Lecture2-2

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A Quick Review Boxplot you commonly see: the whiskers extend out to the farthest points that are within 1.5×IQR of the quartiles Q1 and Q3 outliers are plotted individually Percentile: the value such that a specified percentage of the measurements in a population or sample fall at or below it the first quartile Q1 = 25th percentile the third quartile Q3 = 75th percentile Tolerance interval: an interval of numbers that contains a specified percentage of the individual measurements in a population ( such as 68.26 percent, 95.44 percent, or 99.73 percent ) 2
Empirical Rule: Bell-Shaped, Symmetric If a population has mean ¹ and standard deviation s and is described by a normal curve , then 68.26% of the population measurements lie within one standard deviation of the mean: [ ¹ - , ¹ + ] 95.44% of the population measurements lie within two standard deviations of the mean: [ ¹ -2 , ¹ +2 ] 99.73% of the population measurements lie within three standard deviations of the mean: [ ¹ -3 , ¹ +3 ] 3

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Empirical Rule: Car Mileage Case 4
Random Variables r.v.: a variable that takes on different numerical values determined by the outcome of an experiment represents an uncertain numerical outcome E.g., proportion of Super Bowl viewers surveyed who viewed an ad, day-trading profits for next year, number of additional children a couple with one boy must have in order to get the first girl 5

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Random Variables Discrete random variable: possible values can be counted Number of defective units in a batch of 20, a listener rating (on a scale of 1 to 5) in an AccuRating music survey Continuous random variable: may assume any numerical value in one or more intervals Waiting time for a credit card authorization, interest rate charged on a business loan 6
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