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# Box Plots

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1. Box Plots CCSS 6.7

2. Step 1 – Order Numbers 1. Order the set of numbers from least to greatest

3. Step 2 – Find the Median 2. Find the median. The median is the middle number. If the data has two middle numbers, find the mean of the two numbers. What is the median?

4. Step 3 – Upper & Lower Quartiles 3. Find the lower and upper medians or quartiles. These are the middle numbers on each side of the median. What are they?

5. Step 4 – Draw a Number Line Now you are ready to construct the actual box & whisker graph. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data:

6. Step 5 – Draw the Parts Locate the main median12 using a vertical line just above your number line:

7. Step 5 – Draw the Parts Locate the lower median8.5 and the upper median14 with similar vertical lines:

8. Step 5 – Draw the Parts • Next, draw a box using the lower and upper median lines as endpoints:

9. Step 5 – Draw the Parts Finally, the whiskers extend out to the data's smallest number 5 and largest number 20:

10. Step 6 - Label the Parts of a Box-and-Whisker Plot Lower Quartile Median Upper Quartile Lower Extreme 3 1 2 Upper Extreme 4 5 Name the parts of a Box-and-Whisker Plot

11. Practice • Data Set [10, 10, 14, 15, 17, 20, 20, 21, 22]

12. Sample Problem • Find the median. [10, 10, 14, 15, 17, 20, 20, 21, 22]

13. Sample Problem • Find the median. [10, 10, 14, 15, 17, 20, 20, 21, 22]

14. Sample Problem (ODD) • Find the median. [10, 10, 14, 15, 17, 20, 20, 21, 22]

15. Sample Problem (ODD) • Find the lower quartile. [10, 10, 14, 15, 17, 20, 20, 21, 22]

16. Sample Problem (ODD) • The lower quartile is 12. [10, 10, 14, 15,] 17, [20, 20, 21, 22] 10 + 14 = 24 24 divided by 2 = 12

17. Sample Problem (ODD) • Find the upper quartile. [10, 10, 14, 15,] 17, [20, 20, 21, 22]

18. Sample Problem (ODD) • The upper quartile is 20.5 [10, 10, 14, 15,] 17, [20, 20, 21, 22] 20 + 21 = 41 41 divided by 2 = 20.5

19. Sample Problem (ODD) • Find the lower extreme. [10, 10, 14, 15,] 17, [20, 20, 21, 22]

20. Sample Problem (ODD) • The lower extreme is 10. [10, 10, 14, 15,] 17, [20, 20, 21, 22]

21. Sample Problem (ODD) • Find the upper extreme. [10, 10, 14, 15,] 17, [20, 20, 21, 22]

22. Sample Problem (ODD) • The upper extreme is 22. [10, 10, 14, 15,] 17, [20, 20, 21, 22]

23. Sample Problem (ODD) • The 5 Number Summary for the sample problem with an even number of pieces of data is: [10, 10, 14, 15, 17,20, 20, 21, 22] • Median= 17 • Lower Quartile = 12 • Upper Quartile = 20.5 • Lower Extreme = 10 • Upper Extreme = 22

24. Sample Problem (ODD) • Find the interquartile range for the set of data. [10, 10, 14, 15, 17,20, 20, 21, 22] Median= 17 Lower Quartile = 12 Upper Quartile = 20.5 Lower Extreme = 10 Upper Extreme = 22

25. Sample Problem (ODD) • The interquartile range is 8.5. 20.5 – 12 = 8.5 [10, 10, 14, 15, 17,20, 20, 21, 22] • Median= 17 • Lower Quartile = 12 • Upper Quartile = 20.5 • Lower Extreme = 10 • Upper Extreme = 22

26. Sample Problem (ODD) • Find the range of the data set. [10, 10, 14, 15, 17,20, 20, 21, 22]

27. Sample Problem (ODD) • The range is 12. 22 – 10 = 12 [10, 10, 14, 15, 17,20, 20, 21, 22]

28. Sample Problem • Use the following data set to create a 5 number summary • 1,2,3,4,5,6,7,8,9,10,11,12

29. Sample Problem • What is the median? 1,2,3,4,5,6,7,8,9,10,11,12 The median is the mean of 6 and 7 The median is 6.5

30. Sample Problem • Remember, the median splits the data set in half [1,2,3,4,5,6] 6.5 [7,8,9,10,11,12]

31. Sample Problem • What are the quartiles? [1,2,3,4,5,6] 6.5 [7,8,9,10,11,12] • Remember, if there are an even number of pieces of data in your set, the median is the mean of the middle two numbers

32. Sample Problem • What are the quartiles? [1,2,3,4,5,6] 6.5 [7,8,9,10,11,12] • Upper Quartile = 3.5 • Lower Quartile = 8.5

33. Sample Problem • What is the upper extreme? • What is the lower extreme? [1,2,3,4,5,6] 6.5 [7,8,9,10,11,12] • Upper Extreme = 12 • Lower Extreme = 1

34. Sample Problem • What is the 5 number summary? • Median = 6.5 • Lower Quartile = 3.5 • Upper Quartile = 8.5 • Upper Extreme = 12 • Lower Extreme = 1