1. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data STATISTICS The study of the collection, analysis, interpretation, presentation and organization of data.

2. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data STATISTICS The study of the collection, analysis, interpretation, presentation and organization of data. DATA Data is a set a values of quantitative or qualitative variables. For purposes of what we will study here, let’s just think of data as a set of numerical information.

3. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data We will begin by looking at ways to organize data.

4. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V We will begin by looking at ways to organize data.

5. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Often information that we need to analyze is not easy to deal with in its raw form. We will begin by looking at ways to organize data.

6. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Often information that we need to analyze is not easy to deal with in its raw form. One way of organizing discrete data into a more useful format is a FREQUENCY TABLE We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V

7. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Often information that we need to analyze is not easy to deal with in its raw form. One way of organizing discrete data into a more useful format is a FREQUENCY TABLE Let’s use construct a frequency table for the data above. We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V

8. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V A frequency table organizes the data by counting the number of occurrences (the frequency) of each possible outcome. EVALUATIONFREQUENCY

9. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V A frequency table organizes the data by counting the number of occurrences (the frequency) of each possible outcome. There are 4 ‘Excellent’

10. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V A frequency table organizes the data by counting the number of occurrences (the frequency) of each possible outcome. There are 7 ‘Above Average’

11. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V A frequency table organizes the data by counting the number of occurrences (the frequency) of each possible outcome. There are 8 ‘Average’

12. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V A frequency table organizes the data by counting the number of occurrences (the frequency) of each possible outcome. There are 4 ‘Below Average’

13. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V A frequency table organizes the data by counting the number of occurrences (the frequency) of each possible outcome. There are 2 ‘Poor’

14. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V A frequency table organizes the data by counting the number of occurrences (the frequency) of each possible outcome. There are 25 in all

15. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V This is the frequency table for the data above.

16. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V If we take a frequency table

17. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table.

18. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V EVALUATIONPROBABILITY E A V B P TOTAL If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table.

19. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V EVALUATIONPROBABILITY E A V B P TOTAL If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table.

20. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V EVALUATIONPROBABILITY E A V B P TOTAL If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table.

21. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V EVALUATIONPROBABILITY E A V B P TOTAL If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table.

22. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V EVALUATIONPROBABILITY E A V B P TOTAL If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table.

23. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V EVALUATIONPROBABILITY E A V B P TOTAL1 If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table.

24. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V EVALUATIONRELATIVE FREQUENCY E A V B P TOTAL1 If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table. Often the ‘Probability’ column will be labeled ‘Relative Frequency’.

25. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 We will begin by looking at ways to organize data. 25 viewers evaluated the latest episode of CSI. The possible evaluations are (E)xcellent, (A)bove average, a(V)erage, (B)elow average, (P)oor After the show, the 25 evaluations were as follows: A V V B P E A E V V A E P B V V A A A E B V A B V EVALUATIONRELATIVE FREQUENCY E A V B P TOTAL1 If we take a frequency table …and replace counts with probabilities, we get a RELATIVE FREQUENCY table.

26. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data.

27. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data.

28. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a frequency table using equal sized intervals starting ’50-54’. 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data.

29. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY

30. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 54

31. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 54

32. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542

33. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542 55 - 59

34. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542 55 - 594

35. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542 55 - 594 60 - 64

36. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542 55 - 594 60 - 646

37. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542 55 - 594 60 - 646 65 - 69

38. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542 55 - 594 60 - 646 65 - 698

39. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542 55 - 594 60 - 646 65 - 698

40. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESFREQUENCY 50 - 542 55 - 594 60 - 646 65 - 698 TOTAL20

41. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESRELATIVE FREQUENCY 50 - 542 55 - 594 60 - 646 65 - 698 TOTAL20 If you want a relative frequency table instead, just divide each frequency by 20.

42. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESRELATIVE FREQUENCY 50 - 542/20 55 - 594/20 60 - 646/20 65 - 698/20 TOTAL20 If you want a relative frequency table instead, just divide each frequency by 20.

43. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESRELATIVE FREQUENCY 50 - 542/20 55 - 594/20 60 - 646/20 65 - 698/20 TOTAL20 If you want a relative frequency table instead, just divide each frequency by 20.

44. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data 20 health care workers take an assessment with these scores: 62536768615166 6461 59585664676857656960 Sometimes there are so many different outcomes that a frequency or relative frequency table is not useful without grouping the data. Let’s construct a frequency table using equal sized intervals starting ’50-54’. SCORESRELATIVE FREQUENCY 50 - 541/10 55 - 591/5 60 - 643/10 65 - 692/5 TOTAL20 If you want a relative frequency table instead, just divide each frequency by 20.

45. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH.

46. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH.

47. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 Let’s put the frequencies on the vertical axis. FREQUENCY

48. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 …and the outcomes on the horizontal axis. FREQUENCY E A V B P

49. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 Finally, let the height of each bar represent the corresponding frequency. FREQUENCY E A V B P

50. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 Finally, let the height of each bar represent the corresponding frequency. FREQUENCY E A V B P

51. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 Finally, let the height of each bar represent the corresponding frequency. FREQUENCY E A V B P

52. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 Finally, let the height of each bar represent the corresponding frequency. FREQUENCY E A V B P

53. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 Finally, let the height of each bar represent the corresponding frequency. FREQUENCY E A V B P

54. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 Finally, let the height of each bar represent the corresponding frequency. FREQUENCY E A V B P

55. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If we prefer, we can turn a frequency or relative frequency table into a BAR GRAPH. EVALUATIONFREQUENCY E 4 A7 V8 B4 P2 TOTAL25 Let’s turn the frequency table we constructed earlier into a BAR GRAPH. 2 4 6 8 10 FREQUENCY E A V B P

56. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If the data from a frequency or relative frequency table is continuous rather than discrete, we construct the ‘bars’ with no space between them and call the resulting graph a histogram instead of a bar graph.

57. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If the data from a frequency or relative frequency table is continuous rather than discrete, we construct the ‘bars’ with no space between them and call the resulting graph a histogram instead of a bar graph. We will not be focusing on the difference between discrete and continuous here. If you simply think of ‘discrete values’ as values that are completely distinct from each other and ‘continuous values’ as values that can sort of bleed over into each other, you will be OK for what we will be doing.

58. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If the data from a frequency or relative frequency table is continuous rather than discrete, we construct the ‘bars’ with no space between them and call the resulting graph a histogram instead of a bar graph. We will not be focusing on the difference between discrete and continuous here. If you simply think of ‘discrete values’ as values that are completely distinct from each other and ‘continuous values’ as values that can sort of bleed over into each other, you will be OK for what we will be doing. A quick example to help with this distinction: If you are counting things, the counts are discrete. There is no doubt that 2 is different than 3.

59. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If the data from a frequency or relative frequency table is continuous rather than discrete, we construct the ‘bars’ with no space between them and call the resulting graph a histogram instead of a bar graph. We will not be focusing on the difference between discrete and continuous here. If you simply think of ‘discrete values’ as values that are completely distinct from each other and ‘continuous values’ as values that can sort of bleed over into each other, you will be OK for what we will be doing. A quick example to help with this distinction: If you are counting things, the counts are discrete. There is no doubt that 2 is different than 3. But if you are measuring a person’s height, one person might measure and get 59.99 inches while another person might measure the same person and get 60.01 inches. (In this sense, the values sort of bleed into each other.)

60. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data If the data from a frequency or relative frequency table is continuous rather than discrete, we construct the ‘bars’ with no space between them and call the resulting graph a histogram instead of a bar graph. We will not be focusing on the difference between discrete and continuous here. If you simply think of ‘discrete values’ as values that are completely distinct from each other and ‘continuous values’ as values that can sort of bleed over into each other, you will be OK for what we will be doing. A quick example to help with this distinction: If you are counting things, the counts are discrete. There is no doubt that 2 is different than 3. But if you are measuring a person’s height, one person might measure and get 59.99 inches while another person might measure the same person and get 60.01 inches. (In this sense, the values sort of bleed into each other.) Don’t worry if this distinction is not perfectly clear to you. It really will not have much if any impact on what we are doing here.

61. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a histogram from the frequency table below. Pounds lostFrequency 0 to 1014 10+ to 2023 20+ to 3017 30+ to 4011 Total65

62. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a histogram from the frequency table below. Pounds lostFrequency 0 to 1014 10+ to 2023 20+ to 3017 30+ to 4011 Total65 5 10 15 20 25 FREQUENCY

63. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a histogram from the frequency table below. Pounds lostFrequency 0 to 1014 10+ to 2023 20+ to 3017 30+ to 4011 Total65 5 10 15 20 25 FREQUENCY 0 to 1010+ to 20 Pounds Lost 20+ to 30 30+ to 40

64. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a histogram from the frequency table below. Pounds lostFrequency 0 to 1014 10+ to 2023 20+ to 3017 30+ to 4011 Total65 5 10 15 20 25 FREQUENCY 0 to 1010+ to 20 Pounds Lost 20+ to 30 30+ to 40

65. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a histogram from the frequency table below. Pounds lostFrequency 0 to 1014 10+ to 2023 20+ to 3017 30+ to 4011 Total65 5 10 15 20 25 FREQUENCY 0 to 1010+ to 20 Pounds Lost 20+ to 30 30+ to 40

66. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a histogram from the frequency table below. Pounds lostFrequency 0 to 1014 10+ to 2023 20+ to 3017 30+ to 4011 Total65 5 10 15 20 25 FREQUENCY 0 to 1010+ to 20 Pounds Lost 20+ to 30 30+ to 40

67. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a histogram from the frequency table below. Pounds lostFrequency 0 to 1014 10+ to 2023 20+ to 3017 30+ to 4011 Total65 5 10 15 20 25 FREQUENCY 0 to 1010+ to 20 Pounds Lost 20+ to 30 30+ to 40

68. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data Let’s construct a histogram from the frequency table below. Pounds lostFrequency 0 to 1014 10+ to 2023 20+ to 3017 30+ to 4011 Total65 5 10 15 20 25 FREQUENCY 0 to 1010+ to 20 Pounds Lost 20+ to 30 30+ to 40

69. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data A Stem-and-Leaf plot is another visual way to display data.

70. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data A Stem-and-Leaf plot is another visual way to display data. In constructing a stem-and-leaf display, we view each number as having two parts. The left digit is considered the stem and the right digit the leaf. This is probably best illustrated through an example.

71. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display.

72. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. The left (BLUE) digit is considered the stem

73. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem

74. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem 1975–1989

75. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem 1975–1989 Among the left (blue) digits, there are only threes, fours and fives.

76. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem 1975–1989 Among the left (blue) digits, there are only threes, fours and fives. For the leaves, write down each rightmost (red) digit in numerical order next to the stem that it belongs to.

77. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem 1975–1989

78. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem 1975–1989 1993–2007

79. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem 1975–1989 1993–2007 Among the left (blue) digits, there are only fours, fives, sixes and sevens.

80. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem 1975–1989 1993–2007 Among the left (blue) digits, there are only fours, fives, sixes and sevens. For the leaves, write down each rightmost (red) digit in numerical order next to the stem that it belongs to.

81. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. 1975–1989 1993–2007

82. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data These are the number of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 1993 to 2007. 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 1993–2007: 46, 43, 40, 47, 49, 70, 65, 50, 73, 49, 47, 48, 51, 58, 50 Compare these home run records using a stem-and-leaf display. and the right (RED) digit is considered the leaf. The left (BLUE) digit is considered the stem 1975–1989 1993–2007 We can compare these data by placing the two displays side by side. Some people call this a Back-to-back Stem-and-Leaf plot.

83. MATH 110 Sec 14-1 Lecture: Statistics-Organizing and Visualizing Data In summary, these are the data organization and display methods discussed FREQUENCY TABLE BAR GRAPH RELATIVE FREQUENCY TABLE HISTOGRAM STEM-AND-LEAF PLOT/DISPLAY