Basic Statistics

There are primarily two branches in which statistics are studied:

Descriptive Statistics
Applied to describe the data using numbers, charts, and graphs. Terms such as mean, median, mode, variance, standard deviation are values that summarize data. Descriptive statistics describe the entire group for which the numbers were obtained. These are the actual values for the entire group.

Inferential Statistics
Uses sample statistics to infer relationships of the population parameters.This is most often done in the Analyze and Improve phases using hypothesis testing, correlation analysis, regression analysis, and design of experiments (DOE).

Rarely is it possible to analyze the entire population (such as the average weight of all sharks in the ocean). For this reason a sampling strategy is applied. The analysis of the sample is used to apply inferences to the entire population. The values may or may not be the same values for the entire population so they are often applied with a confidence interval.

Inferential Statistics

A comparison (of means, variance, proportions) is initiated with a hypothesis statement about a population or populations. The sample statistics are studied to determine, with a certain level of confidence and power, that the hypothesis (null hypothesis) is to be proven false or not false (but not necessarily true), see Hypothesis Testing for more information.

The links below cover other topics within basic statistics:

Graphical Summaries


Box Plots

Stem and Leaf Plot

Hypothesis Testing

Hypothesis Testing

Normality Assumption

Analysis of Variance (ANOVA)




"Defect" Metrics

DPU - Defects Per Unit

DPO - Defects Per Opportunity

DPMO - Defects Per Million Opportunities

Process Yield Metrics

FY - Final Yield

TPY - Throughput Yield

RTY - Rolled Throughput Yield

NY - Normalized Yield

The meaning and formula around sigma scores


Yield to Sigma Relationships

Process Capability Indices






Other topics

Hypothesis Tests Flowchart

Hypothesis Testing

Alpha and Beta Risks (Type I Error and Type II Error)

Comparing Samples vs. Population

Short Term versus Long Term sampling

Data Classification



Multi-variate Analysis


Confidence Intervals




Measures of Central Tendency: Mean, Median, Mode

Measures of Dispersion: Range, Standard Dev, Variance, Coefficient of Variation

Probability Density Function

Cumulative Distribution Function

Degrees of Freedom

Box-Cox Transformation



  1. Binomial Distribution
  2. Poisson Distribution
  3. Hypergeometric Distribution


  1. Uniform Distribution
  2. Normal Distribution
  3. Exponential Distribution
  4. t Distribution
  5. Chi-square Distribution
  6. F Distribution

A few other continuous distributions (but are not covered in this website) are Beta, Cauchy, Gamma, Lognormal, Weibull, Double Exponential, Power Normal, Bivariate Normal, Power Log Normal, Triangular, and Tukey-Lambda.

Statistical Evaluation Tools

Statistical Evaluation Tools

Using Excel for Statistical Applications

This package below is the most comprehensive guide on using Excel for statistics as well as a very educational tool that explains the details behind the calculations. There are over 1000 pages of documents and Excel examples. 

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Return to the ANALYZE phase

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The following presentations are available to download.

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Green Belt Program (1,000+ Slides)

Basic Statistics


Process Mapping

Capability Studies


Cause & Effect Matrix


Multivariate Analysis

Central Limit Theorem

Confidence Intervals

Hypothesis Testing

T Tests

1-Way Anova Test

Chi-Square Test

Correlation and Regression


Control Plan


Error Proofing

Advanced Statistics
in Excel

Advanced Statistics in Excel

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