STA 220 Section 3-1 1 .pdf - STA 220 Guided Notes for...

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1STA 220Guided Notes for Section 3-1Measures of CenterA measure of center is a value at the center or middle of a data set.Mean(or Arithmetic Mean)Themean(orarithmetic mean) of a set of data is the measure of center foundby adding all of the data values and dividing the total by the number of datavalues.Important Properties of the MeanSample means drawn from the same population tend to vary less than othermeasures 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 thevalue of the mean substantially. (Using the following definition, we say that themean is notresistant.)A statistic isresistantif the presence of extreme values (outliers) does not causeit to change very much.Notation(Capital Greek letter sigma)denotes the addition of a set of valuesxis thevariableusually used to represent the individual data valuesnrepresents thenumber of valuesin asample(i.e.nis thesample size)Nrepresents thenumber of valuesin apopulation.(i.e.Nis thepopulationsize)x(x-bar) is the mean of a set ofsamplevalues.Sample Mean =xx =nμ(mu)is the mean of all values in apopulation.Population Mean=xμ =NExample: MeanData Set 32 “Airport Data Speeds” in Appendix B includes measures of data speeds ofsmartphones from four different carriers. Find the mean of the first five data speeds forVerizon: 38.5, 55.6, 22.4, 14.1, and 23.1 (all in megabits per second, or Mbps).
2CautionNever use the termaveragewhen referring to a measure of center. The wordaverageis often used for the mean, but it is sometimes used for other measures ofcenter.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 themiddle valuewhenthe original data values are arranged in order of increasing (or decreasing) order.Important Properties of the MedianThe median does not change by large amounts when we include just a few extremevalues, so the median is aresistantmeasure of center.

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