Describing Data: Displaying and Exploring DataSlide 2Dot PlotsDot Plots - ExamplesDot Plot – Minitab ExampleExample: Dot Plots of Vehicle SalesStem-and-LeafStem-and-Leaf – ExampleStem-and-leaf: Another ExampleSlide 10Example: ATM Usage in HawaiiQuartiles, Deciles and PercentilesPercentile ComputationPercentiles - ExamplePercentiles – Example (cont.)Slide 16Another Measure of VariabilityExample: ATM UsageBoxplots – Graphical Use of the 5-Number SummaryBoxplot - ExampleBoxplot ExampleBoxplot – Whitner AutoplexBoxplot – Radio Advertising SpotsSkewnessSkewness - Formulas for ComputingCommonly Observed ShapesSkewness – An ExampleSkewness – An Example Using Pearson’s CoefficientSkewness – Software Share EarningsDescribing Relationship between Two VariablesDescribing Relationship between Two Variables – Scatter Diagram ExamplesDescribing Relationship between Two Variables – Scatter Diagram Excel ExampleContingency TablesContingency Tables – An ExampleExample – Dessert Ordered, by GenderEnd of Chapter 4©The McGraw-Hill Companies, Inc. 2008McGraw-Hill/IrwinDescribing Data: Displaying and Exploring DataChapter 42GOALSDevelop and interpret a dot plot.Develop and interpret a stem-and-leaf display.Compute and understand quartiles, deciles, and percentiles.Construct and interpret box plots.Compute and understand the coefficient of skewness.Draw and interpret a scatter diagram.Construct and interpret a contingency table.3Dot PlotsA dot plot groups the data as little as possible and the identity of an individual observation is not lost. To develop a dot plot, each observation is simply displayed as a dot along a horizontal number line indicating the possible values of the data. If there are identical observations or the observations are too close to be shown individually, the dots are “piled” on top of each other.4Dot Plots - ExamplesReported below are the number of vehicles sold in the last 24 months at Smith Ford Mercury Jeep, Inc., in Kane, Pennsylvania, and Brophy Honda Volkswagen in Greenville, Ohio. Construct dot plots and report summary statistics for the two small-town Auto USA lots.5Dot Plot – Minitab Example6Example: Dot Plots of Vehicle SalesNotice that the scales for the side-by-side dot plots differ. This means that we need to be careful in comparing the two plots. The distribution of monthly counts for Brophy Honda Volkswagen is shifted to the right relative to the distribution for Smith Ford Mercury Jeep, Inc.7Stem-and-LeafIn Chapter 2, we showed how to organize data into a frequency distribution. The major advantage to organizing the data into a frequency distribution is that we get a quick visual picture of the shape of the distribution. One technique that is used to display quantitative information in a condensed form is the stem-and-leaf display. Stem-and-leaf display is a statistical technique to present a set of data. Each numerical value is divided into two parts. The leading digit(s) becomes the stem and the trailing digit the leaf. The stems are located along the vertical axis, and the leaf values are stacked against each other along the horizontal axis.Advantage of the stem-and-leaf display over a frequency distribution - the identity of each observation is not lost.8Stem-and-Leaf – ExampleSuppose the seven observations in the 90 up to 100 class are: 96, 94, 93, 94, 95, 96, and 97. The stem value is the leading digit or digits, in this case 9. The leaves are the trailing digits. The stem is placed to the left of a vertical line and the leaf values to the right. The values in the 90 up to 100 class would appear asThen, we sort the values within each stem from smallest to largest. Thus, the second row of the stem-and-leaf display would appear as follows:9Stem-and-leaf: Another ExampleListed in Table 4–1 is the number of 30-second radio advertising spots purchased by each of the 45 members of the Greater Buffalo Automobile Dealers Association last year. Organize the data into a stem-and-leaf display. Around what values do the number of advertising spots tend to cluster? What is the fewest number of spots purchased by a dealer? The largest number purchased?10Stem-and-leaf: Another Example11Example: ATM Usage in HawaiiAloha Banking Co. is studying ATM use insuburban Honolulu. A sample of 30 ATM’swas selected, and data were collected on thenumber of times each ATM was used on acertain day. We want to study thecharacteristics of the distribution of daily ATMusage. What is the minimum? Maximum? Median?12The standard deviation is the most widely used measure of dispersion. Alternative ways of describing spread of data include determining the location of values that divide a set of observations into equal parts. These measures include quartiles, deciles, and percentiles.Quartiles, Deciles and Percentiles13To formalize the computational procedure, let Lp refer to the location of a desired percentile. So if we wanted to find the 33rd percentile we would use L33 and if we wanted the median, the 50th percentile, then L50. The number of observations is n, so if we want to locate the median, its position is at (n + 1)/2, or we could write this as (n + 1)(P/100), where P is the desired percentile.Percentile Computation14Percentiles - ExampleListed below are the commissions earned last month by a sample of 15 brokers at Salomon Smith Barney’s Oakland, California, office. Salomon Smith Barney is an investment company with offices located throughout the United States.$2,038 $1,758 $1,721 $1,637 $2,097 $2,047 $2,205 $1,787 $2,287 $1,940 $2,311 $2,054 $2,406 $1,471 $1,460Locate the median, the first quartile, and the third quartile for the commissions earned.15Percentiles – Example (cont.)Step 1: Organize the data from lowest to largest value$1,460 $1,471 $1,637 $1,721$1,758 $1,787 $1,940 $2,038$2,047 $2,054 $2,097 $2,205$2,287 $2,311 $2,40616Percentiles – Example (cont.)Step 2: Compute the first and third quartiles. Locate L25 and L75 using:205,2$721,1$lyrespective array, in then observatio 12th and4th theare quartiles thirdandfirst theTherefore,1210075)115( 410025)115(75257525LLLL17Another Measure of VariabilityThe Interquartile Range (IQR) of a numericdata set is the difference between the third andfirst quartiles. IQR = L75 – L25This measure of variability tells the range ofvalues of the middle 50% of the data set.