# Lec02 - Ch 1 Overview Descriptive Statistics IOE/Stat 265...

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1 Run Chart: Total Wait (69 Samples) 0 20 40 60 80 100 120 140 160 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 Total Wait Time (min IOE/Stat 265, Fall 2009 IOE/Stat 265, Fall 2009 Lecture #2: Lecture #2: Graphical Depiction of Data Graphical Depiction of Data 2 Ch 1: Overview & Descriptive Statistics 1-1 Populations, Samples, Processes 1-2 Pictorial &Tabular Methods in Describing Data 1-3 Measures of Location 1-4 Measures of Variability 3 1.2 Summarizing Data: Graphs Dot Plot (alternative to Stem-and-Leaf Diagram) Frequency of unique observed values Typically used for smaller samples, N<30 Histogram ( and Frequency Distributions) Frequency of grouped values General rule: use if N ± 30 ! prefer N>100 Box Plot Alternative to Histogram Easier to use with multiple strata Time Sequence Plot (a.k.a. Run Chart) Show data in time order (dispersion, trends) Probability Plot Alternative to Empirical Cumulative Distribution 4 Using Minitab Graph Stem and Leaf Diagrams Frequency Distributions and Histograms Box Plots Time Sequence Plots Probability Plots Dot Plots

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5 Example 1: Results for: Cycles.MTW Stem-and-Leaf Display: Cycles to Failure Stem-and-leaf of Cycles to Failure N = 70 Leaf Unit = 100 1 0 3 1 0 5 0 7777 10 0 88899 22 1 000000011111 33 1 22222223333 (15) 1 444445555555555 22 1 66667777777 11 1 888899 5 2 011 2 2 22 Stem-and-Leaf Display: Cycles to Failure Stem-and-leaf of Cycles to Failure N = 70 Leaf Unit = 10 1 3 7 1 4 1 5 1 6 5 7 0589 8 8 468 10 9 19 17 10 0111258 22 11 00012 29 12 0235667 33 13 1113 (5) 14 12568 32 15 0012346679 22 16 0047 18 17 3556889 11 18 2889 7 19 14 5 20 2 4 21 03 2 22 16 6 Dot Plot (alternative to Stem-Leaf Plot) Another tool (provided by most advanced statistical software) is a Dot Plot. Dot Plots are shown without grouping into ranges – typically are used with smaller data sets. Example 1 (continued): Dot Plot Using Minitab 7 Dot Plot by Strata 8 Frequency Analysis and Histogram Frequency Analysis is used to summarize occurrences and analyze patterns by grouping data. It involves determining frequencies (# of occurrences) by classes Classes or (Bins) - values or ranges of values (for discrete or continuous variables). E.g., Test Scores: 77, 77, 73, 84, 84, 81, 93, 98 Bin 70-79: values Bin 80-89: values Bin 90-99: values Frequency Table ! Histogram
10 Frequency Table To understand the distribution, we first create a frequency table In general, Frequency (or BIN) Ranges are equal widths ~ 0.4 mpg Inclusion of end values of ranges is often software dependent For Excel: 17.4 - 17.8 would be read as: 17.4 < X ± 17.8 Frequency Range Frequency (# Samples) < 17.4 0 17.4 - 17.8 3 17.8 - 18.2 4 18.2 - 18.6 5 18.6 - 19 14 19 - 19.4 9 19.4 - 19.8 10 19.8 - 20.2 7 20.2 - 20.6 13 20.6 - 21 10 21 - 21.4 9 21.4 - 21.8 6 21.8 - 22.2 7 22.2 - 22.6 2 22.6 - 23 1 > 23 0 total 100 11 Most statistical software (including Excel / Minitab) automatically create frequency bin ranges given a data set. If creating own ranges, some general rules: # of ranges ~ Between 5 – 20 ranges is usually sufficient Frequency Ranges (Classes) # observations 12 Example: Miles per Gallon Suppose you conduct an experiment on gas mileage.

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## This note was uploaded on 03/17/2010 for the course IOE 265 taught by Professor Garyherrin during the Fall '09 term at University of Michigan-Dearborn.

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Lec02 - Ch 1 Overview Descriptive Statistics IOE/Stat 265...

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