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Data are measurements at single point in time l eg

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data are measurements at single point in time l Eg: SIA Sydney housing prices by suburb l Data type can influence what is appropriate by way of analysis l Total number of births per day makes sense l Suppose marital status is coded as Single =1, Married =2, Divorced =3, Widowed=4; l Does it make sense to total the marital status of a sample of individuals?
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17 Descriptive statistics l Difficult to determine key features of data l Need to organize & summarize data in order to extract information l This is role of descriptive statistics l There is a vast range of tools & techniques l Some are graphical, some numerical l Type of data may impact on which to use
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18 Frequency distributions l Want to summarize categorical data with associated counts l UNSW interested in transport issues l How do people travel to campus? ( http://www.facilities.unsw.edu.au/getting-uni ) l Categories need to be mutually exclusive & exhaustive Mode of transport to campus Frequency Relative Frequency Resident Walk Cycle Car Bus Other Total 100
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19 Bar charts & pie charts l Provide graphical representation of frequency distributions l 2011 UNSW Travel Survey sample of 5881 l 47 (0.8%) Resident l 628 (10.7%) Walk l 210 (3.6%) Bike l 1032 (17.5%) Car l 1188 (20.2%) Bus l 2776 (47.2%) Other 0 500 1000 1500 2000 2500 3000 Resident Walk Bike Car Bus Other Bar chart of mode of transport to UNSW campus
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Bar charts & pie charts… l Pie charts show relative frequencies l What’s in the “Other” category? 20 Resident 1% Walk 11% Bike 4% Car 17% Bus 20% Other 47% Pie chart of mode of transport to UNSW campus Resident 1% Walk 11% Bike 4% Car 17% Bus 20% Other 2% Bus & train 45% Modified pie chart of mode of transport to UNSW campus
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21 Histograms l Suppose data are quantitative & not qualitative l Obvious categories may not exist l But we can create categories or classes l Define lower and upper class limits l These need to be mutually exclusive & exhaustive l How many classes? (EXCEL calls them bins ) l Too many  doesn’t summarize l Too few  no information l No set rules although more observations  more classes l Classes need not be of equal width & may be open-ended l Keller Ex 3.3: Business Statistics Marks l Final marks for 60 students
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22 Histograms… "Aussie" Marks histogram 0 5 10 15 20 25 30 35 49 64 74 84 100 Marks Frequency
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23 Histograms… l Beware of EXCEL features l Should be no gaps between bars for quantitative data l Classes defined by upper limits when class mid- points may be more natural l Bar areas should be proportional to frequencies ( refer Ch 8, p 265 ) incorrec t Histogram for Example 2.6 0 5 10 15 20 25 30 50 60 70 80 90 More Bin Frequency
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24 Other distributions & displays l Can convert information in frequency distributions into: l Cumulative frequency or (cumulative) relative frequency distributions l Aussie marks eg - How many students got a credit or better? l Associated cumulative histograms & ogives l Stem-and-leaf displays l May be interesting information lost in histograms l Do examiners avoid marks close to borderline?
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