Measuring Variation 2The Five-Number SummaryTI-83 – Five-Number SummarySlide 4BoxplotsExampleBoxplots and ShapeTI-83 – BoxplotsSlide 9Modified BoxplotsSlide 11Example: DePaul UniversitySlide 13TI-83 – Modified BoxplotsLet’s Do It!Lecture 17Lecture 17Sec. 5.3.3Sec. 5.3.3Mon, Feb 14, 2005Mon, Feb 14, 2005Measuring Measuring Variation 2Variation 2The Five-Number The Five-Number SummarySummaryFive-number summaryFive-number summary – A summary of – A summary of a sample or population consisting of a sample or population consisting of the five numbersthe five numbersMinimumMinimumFirst quartile Q1First quartile Q1MedianMedianThird quartile Q3Third quartile Q3MaximumMaximumThis does a better job of measuring This does a better job of measuring spread than any single number can do.spread than any single number can do.TI-83 – Five-Number TI-83 – Five-Number SummarySummaryUse the TI-83 to find a five-number Use the TI-83 to find a five-number summary of the age data.summary of the age data.Min = 32Min = 32Q1 = 41Q1 = 41Median = 43.5Median = 43.5Q3 = 46.5Q3 = 46.5Max = 51Max = 51The Five-Number The Five-Number SummarySummaryFrom the 5-number summary of the From the 5-number summary of the age data, can we detect skewness in age data, can we detect skewness in the distribution?the distribution?Answer: Maybe.Answer: Maybe.BoxplotsBoxplotsBoxplotBoxplot – A graphical display of a five- – A graphical display of a five-number summary.number summary.Draw and label a scale representing the Draw and label a scale representing the variable.variable.Draw a box over the scale with its left and Draw a box over the scale with its left and right ends at Q1 and Q3.right ends at Q1 and Q3.Draw a vertical line through the box at the Draw a vertical line through the box at the median.median.Draw a left tail (whisker) from the box to the Draw a left tail (whisker) from the box to the minimum.minimum.Draw a right tail from the box to the maximum.Draw a right tail from the box to the maximum.ExampleExampleDraw a boxplot of the age data.Draw a boxplot of the age data.Boxplots and ShapeBoxplots and ShapeWhat would a boxplot for a uniform What would a boxplot for a uniform distribution look like?distribution look like?What would a boxplot for a What would a boxplot for a symmetric distribution look like?symmetric distribution look like?What would a boxplot for a left-What would a boxplot for a left-skewed distribution look like?skewed distribution look like?TI-83 – BoxplotsTI-83 – BoxplotsPress STAT PLOT.Press STAT PLOT.Select Plot1Select Plot1Turn Plot 1 On.Turn Plot 1 On.Select the Boxplot Type.Select the Boxplot Type.Specify list LSpecify list L11..Press WINDOW.Press WINDOW.Set minX and maxX appropriately.Set minX and maxX appropriately.Press GRAPH.Press GRAPH.See the instructions on p. 283.See the instructions on p. 283.TI-83 – BoxplotsTI-83 – BoxplotsPress TRACE.Press TRACE.Use the arrow keys to see the values of Use the arrow keys to see the values of the minimum, Q1, the median, Q3, and the minimum, Q1, the median, Q3, and the maximum.the maximum.Modified BoxplotsModified BoxplotsModified boxplotModified boxplot – A boxplot in – A boxplot in which the outliers are indicated.which the outliers are indicated.Modified BoxplotsModified BoxplotsDraw the box part of the boxplot as Draw the box part of the boxplot as usual.usual.Compute STEP = 1.5 Compute STEP = 1.5 IQR. IQR.The inner fences are at Q1 – STEP and The inner fences are at Q1 – STEP and Q3 + STEP.Q3 + STEP.Extend the whiskers from the box to the Extend the whiskers from the box to the smallest and largest values that are smallest and largest values that are withinwithin the inner fences. the inner fences.Draw as individual dots any values that Draw as individual dots any values that are outside the inner fences. These dots are outside the inner fences. These dots represent represent outliersoutliers..Example: DePaul Example: DePaul UniversityUniversityFor an example of modified boxplots, For an example of modified boxplots, see DePaul University’s see DePaul University’s web page web page on on retention.retention.ExampleExampleDraw a modified boxplot of the age Draw a modified boxplot of the age data.data.Do the age data have any outliers?Do the age data have any outliers?See Example 5.6, p. 286.See Example 5.6, p. 286.TI-83 – Modified BoxplotsTI-83 – Modified BoxplotsFollow the same steps as for a Follow the same steps as for a regular boxplot, but for the Type, regular boxplot, but for the Type, select the modified-boxplot icon, the select the modified-boxplot icon, the first icon in the second row.first icon in the second row.It looks like a boxplot with a couple of It looks like a boxplot with a couple of extra dots.extra dots.Use the TI-83 to find a modified Use the TI-83 to find a modified boxplot of the age data.boxplot of the age data.Let’s Do It!Let’s Do It!Let’s do it! 5.9, p. 286 – Five-number Let’s do it! 5.9, p. 286 – Five-number Summary and Outliers.Summary and Outliers.Let’s do it! 5.10, p. 287 – Cost of Let’s do it! 5.10, p. 287 – Cost of Running Shoes.Running Shoes.Let’s do it! 5.11, p. 288 – Comparing Let’s do it! 5.11, p. 288 – Comparing AgesAges–– Antibiotic Study. Antibiotic
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