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3­1 Measures of Center13­1Measures of CenterKey ConceptThe focus of this section is to obtain a value that measuresthecenterof a data set. In particular, we present measuresof center, includingmeanandmedian. Our objective hereis not only to find the value of each measure of center, butalso to interpret those values.Measure of CenterAmeasure of centeris a value at the center or middle ofa data set.Mean (or Arithmetic Mean)Themean(orarithmetic mean) of a set of data is themeasure of center found by adding all of the data valuesand dividing the total by the number of data values.Important Properties of the MeanSample means drawn from the same population tend tovary less than other measures of center.The mean of a data set uses every data value.A disadvantage of the mean is that just one extremevalue (outlier) can change the value of the meansubstantially. (Using the following definition, we saythat the mean isnot resistant.)ResistantA statistic isresistantif the presence of extreme values(outliers) does not cause it to change very much.Notationdenotes thesumof a set of data values.xis the variable usually used to represent theindividual data values.nrepresents the number of data values in asample.Nrepresents the number of data values in apopulation.µis pronounced “mu” and is the mean of all values in apopulation.Notationis pronounced “x­bar” and is the mean of a set ofsamplevalues.
3­1 Measures of Center2Example: MeanData Set 32 “Airport Data Speeds” in Appendix B includesmeasures of data speeds of smartphones from four differentcarriers. Find the mean of the first five data speeds for Verizon:38.5, 55.6, 22.4, 14.1, and 23.1 (all in megabits per second, orMbps).

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