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TheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand QuartilesThe Five-Number SummaryLecture 16Sections 5.3.1 - 5.3.3ExampleTheFive-NumberSummaryExamplesRobb T. KoetherTI-83Five-NumberSummaryHampden-Sydney CollegeTheInterquartileRangeTue, Feb 10, 2009Percentiles inExcelAssignment

OutlineTheFive-NumberSummary1Homework Review2Percentiles and QuartilesExample3The Five-Number SummaryExamples4TI-83 Five-Number Summary5The Interquartile RangeTheInterquartileRange6Percentiles in ExcelPercentiles inExcel7AssignmentRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryAssignment

TheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentExercise 5.6, p. 311.The salaries of superstar professional athletes receivemuch attention in the media.The million-dollar annual contract is becoming morecommonplace among this elite group with each passingyear.Nevertheless, rarely does a year pass without one ormore of the players’ associations negotiating with teamowners for additional salary and fringe-benefitconsiderations for all players in their particular sports.

TheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentExercise 5.6, p. 311.(a) If the players’ association wanted to support itsargument for higher “average” salaries, which measureof center do you think it should use? Why?(b) To refute the argument, which measure of center shouldthe owners apply to the players’ salaries? Why?

TheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentSolution(a) The players’ association should use the median. Thedistribution of salaries of professional athletes is skewedto the right (towards the larger values). Therefore, themedian should be less than the mean.(b) The owners should use the mean because it should begreater than the median.

Percentiles and QuartilesTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentDefinition (pth Percentile)The pth percentile of a set of numbers is a number thatdivides the lower p% of the numbers from the rest.Definition (1st Quartile)The 1st quartile, denoted Q1 , of a set of numbers is the 25thpercentile.Definition (3rd Quartile)The 3rd quartile, denoted Q3 , of a set of numbers is the 75thpercentile.

Finding QuartilesTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentTo find the quartiles, first find the position of the median.Then the 1st quartile is the median of all the numbersthat are below that position.The 3rd quartile is the median of all the numbers thatare above that position.

ExampleTheFive-NumberSummaryRobb T.KoetherHomeworkReviewExample (Quartiles)Find the median and quartiles of the following sample.Percentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignment5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32

ExampleTheFive-NumberSummaryRobb T.KoetherHomeworkReviewExample (Quartiles)Find the median and quartiles of the following sample.Percentilesand QuartilesExampleTheFive-NumberSummary5, 8, 10, 15, 17, 19, 20, 24, 25, 30, angePercentiles inExcelAssignmentMedian

ExampleTheFive-NumberSummaryRobb T.KoetherHomeworkReviewExample (Quartiles)Find the median and quartiles of the following sample.Percentilesand QuartilesExampleTheFive-NumberSummary5, 8, 10, 15, 17, 19, 20, 24, 25, 30, angePercentiles inExcelAssignmentMedian

ExampleTheFive-NumberSummaryRobb T.KoetherHomeworkReviewExample (Quartiles)Find the median and quartiles of the following sample.Percentilesand QuartilesExampleTheFive-NumberSummary5, 8, 10, 15, 17, 19, 20, 24, 25, 30, angePercentiles inExcelAssignmentQ1MedianQ3

TheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand ition (Five-Number Summary)The five-number summary of a set of numbers consists ofthe five quantitiesMinimum1st quartileMedian3rd tileRangeThese five numbers divide the set of numbers into fourgroups of equal size, each containing one-fourth of theset.Percentiles inExcelAssignment

ExampleTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand QuartilesExampleTheFive-NumberSummaryExample (Five-Number Summary)The five-number summary of the previous sample isMin 5.Q1 10.Med 19.Q3 25.Max RangePercentiles inExcelAssignment5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32MinQ1MedianQ3Max

PracticeTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentPracticeFind the five-number summary of the sample5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32, 35.

TI-83 Five-Number SummaryTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand QuartilesTI-83 Five-Number SummaryFollow the same procedure that was used to find ive-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentWhen the list of statistics appears, scroll down to theones labeledminX, Q1, Med, Q3, maxX.They are the five-number summary.

TI-83 Five-Number SummaryTheFive-NumberSummaryRobb T.KoetherTI-83 Five-Number SummaryHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentUse the TI-83 to find the five-number summary of therainfall data2.82 24.180.20 15.60 22.047.445.169.14 37.36 10.192.16 17.5028.12 11.238.667.246.504.8813.084.01 11.281.96 12.092.927.674.396.606.50 25.430.74

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewIf the distribution were uniform from 0 to 10, what wouldbe the five-number summary?Percentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignment012345678910

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewIf the distribution were uniform from 0 to 10, what wouldbe the five-number summary?Percentilesand ntiles inExcelAssignment012345Med678910

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewIf the distribution were uniform from 0 to 10, what wouldbe the five-number summary?Percentilesand ePercentiles inExcelAssignment0123Q145Med678Q3910

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewWhere would the median and quartiles be in thissymmetric non-uniform distribution?Percentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignment1234567

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewWhere would the median and quartiles be in thissymmetric non-uniform distribution?Percentilesand ntiles inExcelAssignment1234Med567

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewWhere would the median and quartiles be in thissymmetric non-uniform distribution?Percentilesand ePercentiles inExcelAssignment12345Q1MedQ367

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherWhere would the median and quartiles be in thisnon-symmetric non-uniform distribution?HomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignment12345678

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherWhere would the median and quartiles be in thisnon-symmetric non-uniform distribution?HomeworkReviewPercentilesand ntiles inExcelAssignment25%25%12Q134Med5Q3678

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewDescribe the distribution.Percentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentMinQ1MedQ3Max

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewDescribe the distribution.Percentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentMin Q1 MedQ3Max

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewDescribe the distribution.Percentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentMinQ1 Med Q3Max

Five-Number Summaries and DistributionsTheFive-NumberSummaryRobb T.KoetherHomeworkReviewDescribe the distribution.Percentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentMinQ1MedQ3 Max

The Interquartile RangeTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentDefinition (Interquartile Range)The interquartile range, denoted IQR, is the differencebetween Q3 and Q1 .The IQR is a commonly used measure of spread, orvariability.Like the median, it is not affected by extreme outliers.

The IQRTheFive-NumberSummaryRobb T.KoetherHomeworkReviewExample (IQR)The IQR ofPercentilesand Quartiles5, 8, 10, 15, 17, 19, 20, 24, 25, 30, mberSummaryTheInterquartileRangePercentiles inExcelAssignmentisIQR Q3 Q1 25 10 15

The IQRTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand QuartilesExampleTheFive-NumberSummaryPracticeFind the five-number summary and the IQR of thesample5, 20, 30, 45, 60, 80, 100, 140, 175, 200, eRangePercentiles inExcelAssignmentAre the data skewed?

Five-Number Summaries and Stem-and-LeafDisplaysTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentFind a five-number summary of the following Januaryrainfall data.Stem Leaf0 0012224440 5666777891 011231 572 242 5833 7Note: 1 2 means 12.

Salaries of School Board ChairmenTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentPracticeFind the five-number summary of the following salariesof school board overPetersburgSussexNew KentGoochlandDinwiddieColonial ewellCharles CityPrince GeorgeCumberlandKing & QueenKing WilliamWest 02,4000

Excel’s Definition of PercentileTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentDefinition (Excel’s pth percentile)Excel’s pth percentile of a set of numbers is the numberwhose rank (position) is given by p r 1 (n 1).100If r is not a whole number, then interpolate between values.Microsoft’s Excel uses a definition of the pth percentilethat is based on the gaps between the numbers ratherthan on the numbers themselves.

AssignmentTheFive-NumberSummaryRobb T.KoetherHomeworkReviewPercentilesand Five-NumberSummaryTheInterquartileRangePercentiles inExcelAssignmentHomeworkRead Section 5.3.1 - 5.3.2, pages 312 - 315.Work Example 5.4, page 314, as an exercise.

TI-83 Five-Number Summary TI-83 Five-Number Summary Follow the same procedure that was used to find the mean. When the list of statistics appears, scroll down to the ones labeled minX, Q1, Med, Q3, maxX. They are the five-number summary. The Five-Number Summary Robb T. Koether Homework Review Percentiles and Quartiles Example The Five-Number