1. Math 20: Foundations FM20.6 Demonstrate an understanding of normal distribution, including standard deviation and z-scores. FM20.7 Demonstrate understanding of the interpretation of statistical data, including: confidence intervals, confidence levels, margin of error. G. You Can use Statistics to Make Many Important Decisions

2. Getting Started! Comparing Salaries p. 208

4. What do YOU Think? p. 209

5. Outlier - A value in a data set that is very different from other values in the set.

6. 1. Sifting Through the Data FM20.6 Demonstrate an understanding of normal distribution, including standard deviation and z-scores.

9. Mean, median and mode are about the same for both. However, the range for X is more than double Y. Y batteries are closer to mean on the line plot. Brand X has 4 extreme outliers. Brand Y seems like the safer choice.

10. Dispersion - A measure that varies by the spread among the data in a set; dispersion has a value of zero if all the data in a set is identical, and it increases in value as the data becomes more spread out.

11. Reflection p.210

12. Summary p.211

13. Practice Ex. 5.1 (p.211) #1-3

14. 2. Frequency Tables, Polygons and Histograms FM20.6 Demonstrate an understanding of normal distribution, including standard deviation and z-scores.

15. 2. Frequency Tables, Polygons and Histograms

17. Frequency Table How to select you intervals?

19. We could also use a Histogram or a Polygon Graph (line graph) to solve this problem. Lets use a new frequency table to solve using the Histogram or a Polygon Graph

22. Histogram

25. Frequency Polygon

26. We use a different interval width in our frequency table then we did with our two graphs. How did this affect the distribution?

27. If we used an interval width of 200 would that have made it easier to see the flood years in our frequency?

28. Would 2000 be a better interval?

29. Example 2

31. What other factors should be considered besides the rickter scale reading?

32. Summary p.220

34. Practice Ex. 5.2 (p. 221) #1-9 #3-12

35. 3. Standard Deviation FM20.6 Demonstrate an understanding of normal distribution, including standard deviation and z-scores.

36. 3. Standard Deviation Deviation - The difference between a data value and the mean for the same set of data. Standard Deviation - A measure of the dispersion or scatter of data values in relation to the mean; a low standard deviation indicates that most data values are close to the mean, and a high standard deviation indicates that most data values are scattered farther from the mean.

37. Investigate the Math p.226

39. B-E)

40. F-G)

41. Reflecting p.228

42. Example 1

43. Example 2

44. Example 3

45. Summary p. 232

47. Practice Ex. 5.3 (p.233) #2-12 #3-14

48. 4. Normal Distribution FM20.6 Demonstrate an understanding of normal distribution, including standard deviation and z-scores.

49. a) b) c) d)

50. A normal distribution curve is a symmetrical curve that represents the normal distribution; also called a Bell Curve Data that, when graphed as a histogram or frequency polygon, results in a unimodal symmetric distribution around the mean it is referred to as a Normal Distribution

51. Normal Distribution (Bell Curve)

52. If we rolled 2 dice 50,000 times adding the two dice together each time then graphed the results what do you think the graph would look like?

54. What if we rolled three dice?

56. Well lets take a look. Grab a partner and two dice and roll the two dice 50 times each adding the total each time. When you are done see put your results into a histogram. Do you get a bell curve (normal distribution)? What if we add all the results from the class together?

57. The more data the is collected the more likely your data will be distributed normally. When your data is distributed normally, if you where to draw a line of symmetry right in the middle what value would this line have?

58. Mean Median Mode

59. When your data is distributed normally your mean, median and mode are all the same

60. Example 1

62. Example 2

64. Example 3

65. a) b)

66. Example 4

69. What is the probability that it will last less than 18 months?

70. Summary p. 250

73. Practice Ex. 5.4 (p. 251) #1-13 #3-16

74. 5. Working with Z-Scores FM20.6 Demonstrate an understanding of normal distribution, including standard deviation and z-scores.

75. 5. Working with Z-Scores Z-Score - A standardized value that indicates the number of standard deviations of a data value above or below the mean. Standard Normal Distribution - A normal distribution that has a mean of zero and a standard deviation of one.

76. For any given score, x, from a normal distribution x = μ +z σ Where z is the number of standard deviations away from the mean

77. We can rearrange this formula to solve for the number of standard deviations away from the mean a score is.

78. This is the formula we use to find the z-score

79. Again, the z-score is the number of standard deviations away from the mean for a certain score

80. Example 1

82. Which one of Serge’s runs was better?

83. Why would a lower z-score mean a lower time? What does a negative z-score mean? What does a positive z-score mean? What does a 0 z-score mean?

84. Example 2

87. The z-score table gives you the % from 0% to the score you are looking at.

88. Example 3

91. Example 4

93. Example 5

96. Summary p. 263

99. Practice Ex. 5.5 (p. 264) #1-13 #6-17, 20, 22

100. 6. How Confident are You? FM20.7 Demonstrate understanding of the interpretation of statistical data, including: confidence intervals, confidence levels, margin of error.

101. 6. How Confident are You? Margin of Error - The possible difference between the estimate of the value you’re trying to determine, as determined from a random sample, and the true value for the population; the margin of error is generally expressed as a plus or minus percent, such as 65%.

102. Confidence Interval - The interval in which the true value you’re trying to determine is estimated to lie, with a stated degree of probability; the confidence interval may be expressed using ± notation, such as 54.0% ± 3.5%, or ranging from 50.5% to 57.5%.

103. Confidence Level - The likelihood that the result for the “true” population lies within the range of the confidence interval; surveys and other studies usually use a confidence level of 95%, although 90% or 99% is sometimes used.

105. Based on this survey, what is the range for 18- to 34-year-olds who do not have a social networking account?

106. Example 2

108. Example 3

111. Example 4

113. Summary p. 273

115. Practice Ex. 5.6 (p.274) #1-9 #3-11