Chapter 8 Making Sense of Data in Six Sigma and Lean

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

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

MinitabGraphDotplotSimple

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

MinitabGraphTime Series PlotSimple

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.

MinitabGraphTime Series PlotSimple

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

n

xx

N

x


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

1

)( 22

n

xxs

1

)( 2

n

xxs

N

x

22 )(

N

x

2)(


Measures of Variation• Coefficient of Variation (CV)

• Interquartile Range (IQR)

x

sCV

13 QQIQR

Minitab:Stat

Basic StatisticsDisplay Descriptive..•Boxplot

• Minimum• Maximum• Median

• First Quartile• Third Quartile



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

)5.1(1 IQRQ

)5.1(3 IQRQ

)0.3(1 IQRQ )0.3(3 IQRQ


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)

x

zs

xxz

Summarizing Qualitative Data:Graphical Displays

• Pie Chart

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


• Bar Graph

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


• Pareto Analysis with Lorenz Curve

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

Summarizing Bivariate Data:Scatterplot

Minitab:Graph

ScatterplotSimple

• Pearson Correlation Coefficient

Summarizing Bivariate Data:Correlation Coefficient

n

yy

n

xx

n

yxxy

r2

22

2 )()(

))((

Minitab:Stat

RegressionRegression

• 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


)1(

61

2

2

nn

Drs

• Spearman’s Rho () Example


667.)18(8

)28(61

)1(

61

22

2

nn

Drs

GPA 3.99 3.97 3.93 3.92 3.91 3.85 3.84 3.77

Salary 57.7 61.2 57.3 54.6 64.7 55.3 52.2 54.1

GPA Rank 8 7 6 5 4 3 2 1

Salary Rank 6 7 5 3 8 4 1 2

D 2 0 1 2 -4 -1 1 -1

D2 4 0 1 4 16 1 1 1 =28

• 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


1)1(

4

nn

Pr

• Kendall’s Tau () Example• Example


GPA 3.99 3.97 3.93 3.92 3.91 3.85 3.84 3.77

Salary 57.7 61.2 57.3 54.6 64.7 55.3 52.2 54.1

GPA Rank 8 7 6 5 4 3 2 1

Salary Rank 6 7 5 3 8 4 1 2

P 0 0 2 3 0 4 6 6 =21

50.1)18(8

)21(41

)1(

4

nn

Pr

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 Product Cus. Type Satis.

1 1 2 3.54

2 1 3 3.16

1 2 2 2.42

2 2 2 2.70

1 1 3 3.31

2 1 2 4.12

2 2 1 3.24

2 2 2 4.47

2 1 2 3.83

1 1 1 2.94

Cus. Size: 1 = small2 = large

Product: 1 = Consumer2 = Manuf.

Cus. Type: 1 = Gov’t2 = Commercial3 = Education

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

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

Graphical Tool: Multi-Vari Charts

Minitab:StatQuality ToolsMulti Vari Chart

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Chapter 8 Making Sense of Data in Six Sigma and Lean