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3-1 Notes.docx - 3-1 Measures of Center A measure of center...

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3-1 Measures of CenterAmeasure of centeris a value at the center or middle of a data set.MeanVocabularyThemean(orarithmetic mean) of a set of data is the measure of center found by adding all the data values anddividing the total by the number of data values.A statistic isresistantif the presence of extreme values (outliers) does not cause it to change very much.Important Properties of the MeanSample means drawn from the same population tend to vary 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 extreme value (outlier) can change the value of the meansubstantially. (Using the following definition, we say that the mean is notresistant.)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.Calculation and Notation of the Mean´xis pronounced “x-bar” and is the mean of a set ofsamplevalues.´x=∑ xnµis pronounced “mu” and is the mean of all values in apopulation.μ=∑ xNExample 1: MeansListed below are the numbers of Atlantic hurricanes that occurred in each year. The data are listed in order byyear, starting with the year 2000. Find the mean of the data.8987915568412782
MedianThemedianof a data set is the measure of center that is themiddle valuewhen the original data values are arranged inorder of increasing (or decreasing) magnitude.Important Properties of the MedianThe median does not change by large amounts when we include just a few extreme values, so the median is aresistantmeasure of center.

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