Histogram for Sample Data - Critical Defect No. 1 Cost Data Integrity Project
Once Trend Charts have been completed, enter the same observation data into a Histogram to check for Normality - may need to revise and change sample plan before moving to Statistical Process Control. Additional Instructions > Making Histograms Observation Value Describe the Sample Test and Defect Measured: 1 27 Nine observations were made over a 9 month period regarding the posting of 2 22 vendor invoices into the Project Management System. Compare the invoices 3 20 that were processed and paid per the General Ledger with invoices that were 4 26 posted in the Project Management System. Count the number of invoices that 5 21 were not posted in the Project Management System. 6 28 7 25 8 22 9 28 Maximum Minimum Range 28.0 20.0 8.0 3 5 < Minimum Intervals 2
Number of Intervals based on Square Root of Observations > Width of each interval based on Range / (No of Intervals - 1) Histogram Table based on above data: Interval 1 2 3 4 5
Simple Side Ways Plot Freq 1 3 0 2 3
Less than or Equal to 20 Between 21 and 22 Between 23 and 24 Between 25 and 26 Between 27 and 28
Appears to be a Bi Modal Distribution
1
More Formal Histogram Bar Chart:
Frequency Distribution
3.5
3 Frequency
2.5
2
Freq
1.5
1 0.5
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1 2 3 Intervals 4 5
2
Histogram for Sample Data - Critical Defect No. 2 Cost Data Integrity Project
Once Trend Charts have been completed, enter the same observation data into a Histogram to check for Normality - may need to revise and change sample plan before moving to Statistical Process Control. Additional Instructions > Making Histograms Observation Value Describe the Sample Test and Defect Measured: 1 41 For all active employees assigned to projects, how many employees did 2 37 not enter a timesheet into the Project Management System for the 3 35 two week pay period. 4 33 5 36 6 40 7 38 8 36 9 34 Maximum Minimum Range 41.0 33.0 8.0 3 5 < Minimum Intervals 2
Number of Intervals based on Square Root of Observations > Width of each interval based on Range / (No of Intervals - 1) Histogram Table based on above data: Interval 1 2 3 4 5
Simple Side Ways Plot Freq 1 1 3 1 2
Less than or Equal to 33 Between 34 and 35 Between 36 and 37 Between 38 and 39 Between 40 and 41
Need additional samples
More Formal Histogram Bar Chart:
Frequency Distribution
3.5
3 Frequency
2.5
2
Freq
1.5
1 0.5
0
1 2 3 Intervals 4 5
Histogram Results Cost Data Integrity Project
Summarize the results of the histograms for each of the three critical defects: Critical Defect No. 1: The frequency distribution for vendor invoices is bi-modal indicating that stratified sampling needs to be performed. This is most likely due to the fact that each IT investment is managed seperately and as a result, each IT project has its own unique defect rates; i.e. some projects do a good job of processing and posting their invoices, but others do a very poor job. Therefore, each project should represent a sub-group and observations should be taken from each sub group to arrive at proper measurement of defects. Critical Defect No. 2: Similar to defect 1, probably need to conduct subgroup samples on a project by project basis to reach normality.