QMM240_W08_DescriptiveStatistics-II

QMM240_W08_DescriptiveStatistics-II - QMM240 W08...

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QMM240 W08 Descriptive Statistics II Statistical Methods for Business I - Lecture Notes Page: 1 QMM240 Descriptive Statistics II Outline: I) Chebyshev’s Teorem II) Measures of Relative Standing III) Skew and kurtosis I) Chebyshev’s Theorem Developed by mathematicians Jules Bienaymé (1796-1878) and Pafnuty Chebyshev (1821-1894). General result, that is, applies to all shapes of distributions with mean and standard deviation K is a number of standard deviations greater than 1 The Theorem is an inequality At least % 100 * 1 1 2 K of the data will fall in the interval K Example: What percentage of data would you expect, at a minimum, to observe within two standard deviations of the mean?

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QMM240 W08 Descriptive Statistics II Statistical Methods for Business I - Lecture Notes Page: 2 Example: Taxi Time for an airline A sample of n = 278 taxi times from UnitedAirlines.xls (data in minutes): Median = 5, 79 . 5 X , 23 . 3 S What interval traps at least 75% of the taxi times based on Chebyshev’s Theorem? How would you describe this distribution?
QMM240 W08 Descriptive Statistics II Statistical Methods for Business I - Lecture Notes Page: 3 II) Measures of Relative Standing Standardizing Data into Z-scores The number of standard deviations from the mean. Can find the Z score for some value x using the relationship s x x Z where x is the sample mean and s is the sample standard deviation Z score is a dimensionless quantity Z>0 implies value x is > sample mean Z<0 implies value x is < sample mean Unusual observations have Z scores outside s x 2 Outlier observations have Z scores outside s x 3 Example : PERatios.xls let's standardize and then look for outliers What to do about outliers in data?

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