A high-level review of the fundamental terms and concepts associated with statistics, such as population vs. sample data, distributions, etc.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Overview of Statistical Terms and Concepts
Six Sigma-Overview – Lesson 3
A high-level review of the fundamental terms and concepts associated
with statistics, such as population vs. sample data, distributions, etc.
None
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. Population vs. Sample
o What is a population?
• Represents every possible observation. It is ideal but very rare to get and often unnecessary.
o What is a sample?
• A subset of the population that is generally a fair representation of the population.
• An adequate sample can allow someone to make inferences about the population.
• The difference between the conclusions from the sample vs. reality in the population is RISK.
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.
Risk: Does this
sample represent the
population fairly?
Population
Sample Group

3. Distributions
o We expect most things in life to be random and have a normal distribution (bell curve).
• For example, measuring the age of employees or the temperature in different rooms.
o If something is not normally distributed, we tend to think it’s skewed (has bias).
• For example, the age of employees in entry-level positions is probably lower than management
positions. Or the temperature in network server rooms may be lower due to high-tech equip.
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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Positive Skew Negative Skew
No Skew;
data points
fall around
the middle

4. Central Tendency
o Central tendency explains where on a scale most of the data points are centered.
• The type of distribution (normal vs. non-normal) affects the central tendency we use.
o For Normal distributions, the AVERAGE (Mean) is the central tendency.
• Normal distributions don’t include outliers
that could move the average.
• For example, what is the age of people
in an office building?
 We assume the people will mostly be
employees and/or customers and is
therefore a normal distribution.
o For Non-Normal distributions, the MEDIAN (50th percentile) is the central tendency.
• Non-Normal distributions include outliers
which don’t affect the percentile.
• For example, what is the age of people in an
office building on “bring your child to work” day?
 Since children would be included, then it could
skew the results and shift the average.
 How could you reduce the risk of this kind of
bias in your data collection?
– Use the median or limit your sample to just employees.
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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Average ≈ Median
Median
Average

5. Variation
o Variation measures how data is spread around the central tendency (mean/median).
• For two processes of throwing darts, which process would you prefer to have?
• Process A yields a higher score, but Process B is more consistent & predictable (less variation).
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.
 Prices at discount stores – the slogan “Always low prices…Always” implies consistency in low prices.
o Standard Deviation is represented by the Greek lowercase letter σ (sigma).
• Standard Deviation measures variation around the mean (for normal distributions).
• Inter-quartile Range (IQR) and Stability Factor measure variation around the median.
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
3
1
5
3
1
Process A: Process B:

6. Defects and Sigma Levels
o Defects are anything outside the customer’s requirements (Voice of Customer or VOC).
• Customer requirements are tolerances defined as lower or upper spec limits (LSL or USL).
 Anything beyond the LSL or USL (the customer’s requirements) is considered a defect.
o A sigma level measures the # of standard deviations between the mean and LSL/USL.
• Sigma level also measures quality/accuracy as the defects per million opportunities (DPMO).
 One Sigma = 690,000 defects per 1 million opportunities (or 31% accurate)
 Two Sigma = 308,537 defects per 1 million opportunities (or 69.2% accurate)
 Three Sigma = 66,807 defects per 1 million opportunities (or 93.3% accurate)
 Four Sigma = 6,210 defects per 1 million opportunities (or 99.38% accurate)
 Five Sigma = 233 defects per 1 million opportunities (or 99.98% accurate)
 Six Sigma = 3.4 defects per 1 million opportunities (or 99.9997% accurate)
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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Lower Spec
Limit (LSL)
Upper Spec
Limit (USL)
Mean (μ)
Defects Defects
Acceptable

7. Comparing Sigma Levels
o 3 Sigma at 93.3% may sound good enough, so why bother pushing for Six Sigma?
• Remember, it all depends on the amount of RISK the customer is willing to take.
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 Sigma 6 Sigma
•20,000 wrong drug prescriptions per year •25 wrong drug prescriptions per year
•500 incorrect surgical operations per week •One incorrect surgical operation every 2 weeks
Target
2 Sigma
4 Sigma
6 Sigma
Ex. Variation affects sigma level (i.e., standard deviation)
Lower
Spec
Limit
Upper
Spec
Limit

8. Practical Application
o What are the most critical metrics used by your organization?
• Which of those metrics are based on sample data vs. population data?
 For those based on sample data, how confident are you that the sampled results reflect the population?
 What are you basing your confidence on? Is there a way to prove it with data?
– It’s okay if you’re not sure how to prove it with data; that’s what we’ll go over as we learn more about statistical analysis.
• Which of those metrics are measures of central tendency?
 What is the measurement used for central tendency (i.e., mean or median)?
• Which of those metrics are measures of spread or variation?
 Very few organizations use variation as a critical metric. If yours doesn’t, then what risks could there be by
not measuring 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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