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Describing Data Charts and Graphs

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Lecture Objectives You should be able to: 1.Define Basic Terms 2.Recognize Types of Data and Data Scales 3.Draw appropriate graphs based on type of data and type of analysis desired. 4.Interpret the graphs

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Basic Terms 1.Data, Information, and Knowledge 2.Populations and Samples 3.Variables and Observations Types of Data: 1.Categorical and Numerical 2.Cross Sectional and Time Ordered

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Data, Information, and Knowledge Data Information Processing Analysis Reports Application Meaning Relevance Knowledge

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Populations and Samples Sample: Subset of collection Described by Statistics Population: Collection of all possible entities of interest Described by Parameters Statistical Inference Art and science of using samples to make conclusions about populations.

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Variables and Observations Entity Height (inches) Weight (pounds) Age (years) Sex (Category) Person 1 Person 2 Person 3 * * * * Male Female Male * OBSERVATIONSOBSERVATIONS VARIABLES Measurement

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Types of Data: Categorical and Numerical CategoricalNumerical

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Data Scales Data are generally classified into four types: 1. Nominal – Categorical data 2. Ordinal – shows ranks, intervals may vary 3. Interval – intervals are constant, arbitrary 0 4. Ratio – Numeric data with a real 0 value. Ordinal, Interval and Ratio scales are all Numeric data.

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Types of Data: Time Series and Cross-sectional Population Month(Millions) PopulationGDPGender Country(Millions)$ BillionRatio USA China India600 Nigeria100 Japan120 Canada30 Variable(s) over time Variable(s) at one point in time across multiple entities (countries in this case)

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Numeric Data (Interval or Ratio): Frequency Tables A Frequency Table showing a classification of the AGE of attendees at an event. Relative ClassFrequency Percent 10 to to to to to

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Frequency Histograms A graphical display of distribution of frequencies

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Developing Frequency Tables and Histograms 1.Sort Raw Data in Ascending Order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 2.Find Range: = 46 3.Select Number of Classes: 5 (usually between 5 and 15) 4.Compute Class Interval (width): 10 (range/classes = 46/5 then round up) 5.Determine Class Boundaries (limits): 10, 20, 30, 40, 50 6.Compute Class Midpoints: 15, 25, 35, 45, 55 7.Count Observations & Assign to Classes

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Categorical Data: Bar Charts ObsAgeGenderStateSalary 125MFL25 228FSC36 331MGA44 435FGA38 536MSC56 638FFL68 742MSC79 851FFL64 955MGA FFL MGA FSC54 StateFreq FL3 SC5 GA4

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Categorical Data: Pie Charts StateFreq FL3 SC5 GA4

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Numeric Data by Category FM FL GA SC

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Bivariate Numerical Data Scatter Plot

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Two variables, different units Source: 1upto2006basedon2002finalv2.1.xls YearCONox ,18825, ,12825, ,89525, ,90225, ,55825, ,77824, ,85924, ,91124, ,38024, ,54122, ,46522, ,26321, ,23521, ,06220, ,89219, ,72118, ,55218,226

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Chapter Summary Categorization: Bar, Pie charts Distribution: Stem and Leaf, Histogram, Box Plot Relationships: Scatter Plots, Line Charts Multivariate: Spider Plots, Maps, Bubble Charts

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