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L see keller 31 for more discussion examples 25 key

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l See Keller 3.1 for more discussion & examples
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25 Key features: Shapes of histograms l Symmetry l Left half of histogram is a mirror image of right half l Famous bell-shape is symmetric l Skewness l Asymmetric histogram l Long tail to the right ( positively skewed ) l Long tail to the left ( negatively skewed ) ? ? ? ? ? ? ? ? l May be associated with outliers l Number of modal classes l Modal class is class with highest frequency l Histograms may be unimodal or multimodal
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26 A key feature: Shapes of histograms… l From Keller Ex 3.2 l Histogram of returns on Investment A is … l Modal class is … l No. of modal classes? l Therefore histogram is …
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27 Bivariate relations l Want to extend univariate analyses to characterize relationships between variables l Contingency table (Cross-tabulation table) l For relationship between qualitative variables l Scatter plots l For relationship between quantitative variables l If one of the variables is “time” we get a time series plot (line chart)
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Mode of transport example: Staff/student differences? l What does the bar graph highlight? l Is there a better representation? Commuter type Mode Staff Student Total Resident 0 47 47 Walk 97 531 628 Cycle 52 158 210 Car 472 560 1032 Bus 186 1002 1188 Bus & train 230 2439 2669 Other 25 82 107 Total 1062 4819 5881 28 0 500 1000 1500 2000 2500 3000 Resident Walk Bike Car Bus Bus & train Other F req u en cy Mode of transport by commuter type Staff Students
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29 Scatter plots
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30 SIA: Cars in China
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31 SIA: Cars in China… l What are the key features of these data? l Read Keller Ch 3.4 l How does this graph rate in terms of “characteristics for graphical excellence”?
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32 Time series plot l Bivariate relationship between variable Y & time l With time series data order matters l Business cycles defined by extended periods of growth or contraction l SIA: Baby bonus l Relatively sophisticated time plot
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33 SIA: Petrol prices Quarterly unleaded petrol prices: December 1980 to December 2005 0 20 40 60 80 100 120 1982 Sept 1984 Sept 1986 Sept 1988 Sept 1990 Sept 1992 Sept 1994 Sept 1996 Sept 1998 Sept 2000 Sept 2002 Sept 2005 Sept Cents per litre Sydney Melbourne Brisbane
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34 SIA: Petrol prices… l What are the key features of these data? l Do these data inform motorists about the best time to buy petrol?
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35 SIA: Petrol prices…
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36 SIA: Petrol prices… l Pattern representative of daily price movements in Sydney in winter 2006 l Consider daily data June 11 2006-July 10 2006 l Notable price variation from day to day l Determine day of weekly peak and trough l Common day for prices to peak was Thursday l No peaks (or troughs) on Monday, Tuesday, Friday, Saturday or Sunday l Common day for prices to trough was Tuesday l Consider longer period of daily data (not shown) l No troughs on Wednesday, Thursday, Friday or Saturday l No days when prices both peaked & troughed
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37 SIA: Petrol prices… l Would bar or pie charts be useful in displaying the weekly peak & trough data?
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