1. Chapter 8 Descriptive Statistics

2. Dot Plots Dot plot:Dot plot: Horizontal axis represents the data values. Horizontal axis represents the data values. Vertical axis represents the frequency of the data values. Vertical axis represents the frequency of the data values. One dot is for each occurrence of each data value. One dot is for each occurrence of each data value.

3. Example 1 Here’s a dot plot for the test scores: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 89, 93, 95, 96.Here’s a dot plot for the test scores: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 89, 93, 95, 96.

4. Stem-and-Leaf Plot Stem-and-leaf plot:Stem-and-leaf plot: The digit furthest to the right is the leaf. The digit furthest to the right is the leaf. The other digits are called the stem. The other digits are called the stem. The stems and leaves are put in vertical columns, with the leaves in numerical order. The stems and leaves are put in vertical columns, with the leaves in numerical order.

5. Example 2 Here’s a stem- and-leaf plot for test scores: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 89, 93, 95, 96.Here’s a stem- and-leaf plot for test scores: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 89, 93, 95, 96.

6. Example 2, cont’d Notice:Notice: A cluster of values between 54 and 96. A cluster of values between 54 and 96. A gap between 54 and 32. A gap between 54 and 32. 32 and 26 are outliers, separated from the other scores by a large gap. 32 and 26 are outliers, separated from the other scores by a large gap.

7. Example 3 Make a stem-and-leaf plot for pizza prices: $9.20, $10.50, $10.70, $10.80, $12.00, $12.10, $12.20, $12.20, $12.30.Make a stem-and-leaf plot for pizza prices: $9.20, $10.50, $10.70, $10.80, $12.00, $12.10, $12.20, $12.20, $12.30. The dollar amounts will be the stems and the cents will be the leaves.The dollar amounts will be the stems and the cents will be the leaves.

8. Example 3, cont’d Any Clusters? Gaps?Outliers?

9. Bar Graphs Bar graph: any graph in which the height or length of bars is used to represent quantities.Bar graph: any graph in which the height or length of bars is used to represent quantities. A histogram is a special type of bar graph. A histogram is a special type of bar graph.

10. Example 4 Create a bar graph to display the data in the table.Create a bar graph to display the data in the table.

11. Example 4, cont’d

12. Histograms Histogram:Histogram: Data is separated into intervals called measurement classes or bins. Data is separated into intervals called measurement classes or bins. Interval sizes are chosen depending on the situation.Interval sizes are chosen depending on the situation. Frequency table: shows the number of data values in each bin.Frequency table: shows the number of data values in each bin.

13. Example 5 Make a histogram for test scores: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 89, 93, 95, 96.Make a histogram for test scores: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 89, 93, 95, 96. A frequency table, with bins of 10, is already made.A frequency table, with bins of 10, is already made.

14. Example 5, cont’d The height of each bar is equal to the frequency of the bin.The height of each bar is equal to the frequency of the bin.

15. Example 5, cont’d The choice of bin size affects the appearance of the graph.The choice of bin size affects the appearance of the graph. The same data set with a bin size of 5 is shown. The same data set with a bin size of 5 is shown.

16. Example 5, cont’d The same data set with a bin size of 20 is shown. The same data set with a bin size of 20 is shown.

17. Question: Why is the histogram with bin size 10 the best choice to represent this data?

18. Relative Frequency Histograms Relative frequency histogram:Relative frequency histogram: Relative Frequency (percent of the whole data set) of each bin is calculated. Relative Frequency (percent of the whole data set) of each bin is calculated. The height of each bar equals the relative frequency of the bin. The height of each bar equals the relative frequency of the bin. Relative Frequency Table: can help draw a relative frequency histogram.Relative Frequency Table: can help draw a relative frequency histogram.

19. Example 6 Make a relative frequency histogram for test scores: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 89, 93, 95, 96,Make a relative frequency histogram for test scores: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 89, 93, 95, 96, Use a bin size of 10.Use a bin size of 10.

20. Example 6, cont’d The graph is shown below:The graph is shown below:

21. Line Graphs Line graph: graphs data over timeLine graph: graphs data over time Horizontal axis represents the time. Horizontal axis represents the time. Vertical axis represents the data value. Vertical axis represents the data value. Each data value is plotted and the dots are connected by a line. Each data value is plotted and the dots are connected by a line.

22. Example 7 Create a line graph for the data shown in the bar graph below.Create a line graph for the data shown in the bar graph below.

23. Example 7, cont’d Solution:Solution:

24. Pie Charts Pie chart: graphs proportions of quantities.Pie chart: graphs proportions of quantities. Also called a circle graph. Also called a circle graph. Each quantity is a wedge-shaped part of the circle. Each quantity is a wedge-shaped part of the circle.

25. Example 8 This pie chart shows the average number of hours of sleep adults get.This pie chart shows the average number of hours of sleep adults get. Interpret the chart.Interpret the chart.

26. Choosing a Graph Different types of graphs and their uses.Different types of graphs and their uses. Pg. 487

27. Example 10 The table has the average number of hours worked in different countries.The table has the average number of hours worked in different countries. What type of graph would be best?What type of graph would be best?

28. Double-Stem-and-Leaf Plots Double-Stem-and-Leaf Plot:Double-Stem-and-Leaf Plot: The stems are placed in the middle column. The stems are placed in the middle column. The leaves of one data set are placed on the left, and the leaves of the other set on the right. The leaves of one data set are placed on the left, and the leaves of the other set on the right.

29. Example 1 Make a double-stem-and-leaf plot to compare scores from two classes.Make a double-stem-and-leaf plot to compare scores from two classes. Class 1: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 93, 95, 96 Class 1: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 93, 95, 96 Class 2: 34, 45, 52, 57, 63, 65, 68, 70, 71, 72, 74, 76, 76, 78, 83, 85, 85, 87, 92, 99 Class 2: 34, 45, 52, 57, 63, 65, 68, 70, 71, 72, 74, 76, 76, 78, 83, 85, 85, 87, 92, 99

30. Example 1, cont’d Since more leaves are at the top on the left than on the right, Class 1 did better on the test than Class 2.Since more leaves are at the top on the left than on the right, Class 1 did better on the test than Class 2.

31. Comparison Histogram Comparison Histogram :Comparison Histogram : Bin size is the same for both sets. Bin size is the same for both sets. Bars for both sets are placed side-by-side at each interval. Bars for both sets are placed side-by-side at each interval.

32. Example 2 Make a comparison histogram to compare scores from two classes.Make a comparison histogram to compare scores from two classes. Class 1: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 93, 95, 96 Class 1: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 93, 95, 96 Class 2: 34, 45, 52, 57, 63, 65, 68, 70, 71, 72, 74, 76, 76, 78, 83, 85, 85, 87, 92, 99 Class 2: 34, 45, 52, 57, 63, 65, 68, 70, 71, 72, 74, 76, 76, 78, 83, 85, 85, 87, 92, 99

33. Example 2, cont’d Solution: A bin size of 10 was used.Solution: A bin size of 10 was used.

34. Comparison Bar Graphs Comparison Bar Graph :Comparison Bar Graph : Used to represent frequencies, relative frequencies, and trends over time. Used to represent frequencies, relative frequencies, and trends over time. Also called a Double Bar Graph. Also called a Double Bar Graph.

35. Example 3 Make a comparison bar graph for the data.Make a comparison bar graph for the data.

36. Example 3, cont’d

37. Example 4 This comparison bar graph shows that most kids in all age groups use computers, and that older children use the Internet more than younger children.This comparison bar graph shows that most kids in all age groups use computers, and that older children use the Internet more than younger children.

38. Multiple Line Graphs Multiple Line Graph :Multiple Line Graph : Used to show trends over time. Used to show trends over time.

39. Example 5 The double line graph shows the gap between men’s and women’s pay has decreased over the years.The double line graph shows the gap between men’s and women’s pay has decreased over the years.

40. Example 6 Make a double line graph to compare scores from two classes.Make a double line graph to compare scores from two classes. Class 1: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 93, 95, 96 Class 1: 26, 32, 54, 62, 67, 70, 71, 71, 74, 76, 80, 81, 84, 87, 87, 87, 93, 95, 96 Class 2: 34, 45, 52, 57, 63, 65, 68, 70, 71, 72, 74, 76, 76, 78, 83, 85, 85, 87, 92, 99 Class 2: 34, 45, 52, 57, 63, 65, 68, 70, 71, 72, 74, 76, 76, 78, 83, 85, 85, 87, 92, 99

41. Example 6, cont’d

42. Multiple Pie Charts Multiple Pie Charts :Multiple Pie Charts : Are used to show portions of a whole. Are used to show portions of a whole.

43. Example 7 Use multiple pie charts to compare the population over time.Use multiple pie charts to compare the population over time.

44. Example 7, cont’d A pie chart is created for each year.A pie chart is created for each year.

45. Question: Which year had the smallest percentage of children under the age of 15?

46. Proportional Bar Graphs Proportional Bar Graphs: show relative amounts and trends.Proportional Bar Graphs: show relative amounts and trends. All the bars are the same height. All the bars are the same height. Each bar totals to 100% of a whole. Each bar totals to 100% of a whole. Each bar is divided into pieces to represent the portions of the different categories. Each bar is divided into pieces to represent the portions of the different categories.

47. Example 8 This proportional bar graph shows how the U.S. population has been distributed over time.This proportional bar graph shows how the U.S. population has been distributed over time.

48. Example 9 What type of graph should be used to make the comparison between the two years in the following table?What type of graph should be used to make the comparison between the two years in the following table?

49. Example 9, cont’d

50. A double bar graph is one optionA double bar graph is one option

51. Homework Pg. 489 Pg. 489 5, 13, 16, 30, 36(a and b), 44 5, 13, 16, 30, 36(a and b), 44 Pg. 512 Pg. 512 2, 8, 18, 26, 28, 37 2, 8, 18, 26, 28, 37