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ChE253K Spring09 Lecture03.Rev01

# ChE253K Spring09 Lecture03.Rev01 - HW Help Via Blackboard...

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1 28Jan2009 ChE 253K Lecture 03 HW Help Via Blackboard Revisions Announcements Discussions

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2 ChE 253K Lecture 03 28Jan2009 How To Summarize 1-D Data: Centers, Divisions & Spreads Descriptive Statistics
3 28Jan2009 ChE 253K Lecture 03 Outline Of This Lecture Data: Burn Fuel SOx Emissions 1-D Data Model: Meas = Mean ± Error Four-Plots to verify model: unControl, Lag, Histogram, Normal Prob Summary Stats: Excel & Text Centers: Mean, Median, Mode Divisions: Quartiles, Percentiles Spreads: Range, IQR, Std Deviation

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4 28Jan2009 ChE 253K Lecture 03 Readings Re: This Lecture 1-D Data Model NIST Sections 1.2.1-3 Four Plots Lecture 02 Mean, Median, Mode Text Sections 2.5, 2.7 Percentiles & Quartiles Inter-quartile range Text Section 2.6 Sample Std Deviation Text Sections 2.5, 2.7
5 28Jan2009 ChE 253K Lecture 03 Sources: Tenn. Valley Authority; learningoasis.org

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6 28Jan2009 ChE 253K Lecture 03 Data: SOx Emmissions (tons/day) x(i)={15.8 26.4 17.3 11.2 23.9 24.8 18.7 13.9 9.0 13.2 22.7 9.8 6.2 14.7 17.5 26.1 12.8 28.6 17.6 23.7 26.8 22.7 18.0 20.5 11.0 20.9 15.5 19.4 16.7 10.7 19.1 15.2 22.9 26.6 20.4 21.4 19.2 21.6 16.9 19.0 18.5 23.0 24.6 20.1 16.2 18.0 7.7 13.5 23.5 14.5 14.4 29.6 19.4 17.0 20.8 24.3 22.5 24.6 18.4 18.1 8.3 21.9 12.3 23.3 13.3 11.8 19.3 20.0 25.7 31.8 25.9 10.5 15.9 27.5 18.1 9.4 17.9 24.1 20.1 28.5} (N=80) Sources: Miller & Freund’s Prob & Stat for Engineers, 7 th Ed.
7 28Jan2009 ChE 253K Lecture 03 1-D Data Model Measurement = TrueValue ± RandomError X(i) = Mean ± (StDev × NormalRandom) 0 10 20 30 40 50 0 20 40 60 80 Sequence Measurements 0 5 10 15 20 25 30 <9 11 15 19 21 27 31 Interval Midpoint Frequen

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8 28Jan2009 ChE 253K Lecture 03 1-D Data Model Assumptions Assumptions Plots Check? Stable location and spread unControl Chart Random and uncorrelated Lag Plot X(i) vs. X(i-1) Single, clear center Standard shape Histogram Normal distribution Normal Probability Paper Plot
9 28Jan2009 ChE 253K Lecture 03 (un)Control Chart Stable or trending center & spread? Plot measurements vs. time or sequence # Scale measurements to see trends, not points Center Line: Mean Spread Lines: Mean ± 2 Std Deviations unControl Chart 0 100 200 300 0 25 50 75 100 Sequence Measurement

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10 28Jan2009 ChE 253K Lecture 03 unControl Chart: SOx Emissions X(i) = {15.8 26.4 17.3 ... 24.1 20.1 28.5} Mean = 18.9 Std Deviation = 5.7 N = 80 0 10 20 30 40 50 0 20 40 60 80 Sequence Measurements
11 28Jan2009 ChE 253K Lecture 03 Lag Plot Random or auto-correlated? Plot X(i) vs. X(i–1) Shaped Correlated Shapeless Random Lag Plot 0 100 200 300 0 100 200 300 X(i-1) X(i)

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12 28Jan2009 ChE 253K Lecture 03 Lag Plot: SOx Emissions x(i-1) x(i) 15.8 26.4 26.4 17.3 17.3 11.2 11.2 23.9 ... ...
13 28Jan2009 ChE 253K Lecture 03 1-D Data Model Assumptions Assumptions Plots Check?

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