1. 6-3 Measures of Variation Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 6-3 Measures of Variation Do Now Find the mean and median of each data set. 1. 14,24,12,20,15,22,12 2. 7,3,16,9,15,6

3. 6-3 Measures of Variation SWBAT calculate, interpret, and compare measures of variation in a data set. Objective:

4. 6-3 Measures of Variation Vocabulary box-and-whisker plot quartiles variation inter-quartile range (IQR)

5. 6-3 Measures of Variation You can display data using a box-and-whisker plot. A box-and-whisker plot or box plot is a data display that shows how data is distributed using the 5-point summary. Quartiles are three values that divide a data set into fourths. Each quartile contains one-fourth (25%) of the data. The median is considered the 2 nd quartile. A box-and-whisker plot can be used to show how the values in a data set are distributed. Variation (variability) is the spread of the values.

6. 6-3 Measures of Variation First, you must identify the 5 point summary. 1.) Is the data in numerical order? 2.) What are the least and greatest values? 3.) What is the median and two sections of data? 4.) What is the 1 st and 3 rd Quartile? 5 Point Summary Least: Greatest: Median: 1 st Q: 3 rd Q: xxxxxxxx 10 7 13 9 11.5

7. 6-3 Measures of Variation Ex. 1 Find the 5-Point Summary of the following data sets: 5, 7, 8, 2, 0, 9, 4 Least: Greatest: Median: 1 st Q: 3 rd Q:

8. 6-3 Measures of Variation TOYO 1 Find the 5-Point Summary of the following data sets: A.) 4, 1, 12, 1, 6, 7, 2, 9, 10 B.) 3, 9, 11, 2, 5, 3, 6, 11 Least: Greatest: Median: 1 st Q: 3 rd Q:

9. 6-3 Measures of Variation Do Now Find the 5-Point Summary of the following data sets: 1.) 12, 14, 14, 12, 16, 13, 11, 14, 18 2.) 32, 34, 36, 37, 36, 37, 38, 37 Least: Greatest: Median: 1 st Q: 3 rd Q:

10. 6-3 Measures of Variation Page 6 Box-and-Whisker Plot Pg. 6 1.Draw a number line 2.Plot a point for each value in the 5 point- summary 3.Draw a box through the 1 st and 3 rd quartile 4.Draw a vertical line through the median 5.Draw lines from the box to the least and greatest values (Those are the whiskers) Least: Greatest: Median: 1 st Q: 3 rd Q: 10 7 13 9 11.5 7 8 9 10 11 12 13

11. 6-3 Measures of Variation Ex. 2: Box-and-Whisker Plot The average number of hours that several students watch television in a day is given. Plot a Box-and-Whisker plot to display the data: 2, 1, 5, 2, 1, 2, 3, 2, 2.

12. 6-3 Measures of Variation TOYO 2 Ms. Snow asks some of her students how many pets they have. The responses are 9, 0, 4, 1, 1, 2, 3, 5, and 2 pets. Display the data using a Box-and-Whisker Plot.

13. 6-3 Measures of Variation TOYO 3 The next 9 customers in line are waiting to purchase the following number of items: 6, 10, 4, 8, 5, 9, 4, 10, 7, 5 Display the data using a Box-and-Whisker plot.

14. 6-3 Measures of Variation Class Activity In your groups collect the following data and write it down: 1.) Number of in vowels everyone’s full name. 2.) Number of consonants in everyone’s full name. 3.) Number of letters in everyone’s full name. Make a box and whisker plot for each.

15. 6-3 Measures of Variation Activity Results Group 1 Group 2

16. 6-3 Measures of Variation Do Now For the past 4 weeks, it has snowed 8 times. The following are the accumulation results for each time it snowed (in inches): 4, 3, 2, 2, 6, 1, 8, 3. Create a box-and-whisker plot that will display this data.

17. 6-3 Measures of Variation The interquartile range (IQR) is the difference between the first and third quartiles. It is a measure of the spread of the middle 50% of the data. A small IQR means that the data of the middle 50% of the set are close in value. A large IQR means that the data of the middle 50% of the set are spread out.

18. 6-3 Measures of Variation Ex. 3: Finding the Interquartile Range Find the interquartile range for the data set 87, 71, 72, 73, 84, 92, 73. 71, 72, 73, 73, 84, 87, 82 84,73,71,73,82 IQR=87-72=15 The inter-quartile range is 15. 72, 87,

19. 6-3 Measures of Variation TOYO 3 Find the interquartile range for the data set 17, 39, 38, 9, 29, 40, 27

20. 6-3 Measures of Variation Mean Absolute Deviationpg. 7 Another measure of variation is the mean absolute deviation. This is the mean amount that data values differ from the mean of data values. Page 7 1.Find the mean of the data set 2.Find the difference between the mean and each value in the set 3.Find the mean of the differences

21. 6-3 Measures of Variation 75+82+78+67 = 75.5 4 75.5 – 75 = 82 – 75.5 = 78 – 75.5 = 75.5 – 67 = Ex. 4: Finding Mean Absolute Deviation A scientist is studying temperature variation. She determines that the temperature at noon on four days is 75F, 82F, 78F, and 67F. What is the mean absolute deviation of the temperatures?. Goals for finding the Mean Absolute Deviation 1.Find the mean of the data set 2.Find the difference between the mean and each value in the set 3.Find the mean of the differences 0.5 6.5 2.5 8.5 + + + ___________________ 4 = 4.5

22. 6-3 Measures of Variation TOYO 4 A scientist is studying temperature variation. She determines that the temperature at noon on four days is 64F, 75F, 80F, and 78F. What is the mean absolute deviation of the temperatures?

23. 6-3 Measures of Variation Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

24. 6-3 Measures of Variation Exit Ticket A park ranger measures the thickness of ice on a lake in 8 different locations: 19 in., 17 in., 15 in., 15 in., 18 in., 12 in., 16 in., 14 in. 1. Make a box-and-whisker plot of the data.

25. 6-3 Measures of Variation Exit Ticket Jackie and her 4 brothers decided to record how many hot dogs they can eat in 10 minutes. Jackie ate 7, Rich ate 10, Tom ate 8, Justin ate 11, and Jimmy ate 16 hotdogs. Find the inter-quartile range of how many hotdogs they ate. Find the mean absolute value deviation of the data set.

26. 6-3 Measures of Variation 1. Find the inter-quartile range of the data. 2.Find the mean absolute deviation of the data, to the nearest tenth. Lesson Quiz for Student Response Systems The number of text messages 7 people sent in one day are as follows: 8, 4, 3, 17, 2, 1, and 10.

27. 6-3 Measures of Variation The mode of Nevin’s four math quiz scores last month is 85 points. On three of the quizzes, he earned the following scores: 90, 86, and 85. What was the score of Nevin’s other quiz?

28. 6-3 Measures of Variation Tammy is 14 years old. She has a younger sister and an older brother. Her sister is 12 years old. The mean of all their ages is 14. How old is Tammy’s brother?

29. 6-3 Measures of Variation The table shows some of the years in which the Super Bowl was won by the most points. Find the mean, median, and mode. YearPoints Won By 196725 197221 198522 199523 200127 Super Bowl Winning Margins The 1990 Super Bowl had the largest winning margin, which was 45 points. Add this number to the data in the table and find the mean, median, and mode. Which best describes the data?

30. 6-3 Measures of Variation The amount of snowfall (in inches) for each of the first 6 weeks of winter is 1.5, 3.7, 9, 4.5, 7.3, and 4. What is the mean absolute deviation for the number of inches of snow for the first 6 weeks of winter?