3.2Measure of Dispersion1We measured thecenterof the data, themeanand themedian.We also looked at the shape of thedata,uniform, symmetric or skewed.Now we will look at how spread out the data is.Dispersion:Degree to which the data are spread outTo order food at aMcDonald’s restaurant, one must choose from multiple lines, while at Wendy’sRestaurant, one enters a single line.The following data represent the wait time (in minutes) in line for asimple random sample of 30 customers at each restaurant during the lunch hour.For each sample,answer the following:Wait Time at Wendy’sWait Time at McDonald’s1.500.791.011.660.940.673.500.000.380.431.823.042.531.201.460.890.950.900.000.260.140.602.332.541.882.941.401.331.200.841.970.712.224.540.800.503.991.901.001.540.990.350.000.280.441.380.921.170.901.230.921.091.722.003.082.750.363.102.190.23Mean =1.3906667Mean =1.3893333Go to your book in Blackboard.Go to StatCrunchand choose data.In search type in Wendy’ andMcDonald’s wait time.The data will load into StatCrunch.Find the mean for both.Draw a relativefrequency histogram for both Wendy’ and McDonald’swait time.Bin startat 0width.5Markers:Check: Mean and Median..TitleeachWait Time at Wendy’sandWait Time atMcDonald’sCopy to your notes.Shrink the graphs to fit.Which restaurant’s wait time appears more dispersed?McDonald’sWhy?The wait time ranges from 0 to 5 minutes, andWendy’s is 0 to 4 minutes.Which line would you prefer to wait in?Wendy’sWhy?There’s more % of people wait time is in therange of .5 to 2 minutes.

3.2Measure of Dispersion2Our goal in this section is to discussnumerical measures of dispersion so that we can quantify thespread of data.We will discuss three numerical measures for describing the spread of data (dispersion)1.Range2.Variance3.Standard DeviationTheRangeis one measure to look at how spread out the data is.Therange,R,of a variable is the difference of themaximumvalue minus theminimumvalueR = max - minThe range of a data set is a useful piece of information when there areno outliersin the data. In thepresence of outliers, the range tells a distorted story.EXAMPLEFinding the Range of a Set of DataThe following data represent the travel times (in minutes) to work for all seven employees of a start-upweb development company.23, 36, 23, 18, 25, 26, 43Find the range. 43-18=25The range does not tell us much about the spread.A better measure would summarize thedeviationfrom the center of the data.Objective 2 & 3:Determine the Variance and Standard Deviation of a Variable from Raw DataThe most important and most commonly used measure of spread for a data set is thestandarddeviation.(sigma, lower case)Definition of 'Standard Deviation'1.The key concept for understanding the standard deviation is the concept of deviation from themean.

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Term

Fall

Professor

Gubitose,C

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