A review of the various measurements for spread or variation that include variance, standard deviation, inter-quartile range, etc.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Spread
Six Sigma-Measure – Lesson 12
A review of the various measurements for spread or variation that include
variance, standard deviation, inter-quartile range, etc.
Six Sigma-Measure #11 – Central Tendency
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 is 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. Spread or Variation Defined
o What is variation or spread?
• It measures the distance each data point is from the central tendency (mean/median).
o Why is variation so important?
• The central tendency only tells the output performance of all data points. It
doesn’t tell the severity or capability of the process itself.
 “Place one foot on ice and one foot in the fire, then on the average you should be warm.”
o Remember the two processes of throwing darts?
• Which has a higher score? Which has a higher central tendency? Which is “better” and why?
o Variation reflects where we have less control and where we feel the most pain.
• The degree of variation affects the degree of difficulty to correct/fix.
• The degree of predictability affects the degree of control and comfort.
 Thermostat Calibration – consistently 3 degrees too low is easier to control than inconsistently high & low.
• To understand our data, we must understand both its central tendency and 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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3
1
5
3
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Process A: Process B:

4. Measurements of Spread
o There are several ways to measure variation or spread for normal distributions:
• Range – the entire extent of the dataset; the difference between the min and max data points.
• Deviation – the distance a data point is from the mean or (X - μ).
• Variance – the average squared deviation (or differences) about the mean or (X - μ)2 / N or σ2
 The variance is intended to measure how spread out the distribution is from the mean.
• Standard Deviation (σ or s)– the square root of the variance or √(X - μ)2 / N
 The standard deviation measures the average distance to the mean for all data points.
 It is the most common measure of variation across entire datasets that are normally distributed.
o How is variation measured for non-normal distributions (which don’t use the mean)?
• Stability Factor – the relative spread of data points about the median or (Q1 / Q3)
 The closer the stability factor is to 1, the more likely there is little variation in the distribution.
 The Inter-quartile Range (IQR), measured as (Q3 – Q1), can also suggest the amount of variation by
expressing the range of the middle 50% of the data points.
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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Deviation = 9 – 5 = 4
Minimum
Range
Maximum

5. Practical Application
o What metrics (if any) does your organization use for measuring spread or variation?
• Unfortunately, very few organizations use spread or variation as a critical metric.
o If your organization doesn’t have metrics like this, then try doing the following:
• Identify at least 3 metrics used by your organization that are based on continuous values.
• Pull some historical data for each metric and run a normality test on the data.
 If the distribution is normal, then calculate the variance and standard deviation.
 If the distribution is non-normal, then calculate the IQR and stability factor.
• What do these results tell you about the variation in each metric?
 Which metric has the most variation?
 Have you observed if your organization more frequently over-reacts to changes in that particular metric? If
so, then it could indicate an ideal pain-point in your organization that needs to be addressed.
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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