A comparison of different types of simple distributions and how to run and interpret Minitab's graphical summary.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Comparing Distributions and
Using the Graphical Summary
Six Sigma-Measure – Lesson 13
A review of the various measurements for spread or variation that include
variance, standard deviation, inter-quartile range, etc.
Six Sigma-Measure #12 – Spread
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. Characteristics of Distributions
o Remember, 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.
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

3. Comparing Distributions
o The mean and standard deviation can make a difference when comparing distributions:
• Example 1: Different means and same standard deviations.
• Example 2: Same means and different standard deviations.
• Example 3: Different means and different standard deviations.
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.

4. Graphical Summary
o Minitab’s graphical summary provides a visual and statistical description of the data.
• In Minitab go to Stat > Basic Statistics > Graphical Summary…
 “Variables” must be a continuous value in the dataset.
 “By Variables” creates a separate graphical summary for each discrete value in the selected column.
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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5. Practical Application
o Identify at least 3 metrics used by your organization based on continuous values.
• Pull some historical data for each metric and run a graphical summary on each.
• Answer the following questions for each metric:
 Is the data normal or non-normal?
 Is the data multi-modal?
 What is the central tendency for each metric?
 What is the spread or variation for each metric?
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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