Descriptive Statistics - Tabular and Graphical Presentations Part 1

Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations Learning Objectives 1. Learn how to construct and interpret summarization procedures for qualitative data such as: frequency and relative frequency distributions, bar graphs and pie charts. 2. Learn how to construct and interpret tabular summarization procedures for quantitative data such as: frequency and relative frequency distributions, cumulative frequency and cumulative relative frequency distributions. 3. Learn how to construct a dot plot, a histogram, and an ogive as graphical summaries of quantitative data. 4. Learn how the shape of a data distribution is revealed by a histogram. Learn how to recognize when a data distribution is negatively skewed, symmetric, and positively skewed. 5. Be able to use and interpret the exploratory data analysis technique of a stem-and-leaf display. 6. Learn how to construct and interpret cross tabulations and scatter diagrams of bivariate data. Chapter 2 Solutions: 1. Class A B C 2. a. 1 - (.22 + .18 + .40) = .20 b. .20(200) = 40 Frequency 60 24 36 120 Relative Frequency 60/120 = 0.50 24/120 = 0.20 36/120 = 0.30 1.00 c/d. Class A B C D Total 3. a. 360° x 58/120 = 174° b. 360° x 42/120 = 126° Frequency .22(200) = 44 .18(200) = 36 .40(200) = 80 .20(200) = 40 200 Percent Frequency 22 18 40 20 100 c. No 35.0% Yes 48.3% No Opinion 16.7% Descriptive Statistics: Tabular and Graphical Presentations d. 70 60 Frequency 50 40 30 20 10 0 Yes No No Opinion Response a. Categorical b. TV Show Law & Order CSI Without a Trace Desperate Housewives Total: Frequency 4. Frequency 10 18 9 13 50 Percent Frequency 20% 36% 18% 26% 100% 20 18 16 14 12 10 8 6 4 2 0 L&O CSI Trace TV Show Housewives Chapter 2 L&O 20% Housewives 26% Trace 18% CSI 36% d. CSI had the largest viewing audience. Desperate Housewives was in second place. a. Name Brown Davis Johnson Jones Smith Williams Frequency 7 6 10 7 12 8 50 Relative Frequency .14 .12 .20 .14 .24 .16 1.00 Percent Frequency 14% 12% 20% 14% 24% 16% b. 14 12 10 Frequency 5. 8 6 4 2 0 Brown Davis Johnson Name c. Brown Davis Johnson Jones Smith Williams .14 x 360 = 50.4 .12 x 360 = 43.2 .20 x 360 = 72.0 .14 x 360 = 50.4 .24 x 360 = 86.4 .16 x 360 = 57.6 Jones Smith Williams Descriptive Statistics: Tabular and Graphical Presentations Williams 16% Smith 24% Brown 14% Jones 14% Johnson 20% d. Most common: Smith, Johnson and Williams a. Network ABC CBS FOX NBC Total Frequency 15 17 1 17 50 Percent Frequency 30% 34% 2% 34% 100% 18 16 14 Frequency 6. Davis 12% 12 10 8 6 4 2 0 ABC CBS FOX NBC Network b. CBS and NBC are tied, each with 17 of the top rated television shows. ABC is a close third with 15. The fact that the three networks are so close is surprising. FOX, the newest television network, does not have the history to compete with the other three networks in term of the top rated shows in television history. Chapter 2 7. Rating Outstanding Very Good Good Average Poor Frequency 19 13 10 6 2 50 Relative Frequency 0.38 0.26 0.20 0.12 0.04 1.00 Management should be pleased with these results. 64% of the ratings are very good to outstanding. 84% of the ratings are good or better. Comparing these ratings with previous results will show whether or not the restaurant is making improvements in its ratings of food quality. 8. a. Position Pitcher Catcher 1st Base 2nd Base 3rd Base Shortstop Left Field Center Field Right Field 9. Frequency 17 4 5 4 2 5 6 5 7 55 b. Pitchers (Almost 31%) c. 3rd Base (3 - 4%) d. Right Field (Almost 13%) e. Infielders (16 or 29.1%) to Outfielders (18 or 32.7%) a. Living Area City Suburb Small Town Rural Area Total Live Now 32% 26% 26% 16% 100% Ideal Community 24% 25% 30% 21% 100% Relative Frequency 0.309 0.073 0.091 0.073 0.036 0.091 0.109 0.091 0.127 1.000 Descriptive Statistics: Tabular and Graphical Presentations b. Where do you live now? What do you consider the ideal community? c. Most adults are now living in a city (32%). d. Most adults consider the ideal community a small town (30%). e. Percent changes by living area: City -8%, Suburb -1%, Small Town +4%, and Rural Area +5%. Suburb living is steady, but the trend would be that living in the city would decline while living in small towns and rural areas would increase. 10. a. Rating Excellent Frequency 20 Good 101 Fair 528 Bad 244 Terrible Total 122 1015 Chapter 2 b. Percent Frequency Rating Excellent 2 Good 10 Fair 52 Bad 24 Terrible 12 Total 100 c. d. 24% + 12% = 36% of adults in the United Sates think the Federal Bank is doing a bad or a terrible job in handling the credit problems. Only 10% + 2% = 12% think the Federal Bank is doing a good or excellent job. e. 40% + 10% = 50% of adults in Spain think the European Central Bank is doing a bad or terrible job in handling the credit problems. Only 4% of adults in Spain think the European Central Bank is doing a good or excellent job. Both countries show pessimism and relatively low confidence in how the banks are handling the credit problems in the financial markets. But in comparing the two countries, adults in Spain show more concern and more pessimism about the bank’s ability compared to adults in the United States. 11. Class 12-14 15-17 18-20 21-23 24-26 Total Frequency 2 8 11 10 9 40 Relative Frequency 0.050 0.200 0.275 0.250 0.225 1.000 Percent Frequency 5.0 20.0 27.5 25.0 22.5 100.0 Descriptive Statistics: Tabular and Graphical Presentations 12. Class less than or equal to 19 less than or equal to 29 less than or equal to 39 less than or equal to 49 less than or equal to 59 Cumulative Frequency 10 24 41 48 50 Cumulative Relative Frequency .20 .48 .82 .96 1.00 13. 18 16 14 Frequency 12 10 8 6 4 2 0 10-19 20-29 30-39 40-49 50-59 1.0 .8 .6 .4 .2 0 14. a. 10 20 30 40 50 60 Chapter 2 b/c. Class 6.0 - 7.9 8.0 - 9.9 10.0 - 11.9 12.0 - 13.9 14.0 - 15.9 Frequency 4 2 8 3 3 20 Percent Frequency 20 10 40 15 15 100 15. a/b. Waiting Time 0-4 5-9 10 - 14 15 - 19 20 - 24 Totals Frequency 4 8 5 2 1 20 Relative Frequency 0.20 0.40 0.25 0.10 0.05 1.00 c/d. Waiting Time Less than or equal to 4 Less than or equal to 9 Less than or equal to 14 Less than or equal to 19 Less than or equal to 24 e. 12/20 = 0.60 16. a. Salary 150-159 160-169 170-179 180-189 190-199 200-209 210-219 Total Frequency 1 3 7 5 1 2 1 20 Salary 150-159 160-169 170-179 180-189 190-199 200-209 210-219 Total Percent Frequency 5 15 35 25 5 10 5 100 b. Cumulative Frequency 4 12 17 19 20 Cumulative Relative Frequency 0.20 0.60 0.85 0.95 1.00 Descriptive Statistics: Tabular and Graphical Presentations c. Cumulative Percent Frequency Salary Less than or equal to 159 5 Less than or equal to 169 20 Less than or equal to 179 55 Less than or equal to 189 80 Less than or equal to 199 85 Less than or equal to 209 95 Less than or equal to 219 100 Total 100 d. e. There is skewness to the right. f. (3/20)(100) = 15% 17. a. b. The highest price stock is for IBM with a price of $107 per share. The lowest price stock is for Alcoa with a price of $11 per share. A class size of 10 results in 10 classes. Price per Share $10-19 $20-29 $30-39 $40-49 $50-59 $60-69 $70-79 $80-89 $90-99 $100-109 Frequency 5 10 3 2 6 2 1 0 0 1 Chapter 2 c. The general shape of the distribution is skewed to the right. Half of the companies (15) have a price per share less than $30. A mid-priced stock appears to be in the $30 to $49 range, while the most frequently priced stock is in the $20 to $29 range. Five stocks are less than $20 per share (Alcoa, Bank of America, General Electric, Intel and Pfizer). Four stocks are $60 or more per share (3M, Chevron, ExxonMobil and IBM). d. 18. a. b. A variety of comparisons are possible depending upon when the study is done. The lowest holiday spending is $180; the highest $2050. Spending 0-249 250-499 500-749 750-999 1000-1249 1250-1499 1500-1759 1750-1999 2000-2249 Total Frequency 3 6 5 5 3 1 0 1 1 25 Percent 12 24 20 20 12 4 0 4 4 100 Descriptive Statistics: Tabular and Graphical Presentations c. The distribution shows a positive skewness. 7 Frequency 6 5 4 3 2 1 0 0-249 250-499 500-749 750-999 10001249 12501499 15001759 17501999 20002249 Holiday Spending d. The holiday spending ranges from $0 to less than $2250. The majority of the spending is between $250 and $1000 with 16 of the 25 customers, 64%, in this range. The middle or average spending is around $750 per customer. The distribution has a positive skewness with two consumers above $1750. O ne consumer is above $2000. 19. a/b/c/d. Class (Minutes) 1-5 6-10 11-15 16-20 21-25 26-30 31-34 Frequency 12 3 2 1 1 0 1 Relative Frequency .60 .15 .10 .05 .05 .00 .05 Cumulative Frequency 12 15 17 18 19 19 20 Cumulative Relative Frequency .60 .75 .85 .90 .95 .95 1.00 e. 1 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 30 35 Time f. 60% of office workers spend 5 minutes or less on unsolicited email and spam. However, 25% of office workers spend more than 10 minutes per day on this task.