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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 * 67 61 72 * 170 120 220 * 33 38 62 * 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) 190056 191058 192060 193065 194076 195084 196095 1970120 1970 PopulationGDPGender Country(Millions)$ BillionRatio USA1605750.998 China8001551.105 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 2030.1515 20 to 3060.3030 30 to 4050.2525 40 to 5040.2020 50 to 6020.1010 201.00100

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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: 58 - 12 = 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 955MGA88 1061FFL71 1162MGA92 1265FSC54 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 FL66.0025.00 GA70.0074.67 SC53.6767.50

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Bivariate Numerical Data Scatter Plot

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Two variables, different units Source: http://www.epa.gov/ttn/chief/trends/trends06/nationaltier 1upto2006basedon2002finalv2.1.xls YearCONox 1990154,18825,527 1991147,12825,180 1992140,89525,261 1993135,90225,356 1994133,55825,350 1995126,77824,955 1996128,85924,786 1997117,91124,706 1998115,38024,347 1999114,54122,843 2000114,46522,599 2001106,26321,546 2002109,23521,277 2003107,06220,476 2004104,89219,564 2005102,72118,947 2006100,55218,226

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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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