STA 282QR Chapter ThreeProblem-Based Study NoteMeasures of Central Tendency (Mean, Median, and Mode)•Aparameteris a number that describes a population characteristic. For example,population mean.•Astatisticis a number that describes a sample characteristic. For example,sample mean.Thepopulation meanis aparameter, and is computed using allthe individuals in apopulation. The population mean,μ, is given by the following.Where, N is the total # of all individuals in the population.Thesample meanis computed using sample data.The sample mean is astatisticthat is an unbiased estimator of the population mean.Note: In real world applications, population mean,μ,is usually not known, and isestimated by using sample mean.Themedian(m) of a variable is the value that lies in themiddleof the data whenarranged in ascending order.That is, half of the data are below the median and half of thedata are above the median.Themodeof a variable is the most frequent observation of the variable that occurs in thedata set. We useMto represent the mode. If no data value is repeated, the data set hasnomode.If two data values occur with the same greatest frequency, each data value is amode and the data set is calledbimodal.The mean issensitive(not resistant, not robust) to extreme data values.Median isnot sensitive(resistant, robust) to extreme data values.The mode isnot sensitiveto extreme values.
