2_stat review

2_stat review - Spring 2008 EMSE 182, 282, Professor Jim...

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Spring 2008 EMSE 182, 282, Professor Jim Mazzuchi, Stat Review - 1 STATISTICAL REVIEW EXPLORATORY DATA ANALYSIS Single variable methods Data : 48, 53, 49, 52, 51, 52, 63, 60, 53, 64, 59, 54, 47, 49, 45, 64, 79, 65, 62, 60, 68, 65, 73, 88, 69, 83, 78, 81, 86, 92, 75, 85, 81, 77, 82, 76, 75, 91, 73, 82 • Stem and Leaf Plot Feel of distribution shape without loss of data Ä Reasonable breakpoints in units of tens, some modeification possible Ä STEM LEAF FREQUENCY 4 5, 7, 8, 9, 9 5 5 1, 2, 2, 3, 3, 4, 9 7 6 0, 0, 2, 3, 4, 4, 5, 5, 8, 9 10 7 3, 3, 5, 5, 6, 7, 8, 9 8 8 1, 1, 2, 3, 5, 6, 8 7 9 1, 2, 2 3
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Spring 2008 EMSE 182, 282, Professor Jim Mazzuchi, Stat Review - 2 • Frequency Histogram Data are put into groupings (called cells) and the frequency of each Ä cell is displayed graphically as a rectangle about the midpoint of the grouping Groupings and their number are at the discretion of the modeler Ä with the rule of thumb that # each cell >5 Grouping need not be of same size but usually are, it is the best Ä procedure for distribution representation. Grouping may change histogram shape Ä
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Spring 2008 EMSE 182, 282, Professor Jim Mazzuchi, Stat Review - 3 With enough data, a histogram approximates distributional forms Ä • Empirical CDF, F (x) n Plot of estimate of the CDF Ä Pr{X x} , for x x for x x x Ÿœ ! Ÿ œ Ð"Ñ 3 Ð3Ñ Ð3"Ñ n where x ith smallest x value,x 0, and n sample size Ð3Ñ Ð Ñ œ´ œ 0
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Spring 2008 EMSE 182, 282, Professor Jim Mazzuchi, Stat Review - 4 • Time Serries Plot Sequential plot of data vs time or sample number Ä Helpful in visualizing variability, trends, cycles, or dependance Ä
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Spring 2008 EMSE 182, 282, Professor Jim Mazzuchi, Stat Review - 5 Multiple variable methods Observations Concentration Group 123456T o t a l s A v e r a g e 1 7 8 15 11 9 10 60 10.00 2 12 17 13 18 19 15 94 15.67 3 14 18 19 17 16 18 102 17.00 4 19 25 22 23 18 20 127 21.17 383 15.96
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Spring 2008 EMSE 182, 282, Professor Jim Mazzuchi, Stat Review - 6 • Box Plot • Tier Plot
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Spring 2008 EMSE 182, 282, Professor Jim Mazzuchi, Stat Review - 7 PROBABILITY Basic Rules • Complimentary Probability P r { A } = 1 P r { A } • Additive Law (For sets A and B Pr A = Pr A + Pr B - Pr A ) Ö ×Ö × Ö × BB Pr{A A } Pr{A } Pr{A A } "8 3 3 4 3œ" 3œ" 88 43 ∪â∪ œ ±± ± P r { A A A } ±±± 3œ" 8 43 54 345 ∩∩ â ( 1 ) P r { A A }  ∩â∩ 8" 8 1 • Multiplicative Law P r { A A } P r { A } P r { A | A } "8" " œ 2 P r { A | A A } P r { A | A A } 3 "# 8 " 8 " ∩‡ â â • Law of Total Probability Pr{B} Pr{B A } Pr{B|A }Pr{A }, œ∩ œ ii i œ" œ" w h e r e A A ( M E ) , a n d A ( C E ) 34 3 3œ" 8 ∩œ g ∪œ W •Bayes Law Pr{A |B} , where A , . .., A are ME and CE 3 œ Pr{B|A }Pr{A } Pr{B|A }Pr{A } 1n 33 4œ" 8 44 ±
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Spring 2008 EMSE 182, 282, Professor Jim Mazzuchi, Stat Review - 8 - given a batch with 10 out of 100 defectives Example • What is the probability of selecting a nondefective? D ´ H/0/->3@/ Complimentary Probability P(D) = 10/100 = .1 P(D) 1 P(D) .9; Êœ œ • What is the probability of selecting a defective on the first three draws?
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This note was uploaded on 01/02/2010 for the course EMSE 282 taught by Professor Harris during the Spring '07 term at GWU.

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2_stat review - Spring 2008 EMSE 182, 282, Professor Jim...

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