.

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Example of a Histogram

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Uses for a Histogram

• A Histogram can be used
• to display large amounts of data values in a
  relatively simple chart form.
• to tell relative frequency of occurrence.
• to easily see the distribution of the data.
• to see if there is variation in the data.
• to make future predictions based on the data.

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Where did the Histogram Come From?

• The Histogram was first implemented by Kaoru
  Isikawa, one of Japans most renowned experts on
  quality improvement.
• Isikawa spent his life trying to improve quality
  in Japan.

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Where did the Histogram Come From? (cont.)

• His major contributions to quality improvement
  are known as the basic seven tools of quality.
• Included in his basic seven tools of quality is
  the Histogram.

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How do Histograms Work?

• First, you need need to pick a process to
  analyze.
• Next, you need a large amount of data, at least
  100 data values so that patterns can become
  visible.
• Then, you need to assemble a table of the data
  values that you collected with regards to
  frequency of data values.

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How do Histograms Work? (cont)

• Next, you need to calculate some statistics for
  the Histogram, including mean, minimum, maximum,
  standard deviation, class width, number of
  classes, skewness, and kurtosis.
• Then, you actually create the Histogram using
  these statistics.

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How do Histograms Work? (cont)

• After you have created a Histogram, it will take
  one of five shapes
• Normal Distribution

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How do Histograms Work? (cont)

• Positively Skewed
• Negatively Skewed

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How do Histograms Work? (cont)

• Bi-Modal Distribution
• Multi-Modal Distribution

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How do Histograms Work? (cont)

• Once your Histogram is complete, you can analyze
  its shape, as well as the statistics that you
  came up with.
• This analysis will help you to make better
  decisions toward quality improvements.

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Real World Example

• The next slide contains a real world example of a
  histogram. It plots the relative frequency of
  the heights of some students based on the data
  below.

                             FrequencyHeight
(feet)          (Number of pupils)     Relative
frequency0-2                        0          
                     02-4                      
 1                                14-5          
             4                              
 85-6                        8                  
             166-8                        2    
                           2
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Real World Example

• This Histogram is courtesy of http//www.gcsemaths
  .fsnet.co.uk/page5.html

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Exercise

• A great exercise which would help you better
  understand what a histogram is all about can be
  found at
• http//www.usfca.edu/histogram_explorer/he.
  html
• Here you are walked through the making of a
  histogram. You see all of the aspects that I
  have discussed in this tutorial.

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Summary

• After going through this tutorial you should have
  a better idea of
• What a Histogram is.
• What a Histogram is used for.
• Where the Histogram came from.
• How Histograms work.

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Histograms A Valuable Tool for Quality
Evaluation

• By Perry Katz