Slide 1Slide 2Histograms: Earthquake MagnitudesHistograms: Earthquake Magnitudes (cont.)Histograms: Earthquake Magnitudes (cont.)Changing the Bin Width and SoftwareChanging the Bin Width (Cont.)Stem-and-Leaf DisplaysStem-and-Leaf ExampleStem-and-Leaf Display and SoftwareConstructing a Stem-and-Leaf Display ManuallyStem-and-Leaf: In Class ExerciseDescribing a DistributionSlide 14What is the Shape of the Distribution?HumpsHumps (cont.)Humps (cont.)SymmetrySymmetry (cont.)Anything Unusual?Anything Unusual? (cont.)Class Activity – Guessing Distribution CharacteristicsSlide 24Center of a Distribution – MedianCenter of a Distribution – Median (Cont.)Center of a Distribution – Median (Cont.)Slide 28Spread: Home on the RangeSpread: The Interquartile RangeSpread: The Interquartile Range (cont.)Spread: The Interquartile Range (cont.)Spread: Range vs. IQR (Example)Slide 34Daily Average Wind SpeedsBoxplots and 5-Number Summaries (cont)The Five-Number SummaryDaily Wind Speed: Making BoxplotsConstructing BoxplotsConstructing Boxplots (cont.)Constructing Boxplots (cont.)Constructing Boxplots (cont.)Constructing Boxplots (cont.)Wind Speed: Making Boxplots (cont.)Boxplots and SoftwareClass Activity – Drawing a Box PlotSlide 47Slide 48Center of Symmetric Distributions – The MeanCenter of Symmetric Distributions – The Mean (cont)Center of Symmetric Distributions – The Mean (cont)Slide 52The Spread of Symmetric Distributions: The Standard DeviationSlide 54Slide 55Slide 56Calculating the Standard Deviation, s, “By Hand”Thinking About VariationClass Activity – Groups of 2 (or 3)Class Activity – Groups of 2 (or 3) (Cont.)Histogram PairsHistogram PairsHistogram PairsHistogram PairsHistogram PairsSlide 66What to TellWhat to Tell About Unusual FeaturesMultiple Modes - ExampleSlide 70Cautions About HistogramsCautions About Histograms (Cont.)1Chapter03 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.Chapter 3Displaying and Summarizing Quantitative Data2Chapter03 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.3.1Displaying Quantitative VariablesChapter03 Presentation 06153Copyright © 2014, 2012, 2009 Pearson Education, Inc.Histograms: Earthquake MagnitudesThe chapter example discusses the magnitudes of earthquakes known to have caused tsunamis from 2000 B.C. to the present.We can display such quantitative data in bins.Bins must be equal in widthThe height of the bin represents the total occurrences between those two valuesWe do this to display the distribution of the quantitative variable.Chapter03 Presentation 06154Copyright © 2014, 2012, 2009 Pearson Education, Inc.Histograms: Earthquake Magnitudes (cont.)A histogram plots the bin counts as the heights of bars (like a bar chart). Here is a frequency histogram of these earthquake magnitudes:Chapter03 Presentation 06155Copyright © 2014, 2012, 2009 Pearson Education, Inc.Histograms: Earthquake Magnitudes (cont.)Here is a relative frequency histogram of these earthquake magnitudes:Chapter03 Presentation 06156Copyright © 2014, 2012, 2009 Pearson Education, Inc.Changing the Bin Width and SoftwareIn Excel, it is up to the user to specify the number of bins and the bin width. So, this is completely under the control of the user.Any good statistical software will automatically pick the number of bins and the bin width, but will allow the user to easily change these. JMP is one such software package.Of the two histograms on the next page, which histogram do you prefer?Chapter03 Presentation 06157Copyright © 2014, 2012, 2009 Pearson Education, Inc.Changing the Bin Width (Cont.)Chapter03 Presentation 06158Copyright © 2014, 2012, 2009 Pearson Education, Inc.Stem-and-Leaf DisplaysStem-and-leaf displays show the distribution of a quantitative variable, like histograms do, while preserving the individual values.They are good for relatively small data sets.The shape of a stem-and-leaf plot is exactly the same as a histogram, except it is in a vertical format.Chapter03 Presentation 06159Copyright © 2014, 2012, 2009 Pearson Education, Inc.Stem-and-Leaf ExampleCompare the histogram and stem-and-leaf display for the pulse rates of 24 women at a health clinic. Which graphical display do you prefer?Chapter03 Presentation 061510Copyright © 2014, 2012, 2009 Pearson Education, Inc.Stem-and-Leaf Display and SoftwareThere is no simple way to make a stem-and-leaf display in Excel, but they are easily made in JMP.JMP displays a legend at the bottom explaining how to read the display.Chapter03 Presentation 061511Copyright © 2014, 2012, 2009 Pearson Education, Inc.Constructing a Stem-and-Leaf Display ManuallyFirst, cut each data value into leading digits (“stems”) and trailing digits (“leaves”). Use the stems to label the bins.Use only one digit for each leaf—either round or truncate the data values (if necessary) to one decimal place after the stem.Chapter03 Presentation 061512Copyright © 2014, 2012, 2009 Pearson Education, Inc.Stem-and-Leaf: In Class ExerciseConstruct a “back to back” stem and leaf display of the grades on exam 1 from two small sections of the same graduate class taught by two different professors. What differences to you see? Who’s class would you rather be in?Professor AProfessor B77, 92, 100, 69, 94, 74, 79, 87, 86, 87, 8888, 83, 95, 99, 43, 99, 87, 39, 50, 97109876543Professor AProfessor B720Chapter03 Presentation 061513Copyright © 2014, 2012, 2009 Pearson Education, Inc.Describing a DistributionWhen describing a distribution, make sure to always tell about three things:ShapeCenterSpread14Chapter03 Presentation 0615Copyright © 2014, 2012, 2009 Pearson Education, Inc.3.2ShapeChapter03 Presentation 061515Copyright © 2014, 2012, 2009 Pearson Education, Inc.What is the Shape of the Distribution?1. Does the histogram have a single, central hump or several separated humps?2. Is the histogram symmetric?3. Do any unusual features stick out?Chapter03 Presentation 061516Copyright © 2014, 2012, 2009 Pearson Education, Inc.Humps1. Does the histogram have a single, central hump or several separated humps?Humps in a histogram are called modes.(most frequent numbers) One peak = unimodalTwo peaks = bimodalMore than two = multimodalA flat histogram without peaks is said to be uniform.Chapter03 Presentation 061517Copyright © 2014, 2012, 2009 Pearson Education, Inc.Humps (cont.)A bimodal
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