Elementary Statistics Using Excel PDF

Elementary Statistics Using Excel Sixth Edition Chapter 2 Exploring Data with Tables and...

Elementary Statistics Using Excel Sixth Edition Chapter 2 Exploring Data with Tables and Graphs Copyright © 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved  Exploring Data with Tables and Graphs 2-1 Frequency Distributions for Organizing and Summarizing Data 2-2 Histograms 2-3 Graphs that Enlighten and Graphs that Deceive 2-4 Scatterplots, Correlation, and Regression Copyright © 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved  Key Concept When working with large data sets, a frequency distribution (or frequency table) is often helpful in organizing and summarizing data. A frequency distribution helps us to understand the nature of the distribution of a data set. Copyright © 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved  Frequency Distribution Frequency Distribution (or Frequency Table) Shows how data are partitioned among several categories (or classes) by listing the categories along with the number (frequency) of data values in each of them. Copyright © 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved  Frequency Distributions  Definition  A frequency distribution of a qualitative variable lists all categories and the number of elements that belong to each of the categories. Copyright © 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved  Example 2-1  A sample of 30 persons who often consume donuts were asked what variety of donuts was their favorite. The responses from these 30 persons were as follows: Copyright © 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved  Example 2-1 glazed filled other plain glazed other frosted filled filled glazed other frosted glazed plain other glazed glazed filled frosted plain other other frosted filled filled other frosted glazed glazed filled Construct a frequency distribution table for these data. Copyright © 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved  Example 2-1: Solution Table 2.4 Frequency Distribution of Favorite Donut Variety Copyright © 2018, 2014, 2012 Pearson Education, Inc. All Rights Reserved  Relative Frequency and Percentage Distributions  Calculating Relative Frequency of a Category Frequency of that category Re lative frequency of a category  Sum of all frequencie s Pre Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Relative Frequency and Percentage Distributions  Calculating Percentage Percentage = (Relative frequency) · 100% Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-2  Determine the relative frequency and percentage for the data in Table 2.4. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-2: Solution Table 2.5 Relative Frequency and Percentage Distributions of Favorite Donut Variety Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Case Study 2-1 Will Today’s Children Be Better Off Than Their Parents? Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Graphical Presentation of Qualitative Data  Definition  A graph made of bars whose heights represent the frequencies of respective categories is called a bar graph. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.1 Bar graph for the frequency distribution of Table 2.4 Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Case Study 2-2 Employees’ Overall Financial Stress Levels Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Graphical Presentation of Qualitative Data  Definition  A circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories is called a pie chart. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Table 2.6 Calculating Angle Sizes for the Pie Chart Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.2 Pie chart for the percentage distribution of Table 2.5. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  ORGANIZING AND GRAPHING QUANTITATIVE Frequency Distributions Constructing Frequency Distribution Tables Relative and Percentage Distributions Graphing Grouped Data Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Table 2.7 Weekly Earnings of 100 Employees of a Company Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Frequency Distributions  Definition  A frequency distribution for quantitative data lists all the classes and the number of values that belong to each class. Data presented in the form of a frequency distribution are called grouped data. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Frequency Distributions  Definition  The class boundary is given by the midpoint of the upper limit of one class and the lower limit of the next class. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Frequency Distributions Finding Class Width Class width = Upper boundary – Lower boundary Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Frequency Distributions Calculating Class Midpoint or Mark Lower limit  Upper limit Class midpoint or mark  2 Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Constructing Frequency Distribution Tables Calculation of Class Width Largest va lue - Smallest v alue Approximat e class width  Number of classes Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Table 2.8 Class Boundaries, Class Widths, and Class Midpoints for Table 2.7 Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-3  The following data give the total number of iPods® sold by a mail order company on each of 30 days. Construct a frequency distribution table with 5 classes. 8 25 11 15 29 22 10 5 17 21 22 13 26 16 18 12 9 26 20 16 23 14 19 23 20 16 27 16 21 14 Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-3: Solution The minimum value is 5, and the maximum value is 29. Suppose we decide to group these data using five classes of equal width. Then, 29  5 Approximate width of each class  4.8 5 Now we round this approximate width to a convenient number, say 5. The lower limit of the first class can be taken as 5 or any number less than 5. Suppose we take 5 as the lower limit of the first class. Then our classes will be 5 – 9, 10 – 14, 15 – 19, 20 – 24, and 25 – 29 Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Table 2.9 Frequency Distribution for the Data on iPods Sold Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Relative Frequency and Percentage Distributions Calculating Relative Frequency and Percentage Frequency of that class f Relative frequency of a class   Sum of all frequencie s  f Percentage (Relative frequency) 100% Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-4  Calculate the relative frequencies and percentages for Table 2.9. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-4: Solution Table 2.10 Relative Frequency and Percentage Distributions for Table 2.9 Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Graphing Grouped Data  Definition  A histogram is a graph in which classes are marked on the horizontal axis and the frequencies, relative frequencies, or percentages are marked on the vertical axis. The frequencies, relative frequencies, or percentages are represented by the heights of the bars. In a histogram, the bars are drawn adjacent to each other. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.3 Frequency histogram for Table 2.9. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.4 Relative frequency histogram for Table 2.10. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Case Study 2-3 How Long Does Your Typical One- Way Commute Take? Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Graphing Grouped Data  Definition  A graph formed by joining the midpoints of the tops of successive bars in a histogram with straight lines is called a polygon. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.5 Frequency polygon for Table 2.9. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Case Study 2-4 How Much Does it Cost to Insure a Car? Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.6 Frequency distribution curve. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  SHAPES OF HISTOGRAMS 1. Symmetric 2. Skewed 3. Uniform or Rectangular Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.8 Symmetric histograms. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.9 (a) A histogram skewed to the right. (b) A histogram skewed to the left. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.10 A histogram with uniform distribution. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.11 (a) and (b) Symmetric frequency curves. (c) Frequency curve skewed to the right. (d) Frequency curve skewed to the left. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  CUMULATIVE FREQUENCY DISTRIBUTIONS  Definition  A cumulative frequency distribution gives the total number of values that fall below the upper boundary of each class. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-7  Using the frequency distribution of Table 2.9, reproduced here, prepare a cumulative frequency distribution for the number of iPods sold by that company. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-7: Solution Table 2.14 Cumulative Frequency Distribution of iPods Sold Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  CUMULATIVE FREQUENCY DISTRIBUTIONS  Calculating Cumulative Relative Frequency and Cumulative Percentage Cumulative frequency of a class Cumulative relative frequency  Total observations in the data set Cumulative percentage (Cumulative relative frequency) 100 Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Table 2.15 Cumulative Relative Frequency and Cumulative Percentage Distributions for iPods Sold Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  CUMULATIVE FREQUENCY DISTRIBUTIONS  Definition  An ogive is a curve drawn for the cumulative frequency distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.12 Ogive for the cumulative frequency distribution of Table 2.14. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example: Single valued classes The administration in a large city wanted to know the distribution of vehicles owned by households in that city. A sample of 40 randomly selected households from this city produced the following data on the number of vehicles owned: 5 1 1 2 0 1 1 2 1 1 1 3 3 0 2 5 1 2 3 4 2 1 2 2 1 2 2 1 1 1 4 2 1 1 2 1 1 4 1 3 Construct a frequency distribution table for these data using single- valued classes. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example : Single valued classes solution Table 2.13 Frequency Distribution of Vehicles Owned The observations assume only six distinct values: 0, 1, 2, 3, 4, and 5. Each of these six values is used as a class in the frequency distribution in Table 2.13. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.7 Bar graph for Table 2.13. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Case Study 2-5 How Many Cups of Coffee Do You Drink a Day? Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  STEM-AND-LEAF DISPLAYS  Definition  In a stem-and-leaf display of quantitative data, each value is divided into two portions – a stem and a leaf. The leaves for each stem are shown separately in a display. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-8  The following are the scores of 30 college students on a statistics test: 75 52 80 96 65 79 71 87 93 95 69 72 81 61 76 86 79 68 50 92 83 84 77 64 71 87 72 92 57 98  Construct a stem-and-leaf display. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-8: Solution  To construct a stem-and-leaf display for these scores, we split each score into two parts. The first part contains the first digit, which is called the stem. The second part contains the second digit, which is called the leaf. We observe from the data that the stems for all scores are 5, 6, 7, 8, and 9 because all the scores lie in the range 50 to 98. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.13 Stem-and-leaf display. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-8: Solution  After we have listed the stems, we read the leaves for all scores and record them next to the corresponding stems on the right side of the vertical line. The complete stem-and-leaf display for scores is shown in Figure 2.14. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.14 Stem-and-leaf display of test scores. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-8: Solution  The leaves for each stem of the stem-and-leaf display of Figure 2.14 are ranked (in increasing order) and presented in Figure 2.15. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Figure 2.15 Ranked stem-and-leaf display of test scores. One advantage of a stem-and-leaf display is that we do not lose information on individual observations. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-9  The following data give the monthly rents paid by a sample of 30 households selected from a small town. 880 1081 721 1075 1023 775 1235 750 965 960 1210 985 1231 932 850 825 1000 915 1191 1035 1151 630 1175 952 1100 1140 750 1140 1370 1280  Construct a stem-and-leaf display for these data. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-9: Solution Figure 2.16 Stem-and-leaf display of rents Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  DOTPLOTS  Definition  Values that are very small or very large relative to the majority of the values in a data set are called outliers or extreme values. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-12  Table 2.16 lists the number of minutes for which each player of the Boston Bruins hockey team was penalized during the 2011 Stanley Cup championship playoffs. Create a dotplot for these data. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Table 2.16 Number of Penalty Minutes for Players of the Boston Bruins Hockey Team During the 2011 Stanley Cup Playoffs Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-12: Solution  Step1. Draw a horizontal line with numbers that cover the given data as shown in Figure 2.20  Step 2. Place a dot above the value on the numbers line that represents each number of penalty minutes listed in the table. After all the dots are placed, Figure 2.21 gives the complete dotplot. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-12: Solution  As we examine the dotplot of Figure 2.21, we notice that there are two clusters (groups) of data. Sixty percent of the players had 17 or fewer penalty minutes during the playoffs, while the other 40% had 24 or more penalty minutes. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-13  Refer to Table 2.16 in Example 2-12, which lists the number of minutes for which each player of the 2011 Stanley Cup champion Boston Bruins hockey team was penalized during the playoffs. Table 2.17 provides the same information for the Vancouver Canucks, who lost in the finals to the Bruins in the 2011 Stanley Cup playoffs. Make dotplots for both sets of data and compare them. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Table 2.17 Number of Penalty Minutes for Players of the Vancouver Canucks Hockey Team During the 2011 Stanley Cup Playoffs Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-13: Solution Figure 2.22 Stacked dotplot of penalty minutes for the Boston Bruins and the Vancouver Canucks Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved  Example 2-13: Solution  Looking at the stacked dotplot, we see that the majority of players on both teams had fewer than 20 penalty minutes throughout the playoffs. Both teams have one outlier each, at 63 and 66 minutes, respectively. The two distributions of penalty minutes are almost similar in shape. Prem Mann, Introductory Statistics, 8/E Copyright Copyright © 2018, 2014, 2012 Pearson Education, Inc. © 2013 All Rights John Wiley & Sons. All rights reserved. Reserved