 # Chapter 3(1).docx - Section 3.1-Measures of Center Measure...

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Section 3.1-Measures of CenterMeasure of Center-The focus of this section is to obtain a value that measures thecenterof a data set. Inparticular, we present measures of center, includingmeanandmedian. Our objective here is not only tofind the value of each measure of center, but also to interpret those values.Measure of CenterA________________is a value at the center or middle of a data set.Mean (or Arithmetic Mean)The_______________(orarithmetic mean) of a set of data is the measure of centerfound by adding all of the data values and dividing the total by the number of datavalues.Sample means drawn from the _________________ tend to vary less than othermeasures of center.The mean of a data set uses every data valueA disadvantage of the mean is that just one extreme value (_____________) can changethe value of the mean substantially. (Using the following definition, we say that themean is notresistant.)ResistantA statistic is______________if the presence of extreme values (outliers) does not causeit 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.µis pronounced “mu” and is the mean of all values in apopulation.MeanCautionNever use the termaveragewhen referring to a measure of center. The wordaverageis oftenused for the mean, but it is sometimes used for other measures of center.The termaverageis not used by statisticians.The termaverageis not used by the statistics community or professional journals.MedianThemedianof a data set is the measure of center that is the___________________when theoriginal data values are arranged in order of increasing (or decreasing) magnitude.
The median does not change by large amounts when we include just a few extreme values, sothe median is a__________________measure of center.The median does not directly use _____________________. (For example, if the largest value ischanged to a much larger value, the median does not change.)Calculation and Notation of the MedianTo find the median, first________________the values (arrange them in order) and then follow one ofthese two procedures:1.If the number of data values is_______________, the median is the number located in the exactmiddle of the sorted list.2.If the number of data values is________________,the median is found by computing the meanof the two middle numbers in the sorted list.Mode

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