Central spread symmetry 2.0

1. Central Tendency Spread Symmetry Central Tendency, Spread, or Distribution Shape? Tells you about where the data are clustering or centering. Look for words like, average, mean, median, most common, center point etc. Tells you about how spread out the data are from one another. Look for words like spread, difference, deviation, range, variation, etc. Tells you about the shape of the distribution. Look for words like shape or expressions like • Most of the data in the center. • A few data points to the left or right. • All data evenly distributed. • Shape of the distribution is very peaked. Note – to review what a distribution is go to slide X and then return to this slide.

2. Let’s Practice

3. Problem #1 Question: What is the average number of cyberbullying incidents among freshmen, sophomores, juniors, and seniors?

4. Problem #1 Question: What is the average number of cyberbullying incidents among freshmen, sophomores, juniors, and seniors? Instructions: Which type of description of the distribution (below) is most relevant to the question (above)? Central Tendency Spread Symmetry

5. Problem #1 Question: What is the average number of cyberbullying incidents among freshmen, sophomores, juniors, and seniors? Central Tendency Spread Symmetry

6. Problem #1 Question: What is the average number of cyberbullying incidents among freshmen, sophomores, juniors, and seniors? Central Tendency Spread Symmetry Tells you about where the data are clustering or centering. Look for words like, average, mean, median, most common, center point etc.

7. Problem #1 Question: What is the average number of cyberbullying incidents among freshmen, sophomores, juniors, and seniors? Central Tendency Spread Symmetry Tells you about where the data are clustering or centering. Look for words like, average, mean, median, most common, center point etc.

8. Problem #2 Question: What is the difference between the lowest and highest score on a survey designed to test the impact of a new therapy?

9. Problem #2 Question: What is the difference between the lowest and highest score on a survey designed to test the impact of a new therapy? Instructions: Which type of description of the distribution (below) is most relevant to the question (above)? Central Tendency Spread Symmetry

10. Problem #2 Question: What is the difference between the lowest and highest score on a survey designed to test the impact of a new therapy? Central Tendency Spread Symmetry

11. Problem #2 Question: What is the difference between the lowest and highest score on a survey designed to test the impact of a new therapy? Central Tendency Spread Symmetry Tells you about how spread out the data are from one another. Look for words like spread, difference, deviation, range, variation, etc.

12. Problem #2 Question: What is the difference between the lowest and highest score on a survey designed to test the impact of a new therapy? Central Tendency Spread Symmetry Tells you about how spread out the data are from one another. Look for words like spread, difference, deviation, range, variation, etc.

13. Problem #3 Question: The director of a health clinic has asked you to help her analyze data from the results of patient systolic blood pressure readings. You decide to compute the mean systolic pressure to see where the patient results cluster.

14. Problem #3 Question: The director of a health clinic has asked you to help her analyze data from the results of patient systolic blood pressure readings. You decide to compute the mean systolic pressure to see where the patient results cluster. Instructions: Which type of description of the distribution (below) is most relevant to the question (above)? Central Tendency Spread Symmetry

15. Problem #3 Question: The director of a health clinic has asked you to help her analyze data from the results of patient systolic blood pressure readings. You decide to compute the mean systolic pressure to see where the patient results cluster. Central Tendency Spread Symmetry

16. Problem #3 Question: The director of a health clinic has asked you to help her analyze data from the results of patient systolic blood pressure readings. You decide to compute the mean systolic pressure to see where the patient results cluster. Central Tendency Spread Symmetry Tells you about where the data are clustering or centering. Look for words like, average, mean, median, most common, center point etc.

17. Problem #3 Question: The director of a health clinic has asked you to help her analyze data from the results of patient systolic blood pressure readings. You decide to compute the mean systolic pressure to see where the patient results cluster. Central Tendency Spread Symmetry Tells you about where the data are clustering or centering. Look for words like, average, mean, median, most common, center point etc.

18. Problem #4 Question: An entrance exam for mechanical engineers is very difficult. If it is very difficult you would expect most of the scores to bunched up on the lower end of the score distribution with a few high scores. What is the shape of this distribution?

19. Problem #4 Question: An entrance exam for mechanical engineers is very difficult. If it is very difficult you would expect most of the scores to bunched up on the lower end of the score distribution with a few high scores. What is the shape of this distribution? Instructions: Which type of description of the distribution (below) is most relevant to the question (above)? Central Tendency Spread Symmetry

20. Problem #4 Question: An entrance exam for mechanical engineers is very difficult. If it is very difficult you would expect most of the scores to bunched up on the lower end of the score distribution with a few high scores. What is the shape of this distribution? Central Tendency Spread Symmetry

21. Problem #4 Question: An entrance exam for mechanical engineers is very difficult. If it is very difficult you would expect most of the scores to bunched up on the lower end of the score distribution with a few high scores. What is the shape of this distribution? Tells you about the shape of the distribution. Look for words like shape or expressions like • Most of the data in the center. • A few data points to the left or right. • All data evenly distributed. • Shape of the distribution is very peaked. Central Tendency Spread Symmetry

22. Problem #4 Question: An entrance exam for mechanical engineers is very difficult. If it is very difficult you would expect most of the scores to bunched up on the lower end of the score distribution with a few high scores. What is the shape of this distribution? Tells you about the shape of the distribution. Look for words like shape or expressions like • Most of the data in the center. • A few data points to the left or right. • All data evenly distributed. • Shape of the distribution is very peaked. Central Tendency Spread Symmetry

23. Problem #5 Question: You wish to find out the comfort level seasoned faculty have with emerging educational technologies. You survey 15 faculty who have taught more than 25 years. Two select “no comfort”, twelve select “minimal comfort” and two select moderate comfort.

24. Problem #5 Question: You wish to find out the comfort level seasoned faculty have with emerging educational technologies. You survey 15 faculty who have taught more than 25 years. Two select “no comfort”, twelve select “minimal comfort” and two select moderate comfort. Instructions: Which type of description of the distribution (below) is most relevant to the question (above)? Central Tendency Spread Symmetry

25. Problem #5 Question: You wish to find out the comfort level seasoned faculty have with emerging educational technologies. You survey 15 faculty who have taught more than 25 years. Two select “no comfort”, twelve select “minimal comfort” and two select moderate comfort. Central Tendency Spread Symmetry

26. Problem #5 Question: You wish to find out the comfort level seasoned faculty have with emerging educational technologies. You survey 15 faculty who have taught more than 25 years. Two select “no comfort”, twelve select “minimal comfort” and two select moderate comfort. Central Tendency Spread Symmetry Tells you about the shape of the distribution. Look for words like shape or expressions like • Most of the data in the center. • A few data points to the left or right. • All data evenly distributed. • Shape of the distribution is very peaked.

27. Problem #5 Question: You wish to find out the comfort level seasoned faculty have with emerging educational technologies. You survey 15 faculty who have taught more than 25 years. Two select “no comfort”, twelve select “minimal comfort” and two select moderate comfort. Central Tendency Spread Symmetry Tells you about the shape of the distribution. Look for words like shape or expressions like • Most of the data in the center. • A few data points to the left or right. • All data evenly distributed. • Shape of the distribution is very peaked.

28. What is a Distribution? If necessary explore this question

29. We will illustrate what a distribution is with a data set that describes the hours students’ study

30. Here is the data set:

31. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5

32. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Data

33. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Data Set

34. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 From this data set we will create a distribution:

35. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5

36. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 The X Axis, will be the number of hours of study

37. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5

38. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5

39. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 The Y Axis, indicates the number of times the same number occurs

45. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 Number of Occurrences

46. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences

47. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences

48. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3

61. Student Hours of Study Bart 1 Basheba 2 Bella 2 Bob 3 Boston 3 Bunter 3 Buxby 4 Bybee 4 Bwinda 5 Hours of Study 1 2 3 4 5 NumberofOccurrences 1 2 3 This is a distribution

62. One way to represent a distribution like this:

63. One way to represent a distribution like this:

64. One way to represent a distribution like this: Is like this:

65. One way to represent a distribution like this: Is like this:

66. One way to represent a distribution like this: Is like this: Normal distributions have the majority of the data in the middle

67. One way to represent a distribution like this: Is like this: Normal distributions have the majority of the data in the middle

68. One way to represent a distribution like this: Is like this: With decreasing but equal amounts toward the tails

69. One way to represent a distribution like this: Is like this: With decreasing but equal amounts toward the tails With decreasing but equal amounts toward the tails

70. Distributions can take other forms as well:

71. Distributions can take other forms as well: Hours of Study 1 2 3 4 #ofOccurrences 7

75. Distributions can take other forms as well: Skewed RIGHT

76. Distributions can take other forms as well: Hours of Study 5 6 72 #ofOccurrences 1

77. Distributions can take other forms as well: Skewed to the LEFT

80. Distributions can take other forms as well: Or NON-NORMAL

83. Return to Slide 1

Central spread symmetry 2.0

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Central spread symmetry 2.0

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