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Integrated Math 2 Section 1-6

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Quartiles and Percentiles

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• Integrated Math 2 Section 1-6

1. 1. SECTION 1-6 Quartiles and Percentiles
2. 2. ESSENTIAL QUESTIONS • How do you identify quartiles and calculated percentiles? • How do you create a box-and-whisker plot? • Where you’ll see this: • Education, market research, statistics
3. 3. VOCABULARY 1. Quartiles: 2. Interquartile Range: 3. Box-and-whisker Plot: 4. Whiskers:
4. 4. VOCABULARY 1. Quartiles: Three numbers that group the data into four equal parts 2. Interquartile Range: 3. Box-and-whisker Plot: 4. Whiskers:
5. 5. VOCABULARY 1. Quartiles: Three numbers that group the data into four equal parts 2. Interquartile Range: The difference between the ﬁrst and third quartiles; 3. Box-and-whisker Plot: 4. Whiskers:
6. 6. VOCABULARY 1. Quartiles: Three numbers that group the data into four equal parts 2. Interquartile Range: The difference between the ﬁrst and third quartiles; IQR = Q3 - Q1 3. Box-and-whisker Plot: 4. Whiskers:
7. 7. VOCABULARY 1. Quartiles: Three numbers that group the data into four equal parts 2. Interquartile Range: The difference between the ﬁrst and third quartiles; IQR = Q3 - Q1 3. Box-and-whisker Plot: Shows the distribution of data by separating it into four parts with an equal number of values in each 4. Whiskers:
8. 8. VOCABULARY 1. Quartiles: Three numbers that group the data into four equal parts 2. Interquartile Range: The difference between the ﬁrst and third quartiles; IQR = Q3 - Q1 3. Box-and-whisker Plot: Shows the distribution of data by separating it into four parts with an equal number of values in each 4. Whiskers: Lines that are drawn out from the box (Q1 to Q3) to the highest and lowest values
9. 9. VOCABULARY 5. Outliers: 6. Percentile:
10. 10. VOCABULARY 5. Outliers: Data that is at least 1.5 times the IQR below Q1 or 1.5 times the IQR above Q3 6. Percentile:
11. 11. VOCABULARY 5. Outliers: Data that is at least 1.5 times the IQR below Q1 or 1.5 times the IQR above Q3 Check: Q1 - 1.5(Q3-Q1) or Q3 + 1.5(Q3-Q1) 6. Percentile:
12. 12. VOCABULARY 5. Outliers: Data that is at least 1.5 times the IQR below Q1 or 1.5 times the IQR above Q3 Check: Q1 - 1.5(Q3-Q1) or Q3 + 1.5(Q3-Q1) 6. Percentile: A ranking that shows what percent of a group scored at or below your score
13. 13. VOCABULARY 5. Outliers: Data that is at least 1.5 times the IQR below Q1 or 1.5 times the IQR above Q3 Check: Q1 - 1.5(Q3-Q1) or Q3 + 1.5(Q3-Q1) 6. Percentile: A ranking that shows what percent of a group scored at or below your score # scores ≤ your score Percentile = x 100 total # of scores
14. 14. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240
15. 15. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240 Arrange in order:
16. 16. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240 Arrange in order: 109 159 195 215 229 239 240 255 278 300 360 375 384
17. 17. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240 Arrange in order: 109 159 195 215 229 239 240 255 278 300 360 375 384 Median
18. 18. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240 Arrange in order: 109 159 195 215 229 239 240 255 278 300 360 375 384 Median 240
19. 19. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240 Arrange in order: 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median 240
20. 20. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240 Arrange in order: 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median 205 240
21. 21. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240 Arrange in order: 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240
22. 22. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 360 239 159 278 300 384 109 255 195 375 215 229 240 Arrange in order: 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330
23. 23. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330
24. 24. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205
25. 25. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205 = 125
26. 26. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205 = 125 Q1-1.5(IQR) =
27. 27. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205 = 125 Q1-1.5(IQR) = 205 - 1.5(125)
28. 28. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205 = 125 Q1-1.5(IQR) = 205 - 1.5(125) = 17.5
29. 29. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205 = 125 Q1-1.5(IQR) = 205 - 1.5(125) = 17.5 Q3+1.5(IQR) =
30. 30. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205 = 125 Q1-1.5(IQR) = 205 - 1.5(125) = 17.5 Q3+1.5(IQR) = 330 + 1.5(125)
31. 31. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205 = 125 Q1-1.5(IQR) = 205 - 1.5(125) = 17.5 Q3+1.5(IQR) = 330 + 1.5(125) = 517.5
32. 32. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330 IQR = 330 - 205 = 125 Q1-1.5(IQR) = 205 - 1.5(125) = 17.5 No outliers Q3+1.5(IQR) = 330 + 1.5(125) = 517.5
33. 33. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330
34. 34. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330
35. 35. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330
36. 36. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330
37. 37. WORK WITH DATA Use the data to ﬁnd the median of the prices of bicycles sold at Cycle Garage (dollars) 109 159 195 215 229 239 240 255 278 300 360 375 384 Q1 Median Q3 205 240 330
38. 38. 100 150 200 250 300 350 400
39. 39. 100 150 200 250 300 350 400
40. 40. 100 150 200 250 300 350 400
41. 41. 100 150 200 250 300 350 400
42. 42. 100 150 200 250 300 350 400
43. 43. 100 150 200 250 300 350 400
44. 44. 100 150 200 250 300 350 400
45. 45. USING THE TI-84/83
46. 46. USING THE TI-84/83
47. 47. USING THE TI-84/83
48. 48. USING THE TI-84/83
49. 49. USING THE TI-84/83
50. 50. USING THE TI-84/83
51. 51. USING THE TI-84/83
52. 52. USING THE TI-84/83
53. 53. EXAMPLE 1 Matt Mitarnowski is ranked 75th in his class of 200 students. Fuzzy Jeff is in the same class and has a percentile rank of 75. Who has the higher standing in the class?
54. 54. EXAMPLE 1 Matt Mitarnowski is ranked 75th in his class of 200 students. Fuzzy Jeff is in the same class and has a percentile rank of 75. Who has the higher standing in the class? Find Matt’s percentile
55. 55. EXAMPLE 1 Matt Mitarnowski is ranked 75th in his class of 200 students. Fuzzy Jeff is in the same class and has a percentile rank of 75. Who has the higher standing in the class? Find Matt’s percentile Percentile =
56. 56. EXAMPLE 1 Matt Mitarnowski is ranked 75th in his class of 200 students. Fuzzy Jeff is in the same class and has a percentile rank of 75. Who has the higher standing in the class? Find Matt’s percentile 200 - 74 Percentile = x 100 200
57. 57. EXAMPLE 1 Matt Mitarnowski is ranked 75th in his class of 200 students. Fuzzy Jeff is in the same class and has a percentile rank of 75. Who has the higher standing in the class? Find Matt’s percentile 200 - 74 126 Percentile = x 100 = x 100 200 200
58. 58. EXAMPLE 1 Matt Mitarnowski is ranked 75th in his class of 200 students. Fuzzy Jeff is in the same class and has a percentile rank of 75. Who has the higher standing in the class? Find Matt’s percentile 200 - 74 126 Percentile = x 100 = x 100 = 63 200 200
59. 59. EXAMPLE 1 Matt Mitarnowski is ranked 75th in his class of 200 students. Fuzzy Jeff is in the same class and has a percentile rank of 75. Who has the higher standing in the class? Find Matt’s percentile 200 - 74 126 Percentile = x 100 = x 100 = 63 200 200 Matt is in the 63rd percentile, so Jeff has the higher standing.
60. 60. PROBLEM SET
61. 61. PROBLEM SET p. 30 #1-22 “The highest result of education is tolerance.” - Helen Keller