A review of distributions and how they can be formed using dotplots and histograms.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Distributions: Overview
Six Sigma-Measure – Lesson 8
A review of distributions and how they can be formed using dotplots and
histograms.
Six Sigma-Measure #07 – Data Types
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted by any means
(electronic, mechanical, photographic, photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

2. Building Distributions with Dotplots
o What is a distribution?
• A distribution is created by plotting or
distributing a set of data along a scale.
• The more data that’s plotted, the more
of a shape those data points display.
o See the Dotplot examples at right:
 To build it in Minitab, go to Graphs > Dotplots…
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
As more data points are
included, the columns of plotted
data points become larger.
When you have enough data, it
begins to take on the shape of a
bell curve, like a distribution.

3. Distributions displayed in Histograms
o Limitations of Dot Plots
• Not all data points necessarily stack so neatly
into columns like in the dotplot example.
• Since continuous data can be infinite in scale
or divisibility, when there are more than 50
continuous data points, a Dot Plot can become
less practical at displaying the values.
 Instead, use a histogram.
o What is a histogram?
• A histogram can take the same kind
of data (and a lot more of it) and
group the values into “bins”.
 In Minitab, go to Graph > Histogram…
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
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Vertical axis reflects the frequency or
percent of data points in each bin
Each bin includes all data points
that fall within a specified range
Horizontal axis reflects the scale
for all data points being plotted.
Minitab tries to fit a line
to describe the relative
shape of the data

4. The Shape of Distributions
o The shape of distributions are influenced by 2 characteristics:
• Central Tendency
 Refers to the location on the scale where the majority of data points are concentrated or centralized.
 For normal distributions, the mean (or average) is the measurement for central tendency.
• Variation or Spread
 Refers to how dispersed the data points are spread across the scale.
 For normal distributions, the standard deviation is the measurement for variation.
o What is kurtosis?
• It’s a measure of the shape of the peak near the mean of the distribution.
 A distribution with high or positive kurtosis (leptokurtic) has a sharp peak near the mean.
 A distribution with low or negative kurtosis (platykurtic) appear flat with no peak near the mean.
• Which distribution above appears leptokurtic? Which appears more platykurtic?
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
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Central
Tendency
Variation
or Spread

5. Practical Application
o Open the “Minitab Sample Data.MPJ” file and try to do the following:
• Create a Dotplot each for Metric A and Metric B.
• Create a Histogram each for Metric A and Metric B.
• Which metric appears is more leptokurtic and which is more platykurtic?
o Next, pull some historical data for at least 2 metrics used by your organization and try
following the same steps described above.
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
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