1. StatisticsStatistics Unit 5

2. Example 2 We reviewed the three Measures of Central Tendency: Mean, Median, and Mode. We also looked at one Measure of Dispersion – range. Another Measure of Dispersion is Standard Deviation Standard Deviation is a measure of how the values in a data set vary, or deviate, from the mean. Objective: Students will use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

3. Example 2 Standard deviation is a simple measure of the variability or dispersion of a data set. A low standard deviation indicates that the data points tend to be very close to the same value (the mean). A high standard deviation indicates that the data are “spread out” over a large range of values. Objective: Students will use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

4. Example 3 standard deviation formula: Objective: Students will use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Sigma – represents standard deviation Capital Sigma – represents the sum of a series of numbers. n is the number of values in a data set.

5. Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 1 x1x1 12.6 15.1 11.2 17.9 18.2 15 12.6 – 15 = -2.4 15.1 – 15 = 0. 1 11.2 – 15 = -3.8 17.9 – 15 = 2.9 18.2 – 15 = 3.2 (-2.4) 2 = 5.76 (0. 1) 2 = 0.01 (-3.8) 2 = 14.44 (2.9) 2 = 8.41 (3.2) 2 = 10.24

6. Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x1

7. Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x1 13.4 11.7 18.3 14.8 14.3

8. Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x1 13.414.5 11.714.5 18.314.5 14.814.5 14.314.5

9. Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x1 13.414.5-1.1 11.714.5-2.8 18.314.53.8 14.814.50.3 14.314.5-0.2

10. Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x1 13.414.5-1.11.21 11.714.5-2.87.84 18.314.53.814.44 14.814.50.30.09 14.314.5-0.20.04

11. Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x1 13.414.5-1.11.21 11.714.5-2.87.84 18.314.53.814.44 14.814.50.30.09 14.314.5-0.20.04 4.724

12. Find the mean and standard deviation of each data set. Which data set has a greater standard deviation? Use tables to help organize your work. Data set 1 - {12.6, 15.1, 11.2, 17.9, 18.2} Data set 2 – {13.4, 11.7, 18.3, 14.8, 14.3} Data Set 2 x1x1 13.414.5-1.11.21 11.714.5-2.87.84 18.314.53.814.44 14.814.50.30.09 14.314.5-0.20.04 4.724

13. Turn to page 745 and complete the 4 problems at the bottom of the page. Set up a table for each set of data Data Set x1x1

14. Turn to page 745 and complete the 4 problems at the bottom of the page. Set up a table for each set of data Data Set x1x1

15. POD - Turn to page 745 and complete problem number 1 at the bottom of the page. Set up a table for each set of data Data Set x1x1

16. POD - Turn to page 745 and complete problem number 1 at the bottom of the page. Set up a table for each set of data Data Set x1x1 46-24 8624 561 126636 36-39 9639 561 26-416

17. Example 4 – Find the measures of central tendency, and the measures of dispersion. 1238 2236 3231 4229 5227 6225 7 8224 9 10224 11216 12216 13213 14210 15209 mean median Mode range standard deviation 223 224 29

18. x1x1

19. x1x1 238 236 231 229 227 225 224 216 213 210 209

20. x1x1 238223 236223 231223 229223 227223 225223 225223 224223 224223 224223 216223 216223 213223 210223 209223

21. x1x1 23822315 23622313 2312238 2292236 2272234 2252232 2252232 2242231 2242231 2242231 216223-7 216223-7 213223-10 210223-13 209223-14

22. x1x1 23822315225 23622313169 231223864 229223636 227223416 22522324 22522324 22422311 22422311 22422311 216223-749 216223-749 213223-10100 210223-13169 209223-14196

23. x1x1 23822315225 23622313169 231223864 229223636 227223416 22522324 22522324 22422311 22422311 22422311 216223-749 216223-749 213223-10100 210223-13169 209223-14196 1084/15 = 72.27

24. x1x1 23822315225 23622313169 231223864 229223636 227223416 22522324 22522324 22422311 22422311 22422311 216223-749 216223-749 213223-10100 210223-13169 209223-14196 1084/15 = 72.27

25. Example 4 – Find the measures of central tendency, and the measures of dispersion. 1238 2236 3231 4229 5227 6225 7 8224 9 10224 11216 12216 13213 14210 15209 mean median Mode range standard deviation 223 224 29 8.50

26. Example 5 –Identify the Maximum, Minimum, Upper Quartile, Lower Quartile and the Median. Then create a Box and Whisker Plot. 1238 2236 3231 4229 5227 6225 7 8224 9 10224 11216 12216 13213 14210 15209 Maximum Upper Quartile Median Lower Quartile Minimum 238 229 224 216 209 238 237 236 235 234 233 232 231 230 229 228 227 226 225 224 223 222 221 220 219 218 217 216 215 214 213 212 211 210 209

27. Example 6 – Compute the Interquartile Range (IQR) and then determine if there are any outliers. 1238 2236 3231 4229 5227 6225 7 8224 9 10224 11216 12216 13213 14210 15209 Median + (1.5 x IQR) Median - (1.5 x IQR) 13 19.5 243.5 204.5 Maximum Upper Quartile Median Lower Quartile Minimum 238 229 224 216 209 All of the data falls between 243.5 and 204.5 so there are No Outliers Interquartile Range (IQR) 1.5 x Interquartile Range (IQR)

28. Homework page 745 Number 2

29. Summary: Need to be able to find mean median Mode range standard deviation Maximum Upper Quartile Median Lower Quartile Minimum Interquartile Range (IQR) 1.5 x Interquartile Range (IQR) Median + (1.5 x IQR) Median - (1.5 x IQR) Create a Box and Whisker Plot

30. Example 6 – Number 1

31. Example 6 – Number 2

32. Example 6 – Number 3 160

33. Example 6 – Number 4

34. Example 6 – Number 5

35. Example 6 – Number 6

36. Example 6 – Number 7

37. Homework page 745 Use the data in question # 4 Data set 1 to find the measures of central tendency, measures of dispersion, upper quartile, lower quartile, minimum, maximum and make a box and whisker plot. Find the interquartile range and determine if there are outliers.

38. Homework page 745 (using data set 1 from question 4) mean median Mode range standard deviation Maximum Upper Quartile Median Lower Quartile Minimum Interquartile Range (IQR) 1.5 x Interquartile Range (IQR) Median + (1.5 x IQR) Median - (1.5 x IQR) 144 242 340 435 532 6 728 36.14 35 32 44-28 = 16

39. page 745 data set 1 problem number 4 Data Set x1x1 44 42 40 35 32 28

40. page 745 data set 1 problem number 4 Data Set x1x1 4436.147.8661.78 4236.145.8634.34 4036.143.8614.90 3536.14-1.141.30 3236.14-4.1417.14 3236.14-4.1417.14 2836.14-8.1466.26

41. Homework page 745 (using data set 1 from question 4) mean median Mode range standard deviation Maximum Upper Quartile Median Lower Quartile Minimum Interquartile Range (IQR) 1.5 x Interquartile Range (IQR) Median + (1.5 x IQR) Median - (1.5 x IQR) 144 242 340 435 532 6 728 36.14 35 32 44-28 = 16 5.51 44 42 35 32 28 42-32=10 1.5x10=15 35 + 15 = 50 35 - 15 = 20 All of the data falls between 50 and 20 so there are no outliers.

42. Homework page 745 (using data set 1 from question 4) Maximum Upper Quartile Median Lower Quartile Minimum 144 242 340 435 532 6 728 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 42 35 32 28 44

43. Example of a positively skewed box and whisker plot When the whisker is longer on the positive side we say it is positively skewed.

44. Example of a negatively skewed box and whisker plot When the whisker is longer on the negative side we say it is negatively skewed.

45. Special cases Find the mode: 1) 14, 14, 14, 15,15, 15, 16, 16, 16, 18 2)2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8 3) 33, 35, 36, 39, 41, 43, 47

46. Special Cases Find the median: 1) 12, 14, 14, 15,17, 18, 18, 21, 22, 25 2) 43, 45, 51, 53, 54, 54, 59, 60

47. POD You are one of the finalists at a science fair. The scores of the other finalists are listed in the table. 1.Write an inequality that represents your possible scores if your percentile is 80. What percent of scores must be less than or equal to your score? What is the total number of finalists scores? 87 89 81 85 87 83 86 94 90 97 80 89 85 88

48. 80 81 83 85 85 86 87 87 88 89 89 90 94 97 Maximum Upper Median Lower Maximum Summary: In your notes, explain the difference between range and interquartile range.

49. 80 81 83 85 85 86 87 87 88 89 89 90 94 97 Maximum Upper Median Lower Minimum 97 89 87 85 80 If your percentile rank is 80, then your score must be greater than or equal to 90 and less than 94 Or 90 < x < 94 Summary: In your notes, explain the difference between range and interquartile range. 75%100%

50. Example 9 Turn to page 760 in your textbook. The tables in green are called “Two Way Frequency Tables. Read through Activity 1 and 2 and answer questions 1-10 together with your group. ROUND ALL PERCENTS TO THE NEARES TENTH. Be prepared to make a team sheet for team points. Summary: When your groups finishes, in your notes, explain the difference between range and interquartile range.

51. Example 9 1. 12:90 about 13.3% 2. 12:98 about 12.2% 3. 86:98 about 87.8% 4. 25:103 about 24.3% 5. Martial Arts Champ Story of Love 6. 79:100 79% 7. 55:100 55% 8. 67:100 67% 9. 45:100 45% Summary: When your groups finishes, in your notes, explain the difference between range and interquartile range.

52. Example 9 10. 0.1a + 0.4b + 0.5c Summary: When your groups finishes, in your notes, explain the difference between range and interquartile range. 0.1(0.79) + 0.4(0.55) + 0.5(0.33) 0.079 + 0.22 + 0.165 0.464 or 46.4%