1. Chapter 8 Making Sense of Data in Six Sigma and Lean

2. 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

3. How to tell “story” from dataset? Qualitative Data
Pie Charts
Bar Charts
Pareto Analysis with Lorenz Curve

4. 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

5. How to tell “story” from dataset? Multi-Vari Data
Graphical Methods
Multi-Vari Charts

6. Summarizing Quantitative Data: Dot Plots
Dot plot is one of the most simple types of plots
Example 8.1
Minitab
Graph
Dotplot
Simple

7. 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

8. 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 (%)

9. Summarizing Quantitative Data: Histogram

10. 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

11. 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

12. 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

13. 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

14. Summarizing Quantitative Data: Descriptive Statistics
Measures of Variation
Coefficient of Variation (CV)
Interquartile Range (IQR)

15. Summarizing Quantitative Data: Descriptive Statistics
Minimum
Maximum
Median
First Quartile
Third Quartile
Minitab:
Stat
Basic Statistics
Display Descriptive..
Boxplot

16. 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

17. 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)

18. Summarizing Qualitative Data: Graphical Displays
Pie Chart

19. Summarizing Qualitative Data: Graphical Displays
Bar Graph

20. Summarizing Qualitative Data: Graphical Displays
Pareto Analysis with Lorenz Curve

21. Summarizing Bivariate Data: Scatterplot
Minitab:
Graph
Scatterplot
Simple

22. Summarizing Bivariate Data: Correlation Coefficient
Pearson Correlation Coefficient
Minitab:
Stat
Regression

23. 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

24. Summarizing Bivariate Data: Correlation Coefficient
Spearman’s 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 D -4 -1 D2 16
=28

25. 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

26. Summarizing Bivariate Data: Correlation Coefficient
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 P
=21

27. 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

28. Graphical Tool: Multi-Vari Charts
Cus. Size
Product
Cus. Type
Satis. 1 2
3.54 3
3.16
2.42
2.70
3.31
4.12
3.24
4.47
3.83
2.94
Cus. Size: 1 = small
2 = large
Product: 1 = Consumer
2 = Manuf.
Cus. Type: 1 = Gov’t
2 = Commercial
3 = Education

29. Graphical Tool: Multi-Vari Charts
Minitab:
Stat
Quality Tools
Multi Vari Chart