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Unformatted text preview: Parameters and Statistics Variables can be summarized using statistics. A statistic is a numerical measure that describes a characteristic of the sample A parameter is a numerical measure that describes a characteristic of the population. We use statistics to estimate parameters Common Language and Notations: A population is an entire group of which we want to characterize. Population parameters: mean, variance, standard deviation, proportion. A sample is a collection of observations on which we measure one or more characteristics. Sample statistics: mean, variance, standard deviation, proportion. Population A population is an entire group of which we want to characterize. Population parameters: mean, variance, standard deviation, proportion. A sample is a collection of observations on which we measure one or more characteristics. Sample statistics: mean, variance, standard deviation, proportion. Population Sample Population Sample Notations: Estimation and Inferences n i i 1 n 2 2 i i 1 2 i PopulationParameters: 1 Mean x N 1 Var (x ) N (x ) St. Dev. N proportion p ! ! = = = = " " = # # # Sample Statistics: Mean x = 1 n x i i = 1 n ! Var s 2 = 1 n " 1 (x i " x) 2 i = 1 n ! St. Dev. s = (x i " x) 2 ! n " 1 proportion p The Normal Distribution The Normal Distribution Bell Shaped Symmetrical Mean, Median and Mode are Equal Location is determined by the mean, Spread is determined by the standard deviation, The random variable has an infnite theoretical range: + to Mean = Median = Mode x f(x) By varying the parameters and , we obtain different normal distributions Many Normal Distributions The Normal Distribution Shape x f(x) Changing shifts the distribution left or right. Changing increases or decreases the spread. Given the mean and variance we define the normal distribution using the notation X~N( , ! ) The formula for the normal distribution is Where e = the mathematical constant approximated by 2.71828 = the mathematical constant approximated by 3.14159 = the population mean = the population standard deviation x = any value of the continuous variable, < x < f(x) = 1 2 !...
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 Winter '08
 Ioudina
 Statistics

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