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The most frequent observation in a distribution, mode is the most commonly used measure of central tendency with the nominal data. • Geometric mean. The geometric mean is an appropriate measure of central tendency when averages of rates or index numbers are required. It is the nth root of the product of a positive variable. For example, to estimate the average rate of return of a 3-year investment that earns 10% the first year, 50% the second year, and 30% the third year, the geometric mean of these three rates should be used.

3 Steps Involved in Running the EXCELSAS Macro 1. 2. 2. [{the companion CD-ROM is not available, first verify that the Internet connection is active. sas macro-call file in the SAS PROGRAM EDITOR window. The Appendix provides instructions for downloading the macro-call and sample data files from the book website. sas macro-call file can be found in the mac-call folder on the CD-ROM. sas macro-call file in the SAS PROGRAM EDITOR window. sas to open the MACRO window called EXCELSAS. 3. 4). After inputting all the required macro parameters, check whether the cursor is in the last input field (#6) and that the RESULTS VIEWER window is closed, then hit the ENTER key (not the RUN icon) to submit the macro.

The expected frequencies are calculated by assuming that the null hypothesis is true. The chi-square test statistic is the sum of the squares of the differences between the observed and expected frequencies, with each squared difference being divided by the corresponding expected frequency. 2 Graphical Displays for Categorical Data The graphical techniques employed in this chapter to display categorical data are quite simple, consisting of bar, block, and pie charts. l This section provides a brief - - - ~ -~ - - -- -- ~--- ~ - ~ • 49 Exploratory Data Analysis - - - ' - - - -- - - - ' -- -- ' -- -- description of some simple graphical techniques used in EDA of categorical data.

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