Introduction to Six Sigma Statistics in 8 Easy Steps - This is a very brief intro for those of you who are interested in Six Sigma and who studied it in college!

1. Introduction to Six Sigma
Statistics in 8 Easy Steps
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3. 1. Learn the Scales of Measure
Nominal
• It is in the name
• Marital status, Phone numbers
•
Ordinal
• Relative, unequal value ranking
• Race finish, opinion poll response
• temperature
Interval
• Equal intervals are equal differences
• Calendar year, Fahrenheit
Ratio
• Proportional amount of difference
• Has a real zero value
• Annual income, Kelvin temperature

4. 2. Learn the Measures of Central Tendency
Median: Midpoint in a string of sorted
data, where 50% of the observations, or
values, are below and 50% are above
• Does not necessarily include all values in
calculation
• Is “robust” to extreme scores
• Organize the data from low values to high
when determining the Median
Mean: Arithmetic average of a set of values
• Reflects the influence of all values
• Strongly Influenced by extreme values
Mode: The most frequently occurring value

5. 3. Learn the Measures of Dispersion
Range: the distance between the extreme values of a data set (Highest to Lowest)
• The range is more sensitive to outliers than the variance
Variance: the Average Squared Deviation of each data point from the Mean
Standard Deviation: Square Root of the Variance
• measure of the average deviation about the mean

6. 4. Understand the Different Types of Data
Continuous or Variable Data
(Quantitative)
• Time (seconds)
• Pressure (psi)
• Conveyor Speed (ft/min)
• Rate (inches
Attribute (Qualitative)
• Categories
• Good/Bad (Pass/Fail)
• Machine 1, Machine 2, Machine 3
• Shift number
• Counted things (# of Errors in a
document, # units shipped, etc.)
Convert Attribute to Continuous wherever
possible
Examples of attribute data converted to
continuous data:
• Count of defects to „% defects‟
• Y/N late to „average days late‟
• Leaks/No leaks to „rate of leaks on a
continuous scale‟
• Success or failure of electrical parts to „voltage
flow of good parts‟

7. 5. Gain Knowledge of Descriptive Statistics
• Consists of basic statistics and graphical techniques used to summarize data
• Measures of central location
• Measures of spread (dispersion)
• Evaluation of symmetry & skewness
• Typical graphical techniques
• Histograms
• Boxplots
• Dotplots
• Normal probability plots

8. 6. Be able to Identify Different Data Distributions
Normal Distribution (Bell Curve)
• The “Normal” Distribution is a distribution of data which has certain consistent properties (the
mean, median and mode are equal in value)
• These properties are very useful in our understanding of the characteristics of the underlying
process from which the data were obtained
• Most natural phenomena and man-made processes are distributed normally, or can be
represented as normally distributed
• The Normal Distribution is a continuous distribution which is symmetrical and extreme values
are less likely than moderate values (unimodal)
• An example would be measuring heights of people or the length of a table. In either case the
measurement is continuous and can be broken down into finer increments

9. 6. Cont’d
t-distribution
• The t distribution assumes samples are
drawn from a normal distribution but the
population variance, 2, is not known… The
shape of the t-distribution varies as the
sample size, n, changes
• The distribution becomes more narrow as the
sample size becomes larger. As n becomes
very large, the critical value corresponding to
the area under the curve approaches the
Normal distribution‟s Z value
Poisson Distribution
• Appropriate as a model of number of defects
or nonconformities in a unit of product
• X is number of defects found in a per unit
basis
• Per unit area, per unit volume, per unit time,
etc.
• Area X is a discrete, positive integer
• Area for opportunity is a finite region of space,
time or product
• When the average is high, the distribution can
be approximated by the normal distribution
• When the average is low, the distribution is
skewed to the right

10. 6. Cont’d
F Distribution
A continuous distribution formed from the ratio
of variances calculated from two independent
samples drawn from Normal Distributions
Chi-square Distribution
A continuous distribution used in statistical
hypothesis testing and confidence interval
estimation for many different applications,
including inferences about a population
variance

11. 7. Know About Sample and Population Sizes
• Population is every possible observation (census)
• Samples are subsets of populations
• Data is obtained using samples because we seldom know the entire population
• Descriptive statistics apply to any distribution
• Sample or population
• Population statistics are desired, but often not available
• Samples from a population can be used to „infer‟ or approximate population parameters

12. 8. Know the Statistics and Reporting Tools
The most used Six Sigma tools is Microsoft Excel. Excel provides most of the day to day
uses required to manage most Six Sigma projects. Getting the Data Analysis Pack will allow
you to stretch Excel to its limits by providing additional statistical analysis tools
•Anova
•Correlations
•Covariances
•Descriptive Statistics
•Exponential Smoothing
•F-Tests and Two-Samples for Variances
•Fourier Analysis
•Histograms
•Various t-tests

13. 8. Cont’d
However, the ultimate tool for Six Sigma Black Belts is Minitab. Minitab will get you
going where Excel leaves you hanging.
Minitab‟s features delve deeply into:
•Measurement System Analysis
•Multivariate Analysis
•Anova
•Regression Analysis
•Statistical Process Control
•Reliability/Survival Analysis
•And other great simulations

14. 8. Cont’d
While you are trying out Minitab, don‟t forget to check out the powerful reporting tools that will
provide the following graphical reports:
•Dotplots/Histograms/Normal Plots
•Run charts / Time Series
•Pareto Diagrams
•Stratification (2nd Level Pareto)
•Boxplots
•Scatter Plots
•Checksheets/Concentration Diagrams