Homework ReviewPercentiles and QuartilesThe Five-Number SummaryTI-83 Five-Number SummaryThe Interquartile RangePercentiles in ExcelAssignmentThe 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 Summary Tue, Sep 20, 2011 1 / 40Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 2 / 40Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 3 / 40Exercise 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.avg. =25(82) + 15(74)25 + 15=2050 + 111040=316040= 79.Robb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 4 / 40Exercise 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.avg. =25(82) + 15(74)25 + 15=2050 + 111040=316040= 79.Robb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 4 / 40Exercise 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.avg. =25(82) + 15(74)25 + 15=2050 + 111040=316040= 79.Robb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 4 / 40Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 5 / 40Percentiles and QuartilesDefinition (pthPercentile)The pthpercentile 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 25thpercentile.Definition (3rd Quartile)The 3rd quartile, denoted Q3, of a set of numbers is the 75thpercentile.Robb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 6 / 40Finding 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 Summary Tue, Sep 20, 2011 7 / 40ExampleExample (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 Summary Tue, Sep 20, 2011 8 / 40ExampleExample (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 Summary Tue, Sep 20, 2011 9 / 40ExampleExample (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 Summary Tue, Sep 20, 2011 10 / 40ExampleExample (Quartiles)Find the median and quartiles of the following sample.5, 8, 10, 15, 17, 19, 20, 24, 25, 30, 32MedianQ1Q3Robb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 11 / 40Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 12 / 40Definition (Five-Number Summary)The five-number summary of a set of numbers consists of the fivequantitiesMinimum1stquartileMedian3rdquartileMaximumThese 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 Summary Tue, Sep 20, 2011 13 / 40ExampleExample (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, 32MedianQ1Q3Min MaxRobb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 14 / 40PracticePracticeFind 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 Summary Tue, Sep 20, 2011 15 / 40Outline1Homework Review2Percentiles and Quartiles3The Five-Number Summary4TI-83 Five-Number Summary5The Interquartile Range6Percentiles in Excel7AssignmentRobb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 16 / 40TI-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 Summary Tue, Sep 20, 2011 17 / 40TI-83 Five-Number SummaryTI-83 Five-Number SummaryUse the TI-83 to find the five-number summary of the rainfall data5.94 1.11 9.52 0.08 6.14 8.682.93 2.03 3.60 14.71 4.01 0.856.89 11.07 4.42 3.41 2.85 2.561.92 5.15 1.58 4.44 0.77 4.761.15 3.02 1.73 2.60 2.56 10.01Robb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 18 / 40Five-Number Summaries and DistributionsIf the distribution were uniform from 0 to 10, what would be thefive-number summary?0 987654321 10Robb T. Koether (Hampden-Sydney College) The Five-Number Summary Tue, Sep 20, 2011 19 / 40Five-Number Summaries and DistributionsIf the distribution were uniform from 0 to 10, what would be
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