1. 1 1 Slide © 2006 Thomson/South-Western Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations Part A n Summarizing Qualitative Data n Summarizing Quantitative Data

2. 2 2 Slide © 2006 Thomson/South-Western Summarizing Qualitative Data n Frequency Distribution n Relative Frequency Distribution n Percent Frequency Distribution n Bar Graph n Pie Chart

3. 3 3 Slide © 2006 Thomson/South-Western A frequency distribution is a tabular summary of A frequency distribution is a tabular summary of data showing the frequency (or number) of items data showing the frequency (or number) of items in each of several nonoverlapping classes. in each of several nonoverlapping classes. A frequency distribution is a tabular summary of A frequency distribution is a tabular summary of data showing the frequency (or number) of items data showing the frequency (or number) of items in each of several nonoverlapping classes. in each of several nonoverlapping classes. The objective is to provide insights about the data The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data. The objective is to provide insights about the data The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data. Frequency Distribution

4. 4 4 Slide © 2006 Thomson/South-Western 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

5. 5 5 Slide © 2006 Thomson/South-Western Frequency Distribution Poor Below Average Average Above Average Excellent 2 3 5 9 1 1 Total 20 RatingFrequency

6. 6 6 Slide © 2006 Thomson/South-Western 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 15 15 25 25 45 45 5 5 100 100 Relative RelativeFrequency Percent PercentFrequency Rating.10(100) = 10 1/20 =.05

7. 7 7 Slide © 2006 Thomson/South-Western 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

8. 8 8 Slide © 2006 Thomson/South-Western 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

9. 9 9 Slide © 2006 Thomson/South-Western n Insights Gained from the Preceding Pie Chart Example: Marada Inn One-half of the customers surveyed gave Marada One-half of the customers surveyed gave Marada a quality rating of “above average” or “excellent” a quality rating of “above average” or “excellent” (looking at the left side of the pie). This might (looking at the left side of the pie). This might please the manager. please the manager. For each customer who gave an “excellent” rating, For each customer who gave an “excellent” rating, there were two customers who gave a “poor” there were two customers who gave a “poor” rating (looking at the top of the pie). This should rating (looking at the top of the pie). This should displease the manager. displease the manager.

10. 10 Slide © 2006 Thomson/South-Western Summarizing Quantitative Data n Frequency Distribution n Relative Frequency and Percent Frequency Distributions n Dot Plot n Histogram n Cumulative Distributions n Ogive

11. 11 Slide © 2006 Thomson/South-Western 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.

12. 12 Slide © 2006 Thomson/South-Western Example: Hudson Auto Repair n Sample of Parts Cost for 50 Tune-ups

13. 13 Slide © 2006 Thomson/South-Western 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

14. 14 Slide © 2006 Thomson/South-Western 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 =

15. 15 Slide © 2006 Thomson/South-Western 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

16. 16 Slide © 2006 Thomson/South-Western Relative Frequency and Percent Frequency Distributions 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 4 26 26 32 32 14 14 10 10 100 100 Percent Frequency Frequency 2/50.04(100)

17. 17 Slide © 2006 Thomson/South-Western Only 4% of the parts costs are in the $50-59 class. Only 4% of the parts costs are in the $50-59 class. The greatest percentage (32% or almost one-third) The greatest percentage (32% or almost one-third) of the parts costs are in the $70-79 class. of the parts costs are in the $70-79 class. 30% of the parts costs are under $70. 30% of the parts costs are under $70. 10% of the parts costs are $100 or more. 10% of the parts costs are $100 or more. n Insights Gained from the Percent Frequency Distribution Relative Frequency and Percent Frequency Distributions

18. 18 Slide © 2006 Thomson/South-Western Dot Plot n One of the simplest graphical summaries of data is a dot plot. n A horizontal axis shows the range of data values. n Then each data value is represented by a dot placed above the axis.

19. 19 Slide © 2006 Thomson/South-Western 5060708090100110 50 60 70 80 90 100 110 Cost ($) Dot Plot Tune-up Parts Cost

20. 20 Slide © 2006 Thomson/South-Western 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

21. 21 Slide © 2006 Thomson/South-Western 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

22. 22 Slide © 2006 Thomson/South-Western 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

23. 23 Slide © 2006 Thomson/South-Western 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

24. 24 Slide © 2006 Thomson/South-Western 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

25. 25 Slide © 2006 Thomson/South-Western Cumulative frequency distribution  shows the Cumulative frequency distribution  shows the number of items with values less than or equal to number of items with values less than or equal to the upper limit of each class.. the upper limit of each class.. Cumulative frequency distribution  shows the Cumulative frequency distribution  shows the number of items with values less than or equal to number of items with values less than or equal to the upper limit of each class.. the upper limit of each class.. Cumulative Distributions Cumulative percent distribution – shows Cumulative percent distribution – shows the percentage of items with values less than or the percentage of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative percent distribution – shows Cumulative percent distribution – shows the percentage of items with values less than or the percentage of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class.

26. 26 Slide © 2006 Thomson/South-Western Cumulative Distributions n Hudson Auto Repair < 59 < 59 < 69 < 69 < 79 < 79 < 89 < 89 < 99 < 99 < 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)

27. 27 Slide © 2006 Thomson/South-Western Ogive n An ogive is a graph of a cumulative distribution. n The data values are shown on the horizontal axis. n Shown on the vertical axis are the: cumulative frequencies, or cumulative frequencies, or cumulative relative frequencies, or cumulative relative frequencies, or cumulative percent frequencies cumulative percent frequencies n The frequency (one of the above) of each class is plotted as a point. Use the midpoint of the class. n The plotted points are connected by straight lines.

28. 28 Slide © 2006 Thomson/South-Western Parts Parts Cost ($) Parts Parts Cost ($) 20 40 60 80 100 Cumulative Percent Frequency 50 60 70 80 90 100 110 (89.5, 76) Ogive with Cumulative Percent Frequencies Cumulative Percent Frequencies Tune-up Parts Cost