Lecture2-1

# Lecture2-1 - Boxplot you commonly see the whiskers extend...

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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
If a population has mean μ and standard deviation σ 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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4 The government will offer its tax credit to any automaker selling a middle size care with mean mileage at least 31mpg An automaker wishes to find out the mean mileage of its new midsize model Empirical rule can be used to solve this problem
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If the population mean mileage µ  and variance σ are known, then the problem is fully solved So the question is how to estimate µ and σ 2 We will study the estimation of parameters µ and σ 2 soon 6
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 7

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Lecture2-1 - Boxplot you commonly see the whiskers extend...

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