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

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.

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.

Objectives To have fun. To learn something useful.

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.

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

The following table shows weights of college students.

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

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

Step 1: Tabulate the data into one column (Due to space limitation, the column was broken into 3 pieces.)

Step 2: Sort the data from the largest to the smallest 205 … … … 93

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

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.

Step 3: Divide the entire range approximately into 10 cells (parts/divisions) … 90-99

Step 4: Tally each data point. WeightTally / – 189/// 170 – – 169// 150 – 159//// /// 130 – 139///// // 120 – 129///// ///// // 110 – 119///// ///// ///// // 100 – 109/ 90 – 99///

Worksheet: Tally each data point. Tally

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

Step 5: Frequency (Number of Observations) WeightTallyFrequency /1 190 – – 189///3 170 – – 169//2 150 – 159//// ///3 130 – 139///// //7 120 – 129///// ///// // – 119///// ///// ///// // – 109/1 90 – 99///3 Total53

Worksheet: Frequency (Number of Observations) TallyFrequency

Step 6a: Relative Frequency (Proportion) = Frequency/Total WeightTallyFrequencyRelative Frequency (Proportion) / – – 189/// – – 169// – 159//// /// – 139///// // – 129///// ///// // – 119///// ///// ///// // – 109/ – 99/// Total531.0

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

Step 6b: Relative Frequency (Percentage)= (Frequency/Total)x100 WeightTallyFRelative Frequency (Proportion) Relative Frequency (Percentage) / – – 189/// – – 169// – 159//// /// – 139///// // – 129///// ///// // – 119///// ///// ///// // – 109/ – 99/// Total

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

What weight range has the highest frequency?

Step 7a: Cumulative Frequency: Total number of observations at or below the class (value) WeightTallyFrequencyCumulative Frequency / – – 189/// – – 169// – 159//// /// – 139///// // – 129///// ///// // – 119///// ///// ///// // – 109/14 90 – 99///33 Total53

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

Step 7b: Cumulative Frequency: Cumulative Proportion WeightTallyFCumulative Frequency Cumulative Proportion / – – 189/// – – 169// – 159//// /// – 139///// // – 129///// ///// // – 119///// ///// ///// // – 109/ – 99/// Total53

Worksheet: Cumulative Frequency: Cumulative Proportion TallyFCumulative Frequency Cumulative Proportion

Step 7c: Cumulative Frequency: Cumulative Percent WeightFCumulative Frequency Cumulative Proportion Cumulative Percent – – – – – – – – – – Total53

Worksheet: Cumulative Frequency: Cumulative Percent FCumulative Frequency Cumulative Proportion Cumulative Percent

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?

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%.

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

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