Chapter 1: Describing Data: Graphical 1.1

Chapter 1: Describing Data: Graphical 1.1 1.2 1.3 1.4 1.5 a. Numerical discrete. Since the purchase price comes from a counting process. b. Categorical nominal. Since the state (or country) does not imply ranking of residence, it is nominal. c. Categorical ordinal. Owner s satisfaction level indicates rank ordering. d. Numerical discrete. The number comes from a counting process. a. Categorical, nominal (The response is categorical because the responses can be grouped into classes or categories, in this case yes/no. The measurement levels are nominal because the responses are words that describe the categories.) b. Categorical, ordinal (The response is categorical because the responses can be grouped into classes or categories. The measurement levels are ordinal because these are rankings of the data.) c. Numerical, discrete (The response is numerical because the responses cannot be grouped into classes or categories. Since the response is an actual cost, it is discrete because the value comes from a counting process.) The response is categorical because the responses can be grouped into classes or categories. The measurement levels are ordinal because these are rankings of the data. a. Categorical Qualitative ordinal b. Numerical Quantitative discrete c. Categorical Qualitative nominal d. Categorical Qualitative nominal a. Categorical, nominal (The response is categorical because the responses can be grouped into classes or categories. The measurement levels are nominal because the responses are words that describe the categories.) b. Numerical, discrete (The response is numerical because the responses cannot be grouped into classes or categories. It is discrete because the value comes from a counting process.) 1-1

1-2 Statistics for Business & Economics, 8 th edition c. Categorical, nominal (The response is categorical because the responses can be grouped into classes or categories, in this case yes/no. The measurement levels are nominal because the responses are words that describe the categories.) d. Categorical, ordinal (The response is categorical because the responses can be grouped into classes or categories. The measurement levels are ordinal because these are rankings.) 1.6 1.7 1.8 1.9 a. Categorical Qualitative nominal b. Numerical Quantitative - discrete c. Categorical Qualitative nominal: yes/no response d. Categorical Qualitative ordinal a. An example of ordinal responses: Benefits (1 to 5) b. An example of nominal responses: Gender (male/female 1/2) c. An example of a numerical variable: Time (in seconds) a. Various answers Categorical variable with ordinal responses: PIR_grp (1-5) b. Various answers Categorical variable with nominal responses: female (male/female /1) c. Various answers Numerical variable with continuous responses: daily_cost d. Various answers Numerical variable with discrete responses: PIR_p a. Pie chart Breakdown of Travel Expenses Fees % Other 7% Transportation 31% Food 17% Lodging 25%

Chapter 1: Describing Data: Graphical 1-3 b. Bar chart Breakdown of Travel Expenses 35% 3% Percent of Cost 25% % 15% 1% 5% % Transport Lodging Food Fees Other 1.1 Pareto diagram possible defects for a product line Pareto Chart of Defect Code_Ex1.1 1 15 8 Count 1 6 4 Percent 5 Defect Code_Ex1.1 D B C A E Other Count 9 7 15 1 8 7 Percent 45. 35. 7.5 5. 4. 3.5 Cum % 45. 8. 87.5 92.5 96.5 1.

1-4 Statistics for Business & Economics, 8 th edition 1.11 a. Bar chart Bank Customer Satisfaction 8 Number of Customers 7 6 5 4 3 1 Very Satisfied Moderately Satisfied No Opinion Moderately Dissatisf ied Very Dissatisfied b. Pie chart

Chapter 1: Describing Data: Graphical 1-5 1.12 1.13 Pie chart U.S. federal budget spending Pie Chart of % U.S. Federal Budget Spending Deposit insurance Other fed operations1.% 6.% Interest on debt 14.% Entitlements 46.% Category Entitlements Defense Grants to states Interest on debt Other fed operations Deposit insurance Grants to states 15.% Defense 18.%

1-6 Statistics for Business & Economics, 8 th edition 1.14 a. Bar chart of the number of endangered wildlife species in the United States Endangered Wildlife in the United States 8 7 Number of Species 6 5 4 3 1 Mammals Birds Reptiles Amphibians Fishes b. Bar chart of the number of endangered wildlife species outside the United States Endangered Wildlife outside the United States 3 25 Number of Species 15 1 5 Mammals Birds Reptiles Amphibians Fishes

Chapter 1: Describing Data: Graphical 1-7 c. Bar chart to compare the number of endangered species in the United States to the number of endangered species outside the United States Endangered Wildlife 3 25 Number of Species 15 1 5 In the United States Outside the United States Mammals Birds Reptiles Amphibians Fishes 1.15 a. Pareto diagram of most serious errors by all players 5 4 Pareto Chart of Error 1 8 Count 3 6 4 Percent 1 Error C B D E A Count 12 1 1 7 6 Percent 26.7 22.2 22.2 15.6 13.3 Cum % 26.7 48.9 71.1 86.7 1.

1-8 Statistics for Business & Economics, 8 th edition b. Pareto diagram of most serious errors by male players Pareto Chart of Error by Gender Gender = Male 25 1 8 Count 15 1 6 4 Percent 5 Error C E B A D Count 1 6 4 3 2 Percent 4. 24. 16. 12. 8. Cum % 4. 64. 8. 92. 1. c. Pareto diagram of most serious errors by female players 25 Pareto Chart of Error by Gender Gender = Female 1 Count 15 1 8 6 4 Percent 5 Error D B A C Other Count 8 6 3 2 1 Percent 4. 3. 15. 1. 5. Cum % 4. 7. 85. 95. 1.

Chapter 1: Describing Data: Graphical 1-9 d. Component (stacked) bar chart of errors and gender Chart of Gender, Error 25 Error A B C D E Count 15 1 5 Gender Female Male 1.16 Describe the data graphically

1-1 Statistics for Business & Economics, 8 th edition 1.17 a. Cluster bar chart of the respondents major and gender Student Majors 16 14 Number of Students 12 1 8 6 4 Male Female 2 Accounting Financial Management Marketing Undecided Major b. Pie chart of their majors

Chapter 1: Describing Data: Graphical 1-11 1.18 a. Pie chart of the percent of males in each of the activity level categories. b. Pie chart of the percent of females in each of the activity level categories.

1-12 Statistics for Business & Economics, 8 th edition 1.19 a. Pie chart for worldwide market shares for February 11. b. Answer will vary: Pie chart for worldwide market shares for October 11.

Chapter 1: Describing Data: Graphical 1-13 c. Answers will vary; Pie chart for Asian market shares for October 11. 1. Customers at a New Mall 7 6 Number of Customers 5 4 3 1 Monday Tuesday Wednesday Thursday Friday Saturday Day

1-14 Statistics for Business & Economics, 8 th edition 1.21 Time-series plot of number of males and females enrolled in colleges (undergraduate and postbaccalaureate) in the United States from through 8. 1.22 a. Time-series plot of Gross domestic investment and Gross private domestic

Chapter 1: Describing Data: Graphical 1-15 1.23 a. Time-series plot of the Gross Domestic Product in Manufacturing in current and real (5) dollars by industry for durable goods from to 9. b. Time-series plot of Gross Domestic Product in Manufacturing in chained dollars (5) by industry for nondurable goods from to 9.

1-16 Statistics for Business & Economics, 8 th edition 1.24 a. The Euro (EUR) compared to 1 U.S. Dollar (USD) b. The GBP compared to 1 U.S. Dollar (USD) c. Answers may vary.

Chapter 1: Describing Data: Graphical 1-17 1.25 a. Time-series plot of worldwide market shares of IE, Firefox, Chrome, Safari, and Opera. b. Time-series plot of European market shares of IE, Firefox, Chrome, Safari, and Opera.

1-18 Statistics for Business & Economics, 8 th edition c. Time-series plot of North American market shares of IE, Firefox, Chrome, Safari, and Opera. 1.26 Time-series plot of a stock market index (Dow Jones Industrial Average) over 14 years from the internet

Chapter 1: Describing Data: Graphical 1-19 1.27 Time-series plot of Gold Price data Time Series Plot of PRICE ($) 6 5 PRICE ($) 4 3 1 1 2 3 4 5 6 7 8 YEAR 9 1 11 12 13 14 1.28 Time-series plot of Housing Starts data 12 Time Series Plot of STARTS 11 1 9 STARTS 8 7 6 5 4 2 4 6 8 1 12 14 YEAR 16 18 22 24

argestobsevaion-slestobservationnumberclases1- Statistics for Business & Economics, 8 th edition 1.29 Time-series plot of Earnings per Share 9 Time Series Plot of EARNINGS 8 7 EARNINGS 6 5 4 3 1 3 6 9 12 15 YEAR 18 21 24 27 1.3 a. 5 7 classes b. 7 8 classes c. 8 1 classes d. 8 1 classes e. 1 11 classes 1.31 Lclaswidth=a. w rtofmab. c. d. 85 8 ( round down) 8 19 3 w 8 23 4 w 24( round up) 8 5 14 w 45 8

Chapter 1: Describing Data: Graphical 1-21 1.32 a. frequency distribution Bin Frequency 1 5 3 3 4 8 5 3 6 5 7 4 More b. histogram and c. ogive Histogram Frequency 9 8 7 6 5 4 3 2 1 1 3 4 5 6 7 More 1.% 1.% 8.% 6.% 4.%.%.% Bin Frequency Cumulative % d. stem-and-leaf display Stem-and-Leaf Display: Data_Ex1.32 Stem-and-leaf of Data_Ex1.32 N = 28 Leaf Unit = 1. 2 1 23 5 1 557 7 2 14 8 2 8 9 3 2 (6) 3 567799 13 4 144 9 4 9 5 14 7 5 699 4 6 24 2 6 55

1-22 Statistics for Business & Economics, 8 th edition 1.33 Stem-and-leaf display Stem-and-Leaf Display: StudyHrs_Ex1.33 Stem-and-leaf of StudyHrs_Ex1.33 N = Leaf Unit =.1 1 1 1 1 3 2 34 7 2 6889 8 3 (4) 3 5669 8 4 4 7 4 58 5 5 2 3 5 5 2 6 2 1 6 7 1.34 1.35 Classes Frequency a. Relative Frequency b. Cumulative Frequency c. Cumulative Relative Frequency <1 8 16.33% 8 16.33% 1< 1.41% 18 36.74% <3 13 26.53% 31 63.27% 3<4 12 24.49% 43 87.76% 4<5 6 12.24% 49 1.% Total 49 1.% Scatter plot

Chapter 1: Describing Data: Graphical 1-23 1.36 1.37 a. Construct a cumulative relative frequency distribution Age Percent Relative Cumulative Frequency 18-24 11.3% 11.3% 25-34 19.11% 3.41% 35-44 23.64% 54.5% 45-54 23.48% 77.53% 55+ 22.48% 1.1% Total b. 54.5% c. 69.59% For the file Water - construct a frequency distribution, cumulative frequency distribution, histogram, ogive and stem-and-leaf display. Various answers one possibility is to use 8 classes with a width of.1. Bin Frequency Cum Freq 3.5 3.6 1 1 3.7 8 9 3.8 3 39 3.9 22 61 4 12 73 4.1 1 74 4.2 1 75 More Histogram Frequency 35 3 25 15 1 5 1.% 1.% 8.% 6.% 4.%.%.% Bin Frequency Cumulative %

1-24 Statistics for Business & Economics, 8 th edition Stem-and-Leaf Display: Volume Stem-and-leaf of Volumes N = 75 Leaf Unit =.1 1 35 7 3 36 34 9 36 577799 21 37 111122344444 (17) 37 55566777777889999 37 38 111112222244 24 38 556677899 15 39 1334444 7 39 56689 2 4 2 4 6 1 41 1 1.38 a. Histogram of the Returns data Histogram Frequency 8 7 6 5 4 3 2 1 1 15 25 3 35 4 More Bin Frequency Cumulative % 1.% 1.% 8.% 6.% 4.%.%.% b. stem-and-leaf display Stem-and-Leaf Display: Returns Stem-and-leaf of Returns N = 25 Leaf Unit = 1 1 1 3 4 1 899 11 2 14444 (3) 2 589 11 3 122 4 3 689 1 4 1 4 1 5

Chapter 1: Describing Data: Graphical 1-25 1.39 Describe the data in the Sun data file. Histogram Frequency 4 3 1 224.5 229.5 234.5 239.5 244.5 249.5 More Bin Frequency Cumulative % 1.% 1.% 8.% 6.% 4.%.%.% Stem-and-Leaf Display: weights Stem-and-leaf of weights N = 1 Leaf Unit = 1. 1 22 4 1 22 5 22 8999 16 23 11111111111 25 23 222223333 38 23 4444444445555 (17) 23 66666666677777777 45 23 8888888888999 32 24 111111 24 22222222333 9 24 44455 4 24 67 2 24 99 1.4 Scatter plot

1-26 Statistics for Business & Economics, 8 th edition 1.41 Scatter plot 1.42 Scatter plot

Chapter 1: Describing Data: Graphical 1-27 1.43 Scatter plot of price of orange juice vs. weekly quantities sold Bishops file Scatter plot Bishop s Supermarket Weekly quantities sold - Orange Juice Bishops Supermarket data 3. Price 2.5 2. 3 4 5 Quantity The scatter plot shows the expected negative relationship between price and quantity demanded per unit of time. This is what economic theory suggests for a typical demand curve.

1-28 Statistics for Business & Economics, 8 th edition 1.44 Acme Delivery relation between shipping cost and number of delivery days Shipping Cost versus Number of Delivery Days Acme Delivery 1 9 8 7 Days 6 5 4 3 2 1 3 4 5 6 7 Shipping Cost 8 9 1 Maine to the west coast The relationship appears to be negative; however there is significant variability in delivery time at each of the three shipping costs regular, $3; fast, $5; and lightning, $1. 1.45 a. Row percentages are listed below Rows: Dayweek Columns: SlsLevel 1 2 3 4 All RowPcts 1 6 4 27 41 78.1667 2 29 27 11 11 78.1667 3 29 24 12 14 79.1688 4 28 14 23 11 76.1624 5 18 27 19 15 79.1688 6 7 21 24 26 78.1667 All 117 117 116 118 468 b. Major differences in sales level by day of week indicate that sales levels are highest for days 1 and 6. This is where the largest number of Sales Level 4 occur (the largest daily sales). Days 2 and 3 are similar with most of the sales in the lowest two levels. Days 4 and 5 have sales that are building towards the two largest days of 6 and 1.

Chapter 1: Describing Data: Graphical 1-29 1.46 Scatter plot of Citydat taxbase versus comper Scatterplot of taxbase vs Comper 16 14 1 taxbase 1 8 6 4..5.1.15 Comper No relationship between the two variables and hence no evidence that emphasis on attracting a larger percentage of commercial property increases the tax base. The two outlier points on the right side of the plot might be used to argue that a very high percentage of commercial property will provide a larger tax base. That argument, however, is contrary to the overall pattern of the data...25.3 1.47 a. Misleading histogram of the data (Error: Unequal class widths) Histogram Frequency 35 3 25 15 1 5 Bin Frequency b. Errors include unequal class widths. The first class intervals have widths of 1 whereas later class intervals have widths of and even 5. The classes also overlap. This graph does not accurately reflect the data.

1-3 Statistics for Business & Economics, 8 th edition 1.48 a. Time-series plot with vertical scale from 5 to 57. 57 Time Series Plot of Number_Ex1.48 56 55 Number_Ex1.48 54 53 5 51 5 Month Jan Year 6 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec b. Time-series plot with vertical scale from 4 to 7. 7 Time Series Plot of Number_Ex1.48 65 Number_Ex1.48 6 55 5 45 4 Month Jan Year 6 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec c. Differences between the two graphs include the variability of the data series. One graph suggests greater variability in the data series while the other one suggests a relatively flat line with less variability. Keep in mind the scale on which the measurements are made.

Chapter 1: Describing Data: Graphical 1-31 1.49 a. Time-series plot of Exchange Rates with vertical axis from 92 to 16. 16 Time Series Plot of VALUE 14 12 VALUE 1 98 96 94 92 Jan Feb Mar Apr May Jun Jul Month Aug Sep Oct Nov Dec b. Time-series plot of Exchange Rates with vertical axis from 75 to 1. 1 Time Series Plot of VALUE 11 VALUE 1 9 8 Jan Feb Mar Apr May Jun Jul Month Aug Sep Oct Nov Dec c. Differences between the two graphs include the variability of the data series. One graph suggests greater variability in the data series while the other one suggests a relatively flat line with less variability. Keep in mind the scale on which the measurements are made.

1-32 Statistics for Business & Economics, 8 th edition 1.5 Draw two time-series plots for Inventory Sales with different vertical ranges. 1.6 Time Series Plot of RATIO 1.55 1.5 RATIO 1.45 1.4 1.35 1.3 1 2 3 4 5 6 7 Index 8 9 1 11 12 2. Time Series Plot of RATIO 1.75 RATIO 1.5 1.25 1. 1 2 3 4 5 6 7 Index Differences between the two graphs include the variability of the data series. One graph suggests greater variability in the data series while the other one suggests a relatively flat line with less variability. Keep in mind the scale on which the measurements are made. 8 9 1 11 12

Chapter 1: Describing Data: Graphical 1-33 1.51 Describe graphically the time (in hours) that students studied. Histogram of Hours_Ex1.51 5 4 Frequency 3 2 1 2 3 4 5 Hours_Ex1.51 6 7 Stem-and-Leaf Display: Hours_Ex1.51 Stem-and-leaf of Hours_Ex1.51 N = Leaf Unit =.1 1 2 4 3 2 89 4 3 7 3 669 9 4 4 (3) 4 568 8 5 2 6 5 58 4 6 2 3 6 57 1 7 3 1.52 a. Draw a histogram of forecasted earnings per share. Exercise 1.52 Number of Analysts 1 8 6 4 2 1.445 1.945 11.445 11.945 12.445 1% 8% 6% 4% % % Forecast ($ per share)

1-34 Statistics for Business & Economics, 8 th edition Answer to b., c. and d. are: (b) (c) (d) Relative Cumulative Cumulative Frequency Freq. Freq. % 2.1 2 1.% 8.4 1 5.% 6.3 16 8.% 3.15 19 95.% 1.5 1.% d. Cumulative relative frequencies are in the last column of the table above. These numbers indicate the percent of analysts who forecast that level of earnings per share and all previous classes, up to and including the current class. The third bin of 8% indicates that 8% of the analysts have forecasted up to and including that level of earnings per share. 1.53 Use a pie chart or bar chart to plot internet usage and income data Chart of Internet_Ex1.53 vs Income_Ex1.53 7 6 Internet_Ex1.53 5 4 3 1 <5 5<75 Income_Ex1.53 75+

Chapter 1: Describing Data: Graphical 1-35 1.54 Cluster bar chart for impact of SOX 1.55 Describe the familiarity with tax law data graphically Chart of Frequency_Ex1.55 vs Familiarity_Ex1.55 7 Frequency_Ex1.55 6 5 4 3 1 Child tax credit Marriage penalty Capital gains Familiarity_Ex1.55 Dividends Marginal tax rates Unaware of changes

1-36 Statistics for Business & Economics, 8 th edition 1.56 County Appraiser s Office Data Entry Process a. Pareto diagram Pareto Chart for Defects 8 1 7 6 8 Count 5 4 3 6 4 Percent 1 Defect Count Percent Cum % Posting Error Name Posting Error Parcel Wrong call transfer Deeds received after 23 21 18 6 28.7 26.3 22.5 7.5 28.7 55. 77.5 85. Property Sold 5 6.3 91.3 Posting Error Legal 4 5. 96.3 Others 3 3.8 1. b. Recommendations should include a discussion of the data entry process. The data entry was being made by individuals with no knowledge of the data. Training of the data entry personnel should be a major recommendation. Increasing the size of the monitors used by the data entry staff would also reduce the number of errors.

Chapter 1: Describing Data: Graphical 1-37 1.57 a. Pie chart for Groupons purchased during past week b. Bar chart for Groupons purchased during past week

1-38 Statistics for Business & Economics, 8 th edition 1.58 1.59 Scatter plot of price of paint versus demand for paint. Scatterplot of Price_Ex1.59 vs Qty_Ex1.59 1 9 Price_Ex1.59 8 7 6 5 4 1 1 14 Qty_Ex1.59 16 18 Price and quantity demanded per unit of time are negatively related as predicted by the law of demand.

Chapter 1: Describing Data: Graphical 1-39 1.6 Plot the data for advertising expenditures and total sales Scatterplot of Sales_Ex1.6 vs Advert_Ex1.6 18 Sales_Ex1.6 16 14 1 1 8 6 7 8 9 1 11 Advert_Ex1.6 12 13 14 15 1.61 Plot of quantity versus price, with price on the horizontal axis Scatterplot of Tons_Ex1.61 vs Price_Ex1.61. 17.5 Tons_Ex1.61 15. 12.5 1. 7.5 5. 2 3 4 Price_Ex1.61 5 6

1-4 Statistics for Business & Economics, 8 th edition 1.62 Plot the batting averages vs. hours spent per week in a weight-training program. 1 Scatterplot of BatChg_Ex1.62 vs Hours_Ex1.62 1 BatChg_Ex1.62 8 6 4 5 1 15 Hours_Ex1.62 25 It appears that the number of hours spent per week in a special weighttraining program is positively related to the change in their batting averages from the previous season. 1.63 a. Describe the data with a cross table Type of Account Male Female Subtotal Easy Checking 8 1 18 Intelligent Checking 12 24 36 Super Checking 27 27 54 Ultimate Checking 24 6 3 Subtotal 143 157 3

Chapter 1: Describing Data: Graphical 1-41 b. Describe the data graphically Chart of Easy_Ex1.63, Intelli_Ex2., Super_Ex1.63,... vs Gender_Ex1.6 Gender_Ex1.63 Male Female 15 Data 1 5 Easy_Ex1.63 Intelli_Ex1.63 Super_Ex1.63 Ultimate_Ex1.63 1.64 a. Describe the new product data with a cross table Age Friend Newspaper Subtotal <21 years 3 5 21-35 6 3 9 35+ 18 42 6 Subtotal 18 92 b. Describe the data graphically Chart of <21_Ex1.64, 21-35_Ex1.64, 35+_Ex1.64 vs Intro_Ex1.64 9 8 Intro_Ex1.64 Friend Newspaper 7 6 Data 5 4 3 1 <21_Ex1.64 21-35_Ex1.64 35+_Ex1.64

1-42 Statistics for Business & Economics, 8 th edition 1.65 a. Pie chart of soft drink preferences Pie Chart of Prefer_Ex1.65 vs Brand_Ex1.65 14, 5.8% E A 3, 12.5% B 5,.8% Category A B C D E D 1, 41.7% C 46, 19.2% b. Construct a bar chart 1 Chart of Prefer_Ex1.65 vs Brand_Ex1.65 8 Prefer_Ex1.65 6 4 A B C Brand_Ex1.65 D E

Chapter 1: Describing Data: Graphical 1-43 1.66 a. Scatterplot From the graph, it is evident that the temperature is positively related to the time it takes to mow. 1.67 Time-series plot of population growth for the state of New York 193 Time Series Plot of State of NY Population Number of People 19 NY Population 191 19 189 188 187 186 1997 1998 1999 1 2 Year Source: bea.doc.gov, regional economic account, interactive data tables 3 4 1.68 a. Cross table of method of payment and day of purchase for Florin data file. Payment M T W Th F S Tot Am Ex 7 3 4 3 6 23 MC 1 4 4 2 4 9 24 Visa 6 6 4 5 8 1 39 Cash 3 1 3 9 16 Other 2 4 4 7 6 23 Subtotal 19 11 15 15 25 4 125

1-44 Statistics for Business & Economics, 8 th edition b. Pie chart of day of purchase 1.69 Cross table and bar chart of drink preference vs. type of vehicle Vehicle Beer Wine Subtotal Pickup 71 29 1 Car 32 68 1 Subtotal 13 97 Chart of Beer_Ex1.69, Wine_Ex1.69 vs Vehicle_Ex1.69 1 Vehicle_Ex1.69 Pickup Car 8 Data 6 4 Beer_Ex1.69 Wine_Ex1.69

Chapter 1: Describing Data: Graphical 1-45 1.7 a. Time-series plot of the closing costs b. Answers may vary. 1.71 Time-Series Plot of Facebook New Visitors

1-46 Statistics for Business & Economics, 8 th edition 1.72 a. Histogram of shopping times b. Stem-and-leaf display Stem-and-Leaf Display: Time Stem-and-leaf of Time N = 14 Leaf Unit = 1. 9 1 888888899 19 2 11111333 26 2 5555558 44 3 11113344444444 52 3 77777788 52 4 1222233 41 4 555678 35 5 112222 27 5 5777799 6 334 15 6 7889999 8 7 1133 1.73 Stem-and-leaf display Stem-and-Leaf Display: GPA Stem-and-leaf of GPA N = 156 Leaf Unit =.1 4 21 2689 6 22 25 9 23 13 11 24 56 23 25 113345555668 25 26 25 28 27 889 35 28 2788888 4 29 1289 45 3 15678 6 31 488888888888 74 32 1112444568999 (53) 33 11111111111222223333444444444555566666666677777777999 29 34 22222222222222222 6 35 6 36 57 4 37 12 1 38 5

Chapter 1: Describing Data: Graphical 1-47 1.74 Scatter plot