1. Descriptive Statistics: Tabular and Graphical Presentations n Summarizing Qualitative Data n Summarizing Quantitative Data

2. Summarizing Qualitative Data n Frequency Distribution n Relative Frequency Distribution n Cumulative Frequency n Cumulative Relative Frequency n Bar Graph n Pie Chart

3. Example: Marada Inn Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are: Below Average Below Average Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Below Average Below Average Poor Poor Excellent Excellent Above Average Above Average Average Average Above Average Above Average Below Average Below Average Poor Poor Above Average Above Average Average Average

4. Frequency Distribution Poor Below Average Average Above Average Excellent 2 3 5 9 1 1 Total 20 RatingFrequency CumulativeFrequency 2 5 10 10 19 19 20 20 2+3+5 =10

5. Relative Frequency and Percent Frequency Distributions Poor Below Average Average Above Average Excellent.10.10.15.15.25.25.45.45.05.05 Total 1.00.10.10.25.25.50.50.95.95 1.0 1.0 Relative RelativeFrequency CumulativeRelativeFrequency Rating.10+.15 =.25 1/20 =.05

6. Poor Below Average Below Average Above Average Above Average Excellent Frequency Rating Bar Graph 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 Marada Inn Quality Ratings

7. Below Average 15% Below Average 15% Average 25% Average 25% Above Average 45% Above Average 45% Poor 10% Poor 10% Excellent 5% Excellent 5% Marada InnQuality Ratings Marada Inn Quality Ratings Pie Chart

8. Summarizing Quantitative Data n Frequency Distribution n Relative Frequency Distributions n Histogram n Cumulative Distributions

9. Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide.

10. Example: Hudson Auto Repair n Sample of Parts Cost for 50 Tune-ups

11. Frequency Distribution n Guidelines for Selecting Number of Classes Use between 5 and 20 classes. Use between 5 and 20 classes. Data sets with a larger number of elements Data sets with a larger number of elements usually require a larger number of classes. usually require a larger number of classes. Smaller data sets usually require fewer classes Smaller data sets usually require fewer classes

12. Frequency Distribution n Guidelines for Selecting Width of Classes Use classes of equal width. Use classes of equal width. Approximate Class Width = Approximate Class Width =

13. Frequency Distribution For Hudson Auto Repair, if we choose six classes: 50-59 50-59 60-69 60-69 70-79 70-79 80-89 80-89 90-99 90-99 100-109 100-109 2 2 13 13 16 16 7 7 5 5 Total 50 Parts Cost ($) Frequency Approximate Class Width = (109 - 52)/6 = 9.5  10

14. Relative Frequency Distribution 50-59 50-59 60-69 60-69 70-79 70-79 80-89 80-89 90-99 90-99 100-109 100-109 Parts Cost ($).04.04.26.26.32.32.14.14.10.10 Total 1.00 Relative RelativeFrequency 2/50

15. Cumulative Distributions n Hudson Auto Repair 50 - 59 50 - 59 60 - 69 60 - 69 70 - 79 70 - 79 80 - 89 80 - 89 90 - 99 90 - 99 100 - 109 Cost ($) Cumulative CumulativeFrequency RelativeFrequency CumulativePercent Frequency Frequency 2 2 15 15 31 31 38 38 45 45 50 50.04.04.30.30.62.62.76.76.90.90 1.00 1.00 4 4 30 30 62 62 76 76 90 90 100 100 2 + 13 15/50.30(100) Frequency 2 2 13 13 16 16 7 7 5

16. Histogram 2 2 4 4 6 6 8 8 10 12 14 16 18 Parts Cost ($) Parts Cost ($) Frequency 50  59 60  69 70  79 80  89 90  99 100-110 Tune-up Parts Cost

17. n Symmetric Left tail is the mirror image of the right tail Left tail is the mirror image of the right tail Examples: heights and weights of people Examples: heights and weights of people Histogram Relative Frequency.05.10.15.20.25.30.35 0 0

18. Histogram n Moderately Skewed Left A longer tail to the left A longer tail to the left Example: exam scores Example: exam scores Relative Frequency.05.10.15.20.25.30.35 0 0

19. n Moderately Right Skewed A Longer tail to the right A Longer tail to the right Example: housing values Example: housing values Histogram Relative Frequency.05.10.15.20.25.30.35 0 0

20. Histogram n Highly Skewed Right A very long tail to the right A very long tail to the right Example: executive salaries Example: executive salaries Relative Frequency.05.10.15.20.25.30.35 0 0

21. Scatter Diagram n A Positive Relationship x y

22. Scatter Diagram n A Negative Relationship x y

23. Scatter Diagram n No Apparent Relationship x y

24. Example: Panthers Football Team n Scatter Diagram The Panthers football team is interested The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored. 13213 1424181730 x = Number of Interceptions y = Number of Points Scored Points Scored

25. Scatter Diagram y x Number of Interceptions Number of Points Scored 5 10 15 20 25 30 035 12304

26. Tabular and Graphical Procedures Qualitative Data Quantitative Data Tabular TabularMethods Methods Methods MethodsGraphical Methods MethodsGraphical Graphical Graphical FrequencyFrequency Distribution Distribution Rel. Freq. Dist.Rel. Freq. Dist. Cumulative Freq.Cumulative Freq. Distribution Distribution Cumulative Rel. Freq.Cumulative Rel. Freq. Distribution Distribution Bar GraphBar Graph Pie ChartPie Chart FrequencyFrequency Distribution Distribution Rel. Freq. Dist.Rel. Freq. Dist. Cum. Freq. Dist.Cum. Freq. Dist. Cum. Rel. Freq.Cum. Rel. Freq. Distribution Distribution HistogramHistogram ScatterScatter Diagram Diagram DataData