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3.1 notes.docx - Math 2100 Measures of Center Key concept...

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Math 2100Measures of CenterKey conceptThe focus of this section is to obtain a value that measures the center of adata set. In particular, we present measures of center, including mean andmedian. Our objective here is not only to find the value of each measure ofcenter, but also to interpret those values.What is a Measure of Center?What is the Mean (or Arithmetic Mean)?Properties of the MeanSample means drawn from the same population tend to vary less thanother measures of center.The mean of a data set uses every data value.A disadvantage of the mean is that just one extreme value (outlier) canchange the value of the mean substantially. (Using the followingdefinition, we say that the mean is notresistant.)A statistic isresistantif the presence of extreme values (outliers) does notcause it to change very much.Notationdenotes thesumof a set of data values.xis the variable usually used to represent the individual data values.nrepresents the number of data values in asample.Nrepresents the number of data values in apopulation.´xis pronounced “x -bar” and is the mean of a set ofsamplevalues.´x=¿x / nµis pronounced “mu” and is the mean of all values in apopulation.µ =x / NExampleData Set 32 “Airport Data Speeds” in Appendix B includes measures of dataspeeds of smartphones from four different carriers. Find the mean of the first
five data speeds for Verizon: 38.5, 55.6, 22.4, 14.1, and 23.1 (all in megabitsper second, or Mbps).

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