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# Chapter 8 Making Sense of Data in Six Sigma and Lean PowerPoint PPT Presentation

Chapter 8 Making Sense of Data in Six Sigma and Lean. How to tell “story” from dataset? Quantitative Data. Graphical Methods Dot Plots Stem-and-Leaf Plots Frequency Tables Histograms and Performance Histograms Run Charts Time-Series Plots Numerical Methods: Descriptive Statistics.

Chapter 8 Making Sense of Data in Six Sigma and Lean

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## Chapter 8Making Sense of Data inSix Sigma and Lean

### How to tell “story” from dataset?Quantitative Data

• Graphical Methods

• Dot Plots

• Stem-and-Leaf Plots

• Frequency Tables

• Histograms and Performance Histograms

• Run Charts

• Time-Series Plots

• Numerical Methods: Descriptive Statistics

### How to tell “story” from dataset?Qualitative Data

• Pie Charts

• Bar Charts

• Pareto Analysis with Lorenz Curve

### How to tell “story” from dataset?Bivarite Data

• Graphical Methods

• Scatter Plots

• Numerical Methods: Correlation Coefficient

• Pearson Coefficient

• Spearman’s Rho ()

• Kendall’s Tau () Rank Correlation

### How to tell “story” from dataset?Multi-Vari Data

• Graphical Methods

• Multi-Vari Charts

### Summarizing Quantitative Data:Dot Plots

• Dot plot is one of the most simple types of plots

Example 8.1

Minitab

Graph

Dotplot

Simple

### Summarizing Quantitative Data:Stem-and-Leaf Plots

• Stem-and-Leaf Plots are a method for showing the frequency with which certain classes of values occur.

i160.photobucket.com/.../treediagram.png

### Summarizing Quantitative Data:Frequency Tables

• constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies.

• Absolute frequencies or relative frequencies (%)

www.sci.sdsu.edu/.../Weeks/images/Frequency.png

### Summarizing Quantitative Data: Histogram

www.statcan.gc.ca/.../ch9/images/histo1.gif

### Summarizing Quantitative Data:Run Charts

• A line graph of data points plotted in chronological order that helps detect special causes of variation

Minitab

Graph

Time Series Plot

Simple

### Summarizing Quantitative Data: Time-Series Plots

• A time series plot is a graph showing a set of observations taken at different points in time and charted in a time series.

Minitab

Graph

Time Series Plot

Simple

### Summarizing Quantitative Data:Descriptive Statistics

Measures of Center

• Sample mean

• Population mean

• Median: the "middle" value in the dataset

• Mode: the value that occurs most often

### Summarizing Quantitative Data:Descriptive Statistics

Measures of Variation

• Range: the difference between the largest and the smallest values in the dataset

• Sample variance

• Sample standard deviation

• Population variance

• Population standard deviation

### Summarizing Quantitative Data:Descriptive Statistics

Measures of Variation

• Coefficient of Variation (CV)

• Interquartile Range (IQR)

Summarizing Quantitative Data:Descriptive Statistics

• Minimum

• Maximum

• Median

• First Quartile

• Third Quartile

• Minitab:

• Stat

• Basic Statistics

• Display Descriptive..

• Boxplot

### Summarizing Quantitative Data:Descriptive Statistics

Identifying Potential Outliers

• Lower inner fence (LIF) =

• Upper inner fence (UIF) =

• Lower outer fence (LOF) =

• Upper outer fence (UOF) =

• Mild outliers: data fall between the two lower fences and between the two upper fences

• Extreme outliers: data fall below the LOF or above the UOF

### Summarizing Quantitative Data:Descriptive Statistics

Measures of Positions

• Percentiles

• Percentiles divide the dataset into 100 equal parts

• Percentiles measure position from the bottom

• Percentiles are most often used for determining the relative standing of an individual in a population or the rank position of the individual.

• z scores

• Standard normal distribution ( = 0 and  = 1)

### Summarizing Qualitative Data:Graphical Displays

• Pie Chart

http://techie-teacher-wanna-be.wikispaces.com/file/view/SocialPieChart.png/96606670/SocialPieChart.png

### Summarizing Qualitative Data:Graphical Displays

• Bar Graph

www.creationfactor.net/images/graph-bar.jpg

### Summarizing Qualitative Data:Graphical Displays

• Pareto Analysis with Lorenz Curve

www.spcforexcel.com/files/images/ccpareto.gif

Minitab:

Graph

Scatterplot

Simple

### Summarizing Bivariate Data:Correlation Coefficient

• Pearson Correlation Coefficient

Minitab:

Stat

Regression

Regression

### Summarizing Bivariate Data:Correlation Coefficient

• Spearman’s Rho ()

• A measure of the linear relationship between two variables.

• It differs from Pearson's correlation only in that the computations are done after the numbers are converted to ranks.

• When converting to ranks, the smallest value on X becomes a rank of 1, etc.

• D (Difference) is calculated between the pair of ranks

### Summarizing Bivariate Data:Correlation Coefficient

• Spearman’s Rho () Example

### Summarizing Bivariate Data:Correlation Coefficient

• Kendall’s Tau ()

• A measure of the linear relationship between two variables.

• It differs from Pearson's correlation only in that the computations are done after the numbers are converted to ranks.

• When converting to ranks, the smallest value on X becomes a rank of 1, etc.

• P is # of pairs with both ranks higher

### Summarizing Bivariate Data:Correlation Coefficient

• Kendall’s Tau () Example

• Example

### Summarizing Multi-Vari Data: Multi-Vari Charts

• Show patterns of variation from several possible causes on a single chart, or set of charts

• Obtains a first look at the process stability over time. Can be constructed in various ways to get the “best view”.

• Positional: variation within a part or process

• Cyclical: variation between consecutive parts or process steps

• Temporal: Time variability

### Graphical Tool: Multi-Vari Charts

Cus. Size: 1 = small

2 = large

Product:1 = Consumer

2 = Manuf.

Cus. Type: 1 = Gov’t

2 = Commercial

3 = Education

http://www.qimacros.com/qiwizard/multivari-chart.html

Minitab:

Stat

Quality Tools

Multi Vari Chart