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ECON 2B03 (45)

Lecture #2: Distributions.doc

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McMaster University
Jeff Racine

Lecture #2 (Chap 1 & 2 continued…) Presenting Data: Tables and Graphs • When presenting data either in the form of tables or graphs, it is often desirable to first split the data into groups/classes • How we split the data often depends on the data type (ie. Numeric or Quantative) Data types: -Categorical (nominal or ordinal) -Quantitative (discrete or continuous) • Regardless of the data type, data should be: -Collectively exhaustive: (must exhaust all logical possibilities for classifying available data) -Mutually exclusive: (must not overlap or have data in common) One immediately confronts the issue of how many classes to create Desirable class number: -Should fit the data type -Often recommended: between 5 and 20 classes -Sturgess’s rule: If you don’t know how many classes to use; use this rule. Desirable number of classes=k, where k is the integer closest to (use standard rules for rounding) 1+ 3.3 log 10n, where n is the sample size, and where log 10n is the power to which the base (10) is raised to yield n Ex: If n=1,000 than log 101000=3, so 1+3.3 log 101000=10.9 and therefore k=11 so by Sturgess’s rule you would use 11 classes when n=1,000 Data Classes Desirable class widths: -Class width: the difference between the lower and the upper limits of a class -To achieve uniform class widths in a table, divide the data set width by desirable class number Approximate class width: Largest value- smallest value Desirable class number Tabular Components • We first consider creating effective tabular summaries • An effective table includes: -Number (often based on chapter or page numbers) -Title (focus on what, where and when) -Caption (brief verbal summary) -Footnotes (eg: size of sampling error, likely extent of systematic error, etc..) -Decimals (consistent number or decimals) -Rounding (consistent rounding rules) -Class sums (sum of data pertaining to each class; crucial for open-ended classes) Frequency Distributions • Frequency distributions are an effective way to summarize data • Absolute Frequency Distributions -Absolute class frequency: -Absolute number of observations that fall into a given class (Total number of observations lying in each cla
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