1 1 Slide © 2005 Thomson/South-Western Introduction to Statistics Chapter 2 Descriptive Statistics

2 2 Slide © 2005 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University Slides Prepared by JOHN S. LOUCKS St. Edward’s University

3 3 Slide © 2005 Thomson/South-Western Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations Part A n Summarizing Qualitative Data n Summarizing Quantitative Data

4 4 Slide © 2005 Thomson/South-Western Summarizing Qualitative Data n Frequency Distribution n Relative Frequency Distribution n Percent Frequency Distribution n Bar Graph n Pie Chart

5 5 Slide © 2005 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 non-overlapping classes. in each of several non-overlapping 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 non-overlapping classes. in each of several non-overlapping 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

6 6 Slide © 2005 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

7 7 Slide © 2005 Thomson/South-Western Frequency Distribution Poor Below Average Average Above Average Excellent Total 20 RatingFrequency

8 8 Slide © 2005 Thomson/South-Western The relative frequency of a class is the fraction The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class. belonging to the class. The relative frequency of a class is the fraction The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class. belonging to the class. A relative frequency distribution is a tabular A relative frequency distribution is a tabular summary of a set of data showing the relative summary of a set of data showing the relative frequency for each class. frequency for each class. A relative frequency distribution is a tabular A relative frequency distribution is a tabular summary of a set of data showing the relative summary of a set of data showing the relative frequency for each class. frequency for each class. Relative Frequency Distribution

9 9 Slide © 2005 Thomson/South-Western Percent Frequency Distribution The percent frequency of a class is the relative The percent frequency of a class is the relative frequency multiplied by 100. frequency multiplied by 100. The percent frequency of a class is the relative The percent frequency of a class is the relative frequency multiplied by 100. frequency multiplied by 100. A percent frequency distribution is a tabular A percent frequency distribution is a tabular summary of a set of data showing the percent summary of a set of data showing the percent frequency for each class. frequency for each class. A percent frequency distribution is a tabular A percent frequency distribution is a tabular summary of a set of data showing the percent summary of a set of data showing the percent frequency for each class. frequency for each class.

10 Slide © 2005 Thomson/South-Western Relative Frequency and Percent Frequency Distributions Poor Below Average Average Above Average Excellent Total Relative RelativeFrequency Percent PercentFrequency Rating.10(100) = 10 1/20 =.05 Frequency

11 Slide © 2005 Thomson/South-Western Bar Graph A bar graph is a graphical device for depicting A bar graph is a graphical device for depicting qualitative data. qualitative data. On one axis (usually the horizontal axis), we specify On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes. the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the scale can be used for the other axis (usually the vertical axis). vertical axis). Using a bar of fixed width drawn above each class Using a bar of fixed width drawn above each class label, we extend the height appropriately. label, we extend the height appropriately. The bars are separated to emphasize the fact that each The bars are separated to emphasize the fact that each class is a separate category. class is a separate category.

12 Slide © 2005 Thomson/South-Western Poor Below Average Below Average Above Average Above Average Excellent Frequency Rating Bar Graph Marada Inn Quality Ratings

13 Slide © 2005 Thomson/South-Western Pie Chart The pie chart is a commonly used graphical device The pie chart is a commonly used graphical device for presenting relative frequency distributions for for presenting relative frequency distributions for qualitative data. qualitative data. n First draw a circle; then use the relative frequencies to subdivide the circle frequencies to subdivide the circle into sectors that correspond to the into sectors that correspond to the relative frequency for each class. relative frequency for each class. n Since there are 360 degrees in a circle, a class with a relative frequency of.25 would a class with a relative frequency of.25 would consume.25(360) = 90 degrees of the circle. consume.25(360) = 90 degrees of the circle.

14 Slide © 2005 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

15 Slide © 2005 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.

16 Slide © 2005 Thomson/South-Western In Class Group Exercise NameFrequency Brown7 Davis6 Johnson10 Jones7 Smith12 Williams8 50 The Following are the voices gained by each representative of one class in a school

17 Slide © 2005 Thomson/South-Western 5 a NameFrequency Relative Frequency Percent Frequency Brown7.1414% Davis6.1212% Johnson % Jones7.1414% Smith % Williams8.1616% %

18 Slide © 2005 Thomson/South-Western 5 b

19 Slide © 2005 Thomson/South-Western 5c %Degrees Brown Davis Johnson Jones Smith Williams

20 Slide © 2005 Thomson/South-Western 5 d Most common: Smith, Johnson and Williams