Title: Chapter 8 Making Sense of Data in Six Sigma and Lean
1Chapter 8Making Sense of Data inSix Sigma and
Lean
2How 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
3How to tell story from dataset?Qualitative Data
- Pie Charts
- Bar Charts
- Pareto Analysis with Lorenz Curve
4How to tell story from dataset?Bivarite Data
- Graphical Methods
- Scatter Plots
- Numerical Methods Correlation Coefficient
- Pearson Coefficient
- Spearmans Rho (?)
- Kendalls Tau (?) Rank Correlation
5How to tell story from dataset?Multi-Vari Data
- Graphical Methods
- Multi-Vari Charts
6Summarizing Quantitative DataDot Plots
- Dot plot is one of the most simple types of plots
Example 8.1 Minitab Graph Dotplot Simple
7Summarizing Quantitative DataStem-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
8Summarizing Quantitative DataFrequency 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
9Summarizing Quantitative Data Histogram
www.statcan.gc.ca/.../ch9/images/histo1.gif
10Summarizing Quantitative DataRun Charts
- A line graph of data points plotted in
chronological order that helps detect special
causes of variation
Minitab Graph Time Series Plot Simple
11Summarizing 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
12Summarizing Quantitative DataDescriptive
Statistics
- Measures of Center
- Sample mean
- Population mean
- Median the "middle" value in the dataset
- Mode the value that occurs most often
13Summarizing Quantitative DataDescriptive
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
14Summarizing Quantitative DataDescriptive
Statistics
- Measures of Variation
- Coefficient of Variation (CV)
- Interquartile Range (IQR)
15Summarizing Quantitative DataDescriptive
Statistics
- Minimum
- Maximum
- Median
- First Quartile
- Third Quartile
- Minitab
- Stat
- Basic Statistics
- Display Descriptive..
- Boxplot
16Summarizing Quantitative DataDescriptive
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
17Summarizing Quantitative DataDescriptive
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)
18Summarizing Qualitative DataGraphical Displays
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/view/SocialPieChart.png/96606670/SocialPieChart.p
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19Summarizing Qualitative DataGraphical Displays
www.creationfactor.net/images/graph-bar.jpg
20Summarizing Qualitative DataGraphical Displays
- Pareto Analysis with Lorenz Curve
www.spcforexcel.com/files/images/ccpareto.gif
21Summarizing Bivariate DataScatterplot
Minitab Graph Scatterplot Simple
22Summarizing Bivariate DataCorrelation
Coefficient
- Pearson Correlation Coefficient
Minitab Stat Regression Regression
23Summarizing Bivariate DataCorrelation
Coefficient
- Spearmans 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
24Summarizing Bivariate DataCorrelation
Coefficient
- Spearmans Rho (?) 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
D 2 0 1 2 -4 -1 1 -1
D2 4 0 1 4 16 1 1 1 ?28
25Summarizing Bivariate DataCorrelation
Coefficient
- Kendalls 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
26Summarizing Bivariate DataCorrelation
Coefficient
- Kendalls 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
27Summarizing 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
28Graphical 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 small 2 large Product 1
Consumer 2 Manuf. Cus. Type 1 Govt 2
Commercial 3 Education
http//www.qimacros.com/qiwizard/multivari-chart.h
tml
29Graphical Tool Multi-Vari Charts
Minitab Stat Quality Tools Multi Vari Chart