Section 3.2 Measures of Spread 119 a. Find the sample standard deviation for the weights for the offensive linemen. b. Find the sample standard deviation for the weights for the defensive linemen. c. Is there greater spread in the weights of the offensive or the defensive linemen? 34. Beer: The following table presents the number of active breweries for samples of states located east and west of the Mississippi River. East West State Number of Breweries State Number of Breweries Connecticut 18 Alaska 17 Delaware 10 Arizona 31 Florida 47 California 305 Georgia 22 Colorado 111 Illinois 52 Iowa 21 Kentucky 13 Louisiana 6 Maine 38 Minnesota 41 Maryland 23 Montana 30 Massachusetts 40 South Dakota 5 New Hampshire 16 Texas 37 New Jersey 20 Utah 15 New York 76 North Carolina 46 South Carolina 14 Tennessee 19 Vermont 20 Source: http://www.beerinstitute.org/ a. Compute the sample standard deviation for the number of breweries east of the Mississippi River. b. Compute the sample standard deviation for the number of breweries west of the Mississippi River. c. Compute the range for each data set. d. Based on the standard deviations, which region has the greater spread in the number of breweries? e. Based on the ranges, which region has the greater spread in the number of breweries? f. The sample of western states happens to include California. Remove California from the sample of western states, and compute the sample standard deviation for the remaining western states. Does the result show that the standard deviation is not resistant? Explain. g. Compute the range for the western states with California removed. Is the range resistant? Explain. 35. What’s your favorite TV show? The following tables present the ratings for the top 20 prime-time shows for the 1997–1998 season and for the 2007–2008 season. The rating is the percentage of households with TV sets that watched the program. Top Rated TV Programs: 1997---1998 Program Rating Seinfeld 21.7 ER 20.4 Veronica’s Closet 16.6 Friends 16.1 Monday Night Football 15.0 Touched by an Angel 14.2 60 Minutes 13.8 Union Square 13.6 CBS Sunday Movie 13.1 Frasier 12.0 Home Improvement 12.0 Just Shoot Me 11.9 Dateline NBC —Tuesday 11.5 Dateline NBC —Monday 11.4 The Drew Carey Show 11.1 20/20—Friday 10.9 N.Y.P.D. Blue 10.8 Primetime Live 10.8 The X-Files 10.6 Law and Order 10.2 Source: www.classictvhits.com Top Rated TV Programs: 2007---2008 Program Rating American Idol — Tuesday 16.1 American Idol — Wednesday 15.9 Dancing With the Stars— Monday (2007) 14.0 Dancing With the Stars— Tuesday (2007) 12.7 Dancing With the Stars— Monday (2008) 12.6 Dancing With the Stars— Tuesday (2008) 11.8 Desperate Housewives 11.6 CSI 10.6 House— Tuesday 10.5 Grey’s Anatomy 10.4 Sunday Night Football 9.7 CSI: Miami 9.2 House— Monday 9.2 NCIS 9.2 Survivor: China 9.0 Without a Trace 8.8 The Moment of Truth 8.8 Two and a Half Men 8.5 60 Minutes 8.4 Criminal Minds 8.2 Source: Nielsen Media Research
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