1. Box and Whisker Plot
5 Number Summary for
Odd Numbered Data Sets

2. Finding the Median of Odd Numbered Data Sets
Once the pieces of data (numbers) are arranged in order from least to greatest, then the middle number of the set is the median
[3, 4, 4, 5, 8, 8, 9, 10,11]
The median for this set of data = 8

3. Odd Numbered Data Sets The median splits the data set in half.
[3, 4, 4, 5,] 8, [8, 9, 10,11]
From here we can then find the upper and lower quartiles as well as the upper and lower extremes.

4. The lower quartile for this set of data = 4
The lower quartile is the median of the bottom half of the data (to the left of the median).
If the part of the set we are considering has an even number pieces of data, you must find the mean of the two middle pieces of data to get the lower quartile.
[3, 4, 4, 5,] 8, [8, 9, 10,11]
4 + 4 = divided by 2 = 4
The lower quartile for this set of data = 4

5. Upper Quartile
The upper quartile is the median of the top half of the data (to the right of the median).
If the part of the set we are considering has an even number pieces of data, you must find the mean of the two middle pieces of data to get the upper quartile.
[3, 4, 4, 5,] 8, [8, 9, 10,11]
= 19; 19 divided by 2 = 9.5
The upper quartile for this data set = 9.5

6. Interquartile Range
To find the interquartile range, subtract the lower quartile from the upper quartile.
[3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11]
Upper Quartile – Lower Quartile = _____
9.5 – 4 = 5.5
The intequartile range for this data = 5.5

7. Lower Extreme The lower extreme is the lowest number in the data set.
[3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11]
The lower extreme for this data set = 3

8. Upper Extreme The upper extreme is the highest number in the data set.
[3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11]
The upper extreme for this data set = 11

9. Range
The range of the data can be found by subtracting the lower extreme from the upper extreme.
[3, 4,] 4 [4, 5,] 8, [8, 9] 9.5 [10,11]
11 – 3 = 8
The range for this data set = 8

10. 5 Number Summary Median = 8 Lower Quartile = 4 Upper Quartile = 9.5
[3, 4, 4, 5, 8, 8, 9, 10,11]
Median = 8
Lower Quartile = 4
Upper Quartile = 9.5
Lower Extreme = 3
Upper Extreme = 11

12. Any Questions?

13. Sample Problem (ODD)
Data Set
[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) The median is 17.
[10, 10, 14, 15, 17, 20, 20, 21, 22]

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

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

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

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

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

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

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

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

24. 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

25. 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

26. 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

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

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

29. 5 Number Summary for Even Numbered Data Sets
Box and Whisker Plot
5 Number Summary for
Even Numbered Data Sets

30. Even Numbered Data Sets
If the data set has an even number of pieces of data, we find the mean of the two middle numbers to find the median of the set
2, 4, 5, 6, 7, 8, 9, 11, 19, 20
7 + 8 = 15
15 divided by 2 = 7.5
The median is 7.5
If the data set has an even number of pieces of data, we find the mean of the two middle numbers to find the median of the set
2, 4, 5, 6, 7, 8, 9, 11, 19, 20
7 + 8 = 15
15 divided by 2 = 7.5
The median is 7.5

31. Even Numbered Data Sets
The median splits the data set in half.
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
From here we can then find the upper and lower quartiles as well as the upper and lower extremes.

32. Lower Quartile
The lower quartile is the median of the bottom half of the data (to the left of the median).
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
Lower Quartile for this data = 5

33. Upper Quartile
The upper quartile is the median of the top half of the data (to the right of the median).
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
The upper quartile for this data set = 11

34. Interquartile Range
To find the interquartile range, subtract the lower quartile from the upper quartile.
Upper Quartile – Lower Quartile = _____
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
11 – 5 =6
The intequartile range for this data = 6

35. Lower Extreme The lower extreme is the lowest number in the data set.
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
The lower extreme for this data set = 2

36. Upper Extreme The upper extreme is the highest number in the data set.
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
The upper extreme for this data set = 20

37. Range
The range of the data can be found by subtracting the lower extreme from the upper extreme.
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
20 – 2 = 18
The range for this data set = 18

38. Even Numbered Data Sets
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
Median = 7.5
Lower Quartile = 5
Upper Quartile = 11
Upper Extreme = 20
Lower Extreme = 2

39. Any Questions?

40. 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

41. The median is the mean of 6 and 7
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

42. 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]

43. 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

44. 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

45. 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

46. 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

47. Any Questions?