1. Goal Sharing Team Training Statistical Thinking and Data Analysis (I) Peter Ping Liu, Ph D, PE, CQE, OCP and CSIT Professor and Coordinator of Graduate Programs School of Technology Eastern Illinois University Charleston, IL 61920

2. Meet the Instructor BS, MS and Ph D in Engineering. Registered Professional Engineer (PE) in Illinois. Certified Quality Engineer (CQE). Oracle Certified Professional (OCP). Research: Biomedical materials, total replacement implants, database and quality management.

3. Goals for the Training To be able to measure work performance (and goals) quantitatively and objectively— Goal setting and achieving. To be able to understand the data (goals) across the organization – Goal sharing.

4. Objectives To have fun. To learn something useful.

5. Data: A Way of Life Data is everywhere we go and in everything we do. Examples: time, salary, ??? Our challenge is how to use the data to our benefits.

6. Data Summary: Finding the basic facts We use a simple example to illustrate ways to organize data in order to find some basic facts.

7. 120153186117140 165125128129120 12313211111793 205130112120180 150130120140118 130126166110112 110185105112132 12515011695145 119135118139150 125112116114125 11711695 The following table shows weights of college students.

8. Statistical thinking I: Data has to tell a true story.

9. Statistical thinking II: Data has to be organized to become useful (information).

10. Step 1: Tabulate the data into one column (Due to space limitation, the column was broken into 3 pieces.) 120 165 123 205 150 130 110 125 119 125 153 125 132 130 126 185 150 135 112 116 186 128 111 112 120 166 105 116 118 116 117 129 117 120 140 110 112 95 139 114 140 120 93 180 118 112 132 145 150 125

11. Step 2: Sort the data from the largest to the smallest 205 … 120 119 118 117 … … 93

12. Data Interpretation: Minimum, Maximum and Range. Minimum value: smallest, shortest, lightest. Maximum value: largest, tallest, heaviest. Range=Maximum value – Minimum value.

13. Statistical thinking III: Range is related to the consistency. Smaller range means better consistency. In many applications, our objective is to achieve the best consistency, or smallest range.

14. Step 3: Divide the entire range approximately into 10 cells (parts/divisions). 200-209 190-199 … 90-99

15. Step 4: Tally each data point. WeightTally 200 - 209/ 190 - 199 180 – 189/// 170 – 179 160 – 169// 150 – 159//// 140 - 149/// 130 – 139///// // 120 – 129///// ///// // 110 – 119///// ///// ///// // 100 – 109/ 90 – 99///

16. Worksheet: Tally each data point. Tally

17. Statistical thinking IV: Historical data can be used to predict future performance.

18. Step 5: Frequency (Number of Observations) WeightTallyFrequency 200 - 209/1 190 – 1990 180 – 189///3 170 – 1790 160 – 169//2 150 – 159////4 140 - 149///3 130 – 139///// //7 120 – 129///// ///// //12 110 – 119///// ///// ///// //17 100 – 109/1 90 – 99///3 Total53

19. Worksheet: Frequency (Number of Observations) TallyFrequency

20. Step 6a: Relative Frequency (Proportion) = Frequency/Total WeightTallyFrequencyRelative Frequency (Proportion) 200 - 209/10.018868 190 – 19900.00 180 – 189///30.056604 170 – 17900.00 160 – 169//20.037736 150 – 159////40.075472 140 - 149///30.056604 130 – 139///// //70.132075 120 – 129///// ///// //120.226415 110 – 119///// ///// ///// //170.320755 100 – 109/10.018868 90 – 99///30.056604 Total531.0

21. Worksheet: Relative Frequency (Proportion) = Frequency/Total TallyFrequencyRelative Frequency (Proportion)

22. Step 6b: Relative Frequency (Percentage)= (Frequency/Total)x100 WeightTallyFRelative Frequency (Proportion) Relative Frequency (Percentage) 200 - 209/10.0188681.8868 190 – 19900.0000000.0000 180 – 189///30.0566045.6604 170 – 17900.0000000.0000 160 – 169//20.0377363.7736 150 – 159////40.0754727.5472 140 - 149///30.0566045.6604 130 – 139///// //70.13207513.2075 120 – 129///// ///// //120.22641522.6415 110 – 119///// ///// ///// //170.32075532.0755 100 – 109/10.0188681.8868 90 – 99///30.0566045.6604 Total531.0100

23. Worksheet: Relative Frequency (Percentage)= (Frequency/Total)x100 TallyFRelative Frequency (Proportion) Relative Frequency (Percentage)

24. What weight range has the highest frequency?

25. Step 7a: Cumulative Frequency: Total number of observations at or below the class (value) WeightTallyFrequencyCumulative Frequency 200 - 209/153 190 – 199052 180 – 189///352 170 – 179049 160 – 169//249 150 – 159////447 140 - 149///343 130 – 139///// //740 120 – 129///// ///// //1233 110 – 119///// ///// ///// //1721 100 – 109/14 90 – 99///33 Total53

26. Worksheet: Cumulative Frequency: Total number of observations at or below the class (value) TallyFrequencyCumulative Frequency

27. Step 7b: Cumulative Frequency: Cumulative Proportion WeightTallyFCumulative Frequency Cumulative Proportion 200 - 209/1531.00 190 – 1990520.98 180 – 189///3520.98 170 – 1790490.92 160 – 169//2490.92 150 – 159////4470.89 140 - 149///3430.81 130 – 139///// //7400.75 120 – 129///// ///// //12330.62 110 – 119///// ///// ///// //17210.40 100 – 109/140.08 90 – 99///330.06 Total53

28. Worksheet: Cumulative Frequency: Cumulative Proportion TallyFCumulative Frequency Cumulative Proportion

29. Step 7c: Cumulative Frequency: Cumulative Percent WeightFCumulative Frequency Cumulative Proportion Cumulative Percent 200 - 2091531.00100 190 – 1990520.9898 180 – 1893520.9898 170 – 1790490.9292 160 – 1692490.9292 150 – 1594470.8989 140 - 1493430.8181 130 – 1397400.7575 120 – 12912330.6262 110 – 11917210.4040 100 – 109140.088 90 – 99330.066 Total53

30. Worksheet: Cumulative Frequency: Cumulative Percent FCumulative Frequency Cumulative Proportion Cumulative Percent

31. Data Interpretation What percent of students whose weight is at or below 109 lb? What percent of students whose weight is at or below 159 lb? What percent of students whose weight is at or below 199 lb?

32. Step 8: Percentile Ranks The percentile rank indicates the percentage of observations with similar and smaller values than certain value in the entire population. Refer to Step 7c: If my weight is 135 lb, 75% of people weigh equal or less than me. My percentile rank is 75%.

33. Data Interpretation (Refer to Step 7c) What is your weight percentile rank? (pick up any weight you like)

34. Statistical thinking V: Data can tell where we stand compared with others.