Example:Change one value: instead of 65, value is 0Slide 3From Basic Stats at Palmetto GBAMeasures of Central TendencySummation NotationUniverse vs. Sample QuantitiesMeanExampleMedianModeNow, You TryAnswersBaseball SalariesBaseball SalariesSlide 16Measuring Spread or VariabilityRangeVarianceStandard DeviationExampleExampleSlide 23Slide 24Slide 25Example:Class 1: 65 70 75 76 77 80 82 84 86 89 90 92 93 95 97minimum =Q1 =median = Q3 = maximum = 6576849297Class 1: 65 70 75 76 77 80 82 84 86 89 90 92 93 95 97IQR = range =lower fence =upper fence =Any low outliers?Any high outliers?NONOmean = 1251 / 15 83.40std dev = 9.5183.40Q3 - Q1 = 92 - 76 16max-min=97 - 65 3276 - 24 = 5292 + 24 = 116Q1 - 1.5 * IQR = 76 - 1.5(16) = Q3 + 1.5 * IQR = 92 + 1.5(16) =Change one value: instead of 65, value is 0minimum =Q1 =median = Q3 = maximum = IQR = range =lower fence =upper fence =Any low outliers?Any high outliers?Class 2: 0 70 75 76 77 80 82 84 86 89 90 92 93 95 97076849297YES ==> 0NOClass 2: 0 70 75 76 77 80 82 84 86 89 90 92 93 95 97mean = 1186 / 15 79.07std dev = 23.3079.06Class 1: 65 70 75 76 77 80 82 84 86 89 90 92 93 95 9783.40Q3 - Q1 = 92 - 76 16max-min=97 - 65 3276 - 24 = 5292 + 24 = 116Q1 - 1.5 * IQR = 76 - 1.5(16) = Q3 + 1.5 * IQR = 92 + 1.5(16) =From the homework:In the class poll from the beginning of the year, you were asked what color car you drive. The results are summarized below.(Note that the table shows FREQUENCIES of responses…)(Note that the table shows FREQUENCIES of responses…)From Basic Stats at Palmetto GBAMeasures of Central Tendency•Mean•Median•ModeSummation Notation•The symbol is used to indicate the addition of a range of values - for instance:this shows the sum of the first three values of X32131XXXXjjUniverse vs. Sample Quantities•We frequently use Greek letters to designate a universe quantity (parameter) and English letters to designate the sample estimate•m = universe mean (estimate is )•s2 = universe variance (estimate is s2)•s = universe standard deviation (estimate is s)XMean•The sum of the observations divided by the number of observations, nnXniiX1ExampleX1 = 11X2 = 9 X3 = 12X4 = 8X5 = 1010XXX5505108129115XXXXX54321551iiXXMedian•The middle number, or the average of the two middle numbers, when the measurements are arranged in ascending or descending order Example 1: 15, 23, 25, 28, 35, 37, 42 The median is 28. Example 2: 15, 23, 25, 28, 35, 37, 42, 46 First find the average of the two middle numbers, 28 and 35. The median is 31.5.Mode•The most frequently occurring valueExample 1: Example1: 24, 56, 67, 24, 48, 197The mode is 24Example 2: 36, 45, 52, 52, 36, 18 The modes are 36 and 52Alcoholism 1Paranoid schizophrenia 8Schizophrenia 2Mania-depression 4Neurosis 1Number of Autobiographies of Former Mental Patients (1950-1959)Example3: The mode is Paranoid SchizophreniaNow, You TryFind the mean, median, and mode for the following data values5, 3, 8, 6, 4, 1, 8Answers•Mean = 5•Median = 5•Mode = 8Baseball SalariesRank Player Salary Team1 Rodriguez, Alex 21,680,727 New York Yankees2 J eter, Derek 20,600,000 New York Yankees3 Giambi, J ason 20,428,571 New York Yankees4 Bagwell, J ef 19,369,019 Houston Astros5 Bonds, Barry 19,331,470 San Francisco Giants6 Mussina, Mike 19,000,000 New York Yankees7 Ramirez, Manny 18,279,238 Boston Red Sox8 Helton, Todd 16,600,000 Colorado Rockies9 Pettitte, Andy 16,428,416 Houston Astros10 Ordonez, Magglio 16,200,000 Detroit TigersYear / Top 10 players2006Baseball Salaries•http://asp.usatoday.com/sports/baseball/salaries/totalpayroll.aspx?year=2006•Average team payroll- $77,556,889.50•Median team payroll- 72,250,291.00•World Series winners•2003 – Florida Marlins$48,750,000 (25 of 30)•2004 – Boston Red Sox$127,298,500 (2 of 30)•2005 – Chicago White Sox75,178,000 (13 of 30)Team Total 2006 payroll New York Yankees $ 194,663,079 Boston Red Sox $ 120,099,824 Los Angeles Angels $ 103,472,000 Chicago White Sox $ 102,750,667 New York Mets $ 101,084,963 Los Angeles Dodgers $ 98,447,187 Chicago Cubs $ 94,424,499 Houston Astros $ 92,551,503 Atlanta Braves $ 90,156,876 San Francisco Giants $ 90,056,419 St. Louis Cardinals $ 88,891,371 Philadelphia Phillies $ 88,273,333 Seattle Mariners $ 87,959,833 Detroit Tigers $ 82,612,866 Baltimore Orioles $ 72,585,582 Toronto Blue Jays $ 71,915,000 San Diego Padres $ 69,896,141 Texas Rangers $ 68,228,662 Minnesota Twins $ 63,396,006 Washington Nationals $ 63,143,000 Oakland Athletics $ 62,243,079 Cincinnati Reds $ 60,909,519 Arizona Diamondbacks $ 59,684,226 Milwaukee Brewers $ 57,568,333 Cleveland Indians $ 56,031,500 Kansas City Royals $ 47,294,000 Pittsburgh Pirates $ 46,717,750 Colorado Rockies $ 41,233,000 Tampa Bay Devil Rays $ 35,417,967 Florida Marlins $ 14,998,500Player SalaryPositionPlayer SalaryPosition Ramirez, Manny 18,279,238OutfielderThome, J im 14,166,667FirstPlayer SalaryPosition Schilling, Curt 13,000,000PitcherKonerko, Paul 12,000,000FirstWillis , Dontrelle 4,350,000Pitcher Varitek, J ason 10,000,000CatcherVazquez, J avier 12,000,000PitcherMoehler, Brian 1,500,000Pitcher Clement, Matt 9,825,000 Pitcher Contreras, J ose 9,500,000 Pitcher Helms, Wes 800,000 Third
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