MATH 226 - 9.10.2007

MATH 226 - 9.10.2007 - | Mean = 5.375 million o Measure of...

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MATH 226 – September 10, 2007 Numerical Summaries o Summary of location Sample Median – 0.5 quantile; Q(.5); very center of the data range Sample Mean – sum of all numbers divided by number of numbers x-bar = sigma(x, 1 n)/n Sample Mode – most often occurring value Example: 1, 2, 7, 5, 2 Mode – 2 Median – 2 Mean – 17/5 Sample of salaries of 2005 Boston Red Sox Team Trot Nixon 7.5 million | Curt Shilling 14.5 million Bill Mneller 2.5 million | Bill Mneller 2.5 million John Halama 850,000 | John Halama .85 million Kevin Millar 3.5 million | Kevin Millar 3.5 million ------------------------------------|--------------------------------------------- Median = 3 million | Median = 3 million Mean = 3.5875 million
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Unformatted text preview: | Mean = 5.375 million o Measure of spread Range = max min IQR = Q(0.75) Q(0.5) Middle 50% of data The sample variation s 2 = sigma(xi x-bar, 1 n) 2 /(n-1) The sample standard deviation is s = sqrt(s 2 ) Chebychevs Theorem o For any positive real number k, the fraction of the sample that are between x-bar ks and x-bar + ks is at least 1 1/k 2 A statistic is a function of a sample A theoretical distribution of population is determined by its class and some constant called a parameter Mean of a finite population o = sigma(xi, 1 n)/n o 2 = sigma((xi ) 2 , 1 n)/n...
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