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The Five-Number SummaryLecture 16Sections 5.3.1 - 5.3.3Robb T. KoetherHampden-Sydney CollegeTue, Sep 20, 2011Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20111 / 40

Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20112 / 40

Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20113 / 40

Exercise 5.3, p. 311.A professor teaches two statistics classes. The morning class has 25students, and their average on the first test was 82. The evening classhas 15 students, and their average on the same test was 74. What isthe average on this test if the professor combines the scores for bothclasses?Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20114 / 40

Exercise 5.3, p. 311.A professor teaches two statistics classes. The morning class has 25students, and their average on the first test was 82. The evening classhas 15 students, and their average on the same test was 74. What isthe average on this test if the professor combines the scores for bothclasses?This would be a weighted average.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20114 / 40

Exercise 5.3, p. 311.A professor teaches two statistics classes. The morning class has 25students, and their average on the first test was 82. The evening classhas 15 students, and their average on the same test was 74. What isthe average on this test if the professor combines the scores for bothclasses?This would be a weighted average.25(82) 15(74)25 152050 1110 403160 40 79.avg. Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20114 / 40

Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20115 / 40

Percentiles and QuartilesDefinition (pth Percentile)The pth percentile of a set of numbers is a number that divides thelower p% of the numbers from the rest.Definition (1st Quartile)The 1st quartile, denoted Q1 , of a set of numbers is the 25th percentile.Definition (3rd Quartile)The 3rd quartile, denoted Q3 , of a set of numbers is the 75th percentile.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20116 / 40

Finding QuartilesTo find the quartiles, first find the position of the median.Then the 1st quartile is the median of all the numbers that arebelow that position.The 3rd quartile is the median of all the numbers that are abovethat position.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20117 / 40

ExampleExample (Quartiles)Find the median and quartiles of the following sample.5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20118 / 40

ExampleExample (Quartiles)Find the median and quartiles of the following sample.5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32MedianRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 20119 / 40

ExampleExample (Quartiles)Find the median and quartiles of the following sample.5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32MedianRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201110 / 40

ExampleExample (Quartiles)Find the median and quartiles of the following sample.5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32Q1Robb T. Koether (Hampden-Sydney College)MedianThe Five-Number SummaryQ3Tue, Sep 20, 201111 / 40

Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201112 / 40

Definition (Five-Number Summary)The five-number summary of a set of numbers consists of the fivequantitiesMinimum1st quartileMedian3rd quartileMaximumThese five numbers divide the set of numbers into four groups ofequal size, each containing one-fourth of the set.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201113 / 40

ExampleExample (Five-Number Summary)The five-number summary of the previous sample isMin 5.Q1 10.Med 19.Q3 25.Max 32.5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32MinRobb T. Koether (Hampden-Sydney College)Q1MedianThe Five-Number SummaryQ3MaxTue, Sep 20, 201114 / 40

PracticePracticeFind the five-number summary of the Plant B data from Exercise4.36, page 262.27 29 31 32 32 33 33 34 37 4446 51 56 56 57 58 58 59 62 63Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201115 / 40

Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201116 / 40

TI-83 Five-Number SummaryTI-83 Five-Number SummaryFollow the same procedure that was used to find the mean.When the list of statistics appears, scroll down to the ones labeledminX, Q1, Med, Q3, maxX.They are the five-number summary.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201117 / 40

TI-83 Five-Number SummaryTI-83 Five-Number SummaryUse the TI-83 to find the five-number summary of the rainfall data5.941.11 9.520.08 6.148.682.932.03 3.60 14.71 4.010.856.89 11.07 4.423.41 2.852.561.925.15 1.584.44 0.774.761.153.02 1.732.60 2.56 10.01Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201118 / 40

Five-Number Summaries and DistributionsIf the distribution were uniform from 0 to 10, what would be thefive-number summary?01Robb T. Koether (Hampden-Sydney College)234567The Five-Number Summary8910Tue, Sep 20, 201119 / 40

Five-Number Summaries and DistributionsIf the distribution were uniform from 0 to 10, what would be thefive-number summary?50%01MinRobb T. Koether (Hampden-Sydney College)250%34567MedThe Five-Number Summary8910MaxTue, Sep 20, 201120 / 40

Five-Number Summaries and DistributionsIf the distribution were uniform from 0 to 10, what would be thefive-number summary?25%01MinRobb T. Koether (Hampden-Sydney College)25%23Q1425%5625%7MedThe Five-Number Summary8Q3910MaxTue, Sep 20, 201121 / 40

Five-Number Summaries and DistributionsWhere would the median and quartiles be in this symmetricnon-uniform distribution?1Robb T. Koether (Hampden-Sydney College)2345The Five-Number Summary67Tue, Sep 20, 201122 / 40

Five-Number Summaries and DistributionsWhere would the median and quartiles be in this symmetricnon-uniform distribution?50%1MinRobb T. Koether (Hampden-Sydney College)2350%45MedThe Five-Number Summary67MaxTue, Sep 20, 201123 / 40

Five-Number Summaries and DistributionsWhere would the median and quartiles be in this symmetricnon-uniform distribution?25%25%25%1MinRobb T. Koether (Hampden-Sydney College)225%345Q1MedQ3The Five-Number Summary67MaxTue, Sep 20, 201124 / 40

Five-Number Summaries and DistributionsWhere would the median and quartiles be in this non-symmetricnon-uniform distribution?12Robb T. Koether (Hampden-Sydney College)345The Five-Number Summary678Tue, Sep 20, 201125 / 40

Five-Number Summaries and DistributionsWhere would the median and quartiles be in this non-symmetricnon-uniform distribution?25%25%25%25%12MinQ1Robb T. Koether (Hampden-Sydney College)34Med5Q3The Five-Number Summary678MaxTue, Sep 20, 201126 / 40

Five-Number Summaries and DistributionsDescribe the distribution.MinRobb T. Koether (Hampden-Sydney College)Q1MedThe Five-Number SummaryQ3MaxTue, Sep 20, 201127 / 40

Five-Number Summaries and DistributionsDescribe the distribution.Min Q1 MedRobb T. Koether (Hampden-Sydney College)Q3The Five-Number SummaryMaxTue, Sep 20, 201128 / 40

Five-Number Summaries and DistributionsDescribe the distribution.MinRobb T. Koether (Hampden-Sydney College)Q1 Med Q3The Five-Number SummaryMaxTue, Sep 20, 201129 / 40

Five-Number Summaries and DistributionsDescribe the distribution.MinQ1Robb T. Koether (Hampden-Sydney College)MedThe Five-Number SummaryQ3 MaxTue, Sep 20, 201130 / 40

Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201131 / 40

The Interquartile RangeDefinition (Interquartile Range)The interquartile range, denoted IQR, is the difference between Q3and Q1 .The IQR is a commonly used measure of spread, or variability.Like the median, it is not affected by extreme outliers.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201132 / 40

The IQRExample (IQR)The IQR of5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32isIQR Q3 Q1 25 10 15Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201133 / 40

The IQRPracticeFind the IQR of the Plant B data27 29 31 32 32 3346 51 56 56 57 58and use it to describe the sample.Robb T. Koether (Hampden-Sydney College)The Five-Number Summary3358345937624463Tue, Sep 20, 201134 / 40

Five-Number Summaries and Stem-and-Leaf DisplaysUse the stem-and-leaf display to find a five-number summary ofthe Plant B data.Stem Leaf2 793 12233474 465 16678896 23Note: 1 2 means 12.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201135 / 40

Salaries of School Board ChairmenPracticeFind the five-number summary of the following salaries of schoolboard overPetersburgSussexNew KentGoochlandDinwiddieColonial HgtsRobb T. Koether (Hampden-Sydney nHopewellCharles CityPrince GeorgeCumberlandKing & QueenKing WilliamThe Five-Number 0002,400Tue, Sep 20, 201136 / 40

Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201137 / 40

Excel’s Definition of PercentileDefinition (Excel’s pth percentile)Excel’s pth percentile of a set of numbers is the number whose 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 percentile that isbased on the gaps between the numbers rather than on thenumbers themselves.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201138 / 40

Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201139 / 40

AssignmentHomeworkRead Section 5.3.1 - 5.3.2, pages 312 - 315.Work Example 5.4, page 314, as an exercise.Robb T. Koether (Hampden-Sydney College)The Five-Number SummaryTue, Sep 20, 201140 / 40

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. Robb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 17 / 40