Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74Slide 75Slide 76Slide 77Slide 78Slide 79Slide 80Slide 81Slide 82Slide 83Slide 84Slide 85Slide 86Slide 87Slide 88Slide 89Slide 90Slide 91Slide 92Slide 93Slide 94Copyright © 2013 Pearson Education, Inc. All rights reservedChapter 2Picturing Variation with GraphsChapter 3Numerical Summaries of Center and Variation1 - 2Copyright © 2013 Pearson Education, Inc.. All rights reserved. Visualizing DataOrganize the data using the chart that most effectively visually summarizes the data.Make a picture!Comment on the distribution (shape, center, spread and etc.). Search for patterns. Identify unusual features if any.Draw conclusions and cautiously make predictions.1 - 3Copyright © 2013 Pearson Education, Inc.. All rights reserved. Some Commonly Used Plots1. Organize qualitative data usinga) Frequency and relative frequency table,b) Bar chart,c) Pie chart andd) Pareto chart.2. Organize quantitative data forI. Discrete Data usinga) Frequency and relative frequency table,b) bar chart,c) pie chart andd) Pareto chart.II. Continuous Data usinga) histogram, b) stem-leaf plot, c) time-series plot1 - 4Copyright © 2013 Pearson Education, Inc.. All rights reserved. Organizing Categorical DataFor qualitative data, three measurements are available for different levels in the variable:– the frequency, or raw counts of observations in that category– the relative frequency,i.e. proportion = frequency / total # of obs– the percentageA pie chart is a circular graph showing how the measurements are distributed among the categories.A bar chart displays the distribution of observed categorical values in bars, with the height of each bar equal to its (relative) frequency.A bar chart in which bars are ordered from largest to smallest (with cumulative %) is called a Pareto chart.1 - 5Pie Chart (Example)Organize the data using the chart that most effectively visually summarizes the data.Make a picture!Comment on the distribution (shape, center, spread and etc.). Search for patterns. Identify unusual features if any.Draw conclusions and cautiously make predictions.1 - 61 - 7Pareto Chart (Example from Wikipedia)1 - 8Side-by-Side Bar ChartCopyright © 2013 Pearson Education, Inc.. All rights reserved.1 - 9Segmented Bar Chart1 - 10Copyright © 2013 Pearson Education, Inc.. All rights reserved. Organizing Quantitative DataFor a discrete variable, if it takes only a handful of values, we may use bar chart, pie chart or Pareto chart just as we did for qualitative variables.For a continuous variable, whose values are defined as intervals on the real-number line or one that can assume an infinite number of values, we may use:- Stem and leaf plot, histogram- Time series plot if some measure of time is observed for each value.1 - 11Copyright © 2013 Pearson Education, Inc.. All rights reserved. Dot Plots (for Numerical Variables)A Dot Plot is a chart that contains a dot for each data value.BenefitsShows the individual data valuesEasy to spot outliersDescribes the distribution visuallyDrawbacksNot as common as bar and pie chartsNot great for data that has too many individual values1 - 12Dot Plot ExampleClearly shows an outlier just below $300.The rest of the data is generally uniformly spread out.Copyright © 2013 Pearson Education, Inc.. All rights reserved.1 - 13Copyright © 2013 Pearson Education, Inc.. All rights reserved. Stem and Leaf PlotThis plot presents a graphical display of the data using the actual numerical values of each data point.How to construct a Stem and Leaf Plot:1. Divide each measurement into two parts: the stem and the leaf.2. List the stems in a column, with a vertical line to their right.3. For each measurement, record the leaf portion in the same row as its matching stem.4. Order the leaves from lowest to highest in each stem.5. Provide a leaf unit to your stem and leaf plot so that readers can recreate the list of actual measurements if needed.1 - 141 - 15Histogram ExampleDifferent bin widths depict the same data differently.The smaller width shows more detail.Too small a width shows too much detail and will not clearly display the main features.Copyright © 2013 Pearson Education, Inc.. All rights reserved.1 - 16Relative Frequency HistogramsA Relative Frequency Histogram is a histogram where the vertical axis represents the relative frequencies, or percents, rather than the frequencies.Compute the relative frequency by dividing the frequency by the sample size (Y-axis).The relative frequency histogram always has the same shape as the frequency histogram. The scale of the vertical axis is just changed.Copyright © 2013 Pearson Education, Inc.. All rights reserved.1 - 17Relative Frequency ExampleClearly shows that half of all women score on average between 0.7 and 0.8 goals per game.Shows there are a small number of exceptional players. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Women’s Soccer Players, NCAA Division III 20091 - 18How to Construct a Histogram1 - 19Constructing a Histogram by Hand1 - 20Example: Draw Histogram by Hand1 - 21Differences Between Bar Charts and HistogramsA histogram displays numerical data. A bar chart can display categorical data.The bar widths of a histogram are meaningful and must all be the same size. The bar widths for a bar chart are meaningless.The bars of a histogram usually touch each other. For a bar chart, there are always gaps between bars. There is only one choice, ascending by x, for the order of the bars in a histogram, while there are many choices of order for a bar chart.Copyright © 2013 Pearson Education, Inc.. All rights reserved.1 - 22Three Aspects of a DistributionShapeSymmetryHow a many bumps or modes?Other distinguishing featuresCenterWhat is a typical value?SpreadIs the data all