Stats LEC 2 - DESCRIBING DISTRIBUTIONS NUMERICALLY 1...

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1DESCRIBING DISTRIBUTIONSNUMERICALLY
2Numerical SummariesMeanMedianModeDescribing Data NumericallyVarianceStandard DeviationRangeInterquartile RangeCentral TendencyVariation
3Central TendencyMeanMedianModenxxn1ii!==Midpoint ofranked valuesMost frequentlyobserved valueArithmeticaverageMeasures of center: Mode, Median, Mean
4Measures of Center: ModeA measure of central tendencyValue that occurs most oftenNot affected by extreme valuesUsed for either numerical or categorical dataThere may be no modeThere may be several modes0 1 2 3 4 5 6 7 8 9 10 11 12 13 14Mode = 90 1 2 3 4 5 6No Mode
5In an ordered list, the median is the “middle”number (50% above, 50% below)Not affected by extreme values0 1 2 3 4 5 6 7 8 9 10Median = 30 1 2 3 4 5 6 7 8 9 10Median = 3Measures of Center: Median
6Measures of Center: MedianThe Median the point that divides a distribution in half: 50% ofthe data on the left of the median and the other 50% - on theright.To find the median, arrange the data in ascending (descending) order.If n is odd, the median is the observation with positionIf n is even, the median is the average of the middle two values withthe positionsn12+nnand122+
725Toyota MR22123Mersedes-Benz SLK2302022Mazda Miata1922Audi TT Roadster1820Mersedes-Benz SLK3201720Honda S 20001620BMW Z3 Roadster1520Audi TT Quattro1419Porsche Boxter1319BMW Z3 Coupe1218Chrysler Prowler1118Chevrolet Corvette1017Ford Thunderbird917BMW M Coupe817Acura NSX716Mersedes-Benz SL500615Porsche 911 GT2513Mersedes-Benz SL600413BMW Z8311Ferrari 360 Modena29Lamborghini Murcielago1City mpgModel50% MEDIAN0% MIN100% MAX25% 1st QUARTILE75% 3rd QUARTILE
89Min16Q118Median20Q325Max5 - Number Summary7225
9Boxplotis a visual representation of thefive number summary.There are four steps to built a boxplot:1. Interquartile range IQR= Q3 – Q1, shows the spread of the middle 50% of the data2. Fenceslower fence LF = Q1 – 1.5(IQR)upper fence UF = Q3 + 1.5(IQR)3. Whiskers - extend from Q1 and Q3 to the smallest and largest observations withinthe fences4. outliers (if any) - extreme observations that fall outside the fences
10Boxplot: gas mileage for two-seater cars051015202530Collection 1Box Plot

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