Example 6: Critical Thinking and Measures of CenterSee each of the following illustrating situations in which the mean and median arenot meaningful statistics.a.Zip codes of the Gateway Arch in St. Louis, White House, Air Force Divisionof the Pentagon, Empire State Building and Statue of Liberty: 63102, 20500,

20330, 10118, 10004. (The zip codes don’t measure or count anything. Thenumbers are just labels for geographic locations.)b.Ranks of selected national universities of Harvard, Yale, Duke, Dartmouth,and Brown (from U.S. News & World Report): 2, 3, 7, 10, 14. (The ranksreflect an ordering, but they don’t measure or count anything.)c.Numbers on the jerseys of the starting defense for the Seattle Seahawks whenthey won Super Bowl XLVIII: 31, 28, 41, 56, 25, 54, 69, 50, 91, 72, 29. (Thenumbers on the football jerseys don’t measure or count anything; they are justsubstitutes for names.)d.Top 5 incomes of chief executive officers (in millions of dollars): 131.2, 66.7,64.4, 53.3, 51.5. (Such “top 5” or “top 10” lists include data that are not at allrepresentative of the larger population.)e.The 50 mean ages computed from the means in each of the 50 states. (If youcalculate the mean of those 50 values, the result is not the mean age of peoplein the entire United States. The population sizes of the 50 different states mustbe taken into account, as described in the weighted mean.-In the spirit of describing, exploring, and comparing data, we provide the table below, whichsummarizes the different measures of center for the smartphone data speeds referenced in thebeginning of the chapter.VerizonSprintAT&TT-MobileMean17.603.7110.7010.99Median13.901.608.659.70Mode4.5, 11.10.32.73.2, 4.4, 5.1, 13.3, 15.0, 16.7,27.3Midrange39.3015.3019.8014.003.1B – Beyond the Basics of Measures of Center-Calculating the Mean from a Frequency DistributionThe formula below consists of the same calculation for the mean that was presented bythe formulaMean=∑xn, but it incorporates this approach: When working with datasummarized in a frequency distribution, we make calculations possible by pretending thatall sample values in each class are equal to the class midpoint´x=∑(f ∙ x)∑f

Example 7: Computing the Mean from a Frequency DistributionThe first two columns of the table below shown here are the same as thefrequency distribution of McDonald’s Lunch SERVICE Times.Time (seconds)FrequencyfClass Midpointxf · x75-1241199.51094.5125-17424149.53588.0175-22410199.51995.0225-2743249.5748.5275-3242299.5599.0Totals:∑f=50∑(f ∙ x)=8025.0Remember, when working with data summarized in a frequencydistribution, we make calculations possible by pretending that all samplevalues in each class are equal to the class midpoint. For example, considerthe first class interval of 75-124 with a frequency of 11. We pretend thateach of the 11 service times is 99.5 sec (the class midpoint). With theservice time of 99.5 repeated 11 times, we have a total of 99.5 · 11 =1094.5, as shown in the last column of the table given above. We can thenadd those results to find the sum of all sample values. The bottom row ofthe table given above shows the two components we need for thecalculation of the mean:∑f=50and∑(f ∙ x)=8025.0. We

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