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lecture2 - Statistics 51 Fall 2008 Class 2 Thu Sep 4...

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Statistics 51 – Fall 2008 Class 2: Thu, Sep 4 Outline for Today Summarizing two quantitative variables Graphical summaries for quantitative variable. Numerical summaries of centrality. Shapes of distributions. Numerical summaries of variation. Summarizing two qualitative variables Two categorical variables can be summarized numerically in a contingency table. We first list all combinations of the two variables. Then we compute the frequencies for each combination and summarize them in a form of a two-way table. (These tables are obtained in SPSS using the Crosstab function.) Example: Student Data Student Region Sex 1 Northeast Male 2 West Female 3 South Female 4 Northeast Female 5 Northeast Male 6 Midwest Female 7 West Female 8 International Male 9 South Male 10 Northeast Male 11 Midwest Female 12 West Female 13 Northeast Male 14 International Female 15 Midwest Female 16 South Male 17 South Female 18 Northeast Male 19 Northeast Male 20 Midwest Male Region * Sex Cross tabulation Sex Total Female Male Region International 1 1 2 Midwest 3 1 4 Northeast 1 6 7 South 2 2 4 West 3 0 3 Total 10 10 20
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Two categorical variables can be displayed using separate bar charts or pie charts. Below, we display two separate bar and pie charts for Region, one for each gender. International Midwest Northeast South West Region 0.0 0.5 1.0 1.5 2.0 2.5 3.0 C o u n t Sex: Female International Midwest Northeast South Region 0 1 2 3 4 5 6 C o u n t Sex: Male Summarizing Quantitative Data If the raw data to be summarized are quantitative and come from a single population, then we use descriptive methods such as frequency distributions, histograms, stem-and-leaf displays, and dot plots. These methods basically group the raw data into categories, called classes , and record the number of data that fall into each category.
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