1. Stem and leaf diagrams

2. Introduction Stem and leaf diagrams are used to:
retain raw data values (possibly rounded)
provide a diagrammatic representation of the distribution - like bar chart
find median, quartiles etc

3. Stages in drawing a stem and leaf
Decide on and provide a key for the stem and leaf. The leaf is always the smallest (least significant) digit - you may need to round in some circumstances
Draw a preliminary stem and leaf directly from the raw data - this is likely to mean the leafs are unordered
Draw a new stem and leaf diagram with the leaves put into numerical order.
If needed add the number of leaves

4. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram: 3 4 5 6 7
Completion times
stem
leaf

5. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 7

6. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 7 1

7. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 7 3 1

8. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7
7 3 3 1

9. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 3 1

10. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 3 1

11. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 3
1 8

12. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 3
1 8

13. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 3
1 8 2

14. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7
3 7
1 8 2

15. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7
3 7
1 8 2

16. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7
1 8 2

17. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7
1 8 2

18. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

19. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

20. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

21. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

22. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

23. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

24. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

25. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

26. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

27. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 2

28. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 8 2

29. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 8 2

30. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 8 2

31. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 8 2

32. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 8 2

33. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 8 2

34. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Completion times 3 4 5 6 7 8 2
(3) re draw diagram with leafs in numerical order:

35. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7

36. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

37. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8 1

38. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8
1 2

39. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

40. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

41. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

42. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

43. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

44. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

45. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

46. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

47. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

48. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

49. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

50. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

51. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

52. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

53. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

54. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8 1

55. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8
1 2

56. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

57. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

58. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

59. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

60. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8 1

61. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8
1 3

62. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

63. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Completion times 3 4 5 6 7 8

64. Example - drawing a stem and leaf
Answer (a):- (3) re draw diagram with leafs in numerical order:
Completion times 3 4 5 6 7 8 2
Don’t forget the key
Completion times
4|7 means 47 3 4 5 6 7 8 2

65. Example - drawing a stem and leaf
Question: students were set a simple task. Their completion times to the nearest second were:
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Answer (b):- adding the number of leaves can be helpful when interpreting a diagram
Completion times 3 4 5 6 7 8 2
(1)
(17)
(6)
(4)

66. Example - drawing a stem and leaf
Answer (b):- find the median, quartiles and inter-quartile range
Completion times 3 4 5 6 7 8 2
(1)
(17)
(6)
(4)
The median is the middle value:
n/2 = 29/2 = 14.5
 15th value =
Not whole - so round up
to whole
Find the 15th value

67. Example - drawing a stem and leaf
Answer (b):- find the median, quartiles and inter-quartile range
Completion times 3 4 5 6 7 8 2
(1)
(17)
(6)
(4)
The median is the middle value:
n/2 = 29/2 = 14.5
 15th value =
47 seconds
Not whole - so round up
to whole
Find the 15th value

68. Example - drawing a stem and leaf
Answer (b):- find the median, quartiles and inter-quartile range
Completion times 3 4 5 6 7 8 2
(1)
(17)
(6)
(4)
The median is the middle value:
n/2 = 29/2 = 14.5
 15th value =
47 seconds
The lower quartile, Q1, is the 1/4th value:
n/4 = 29/4 = 7.25
 8th value =
not whole - so round up
to whole

69. Example - drawing a stem and leaf
Answer (b):- find the median, quartiles and inter-quartile range
Completion times 3 4 5 6 7 8 2
(1)
(17)
(6)
(4)
The median is the middle value:
n/2 = 29/2 = 14.5
 15th value =
47 seconds
The lower quartile, Q1, is the 1/4th value:
n/4 = 29/4 = 7.25
 8th value =
44 seconds
not whole - so round up
to whole

70. Example - drawing a stem and leaf
Answer (b):- find the median, quartiles and inter-quartile range
Completion times 3 4 5 6 7 8 2
(1)
(17)
(6)
(4)
The median is the middle value:
n/2 = 29/2 = 14.5
 15th value =
47 seconds
The lower quartile, Q1, is the 1/4th value:
n/4 = 29/4 = 7.25
 8th value =
44 seconds
The upper quartile, Q3, is the 3/4th value:
3n/4 = 3x29/4 = 21.75
 22nd value =
not whole - so round up
to whole

71. Example - drawing a stem and leaf
Answer (b):- find the median, quartiles and inter-quartile range
Completion times 3 4 5 6 7 8 2
(1)
(17)
(6)
(4)
The median is the middle value:
n/2 = 29/2 = 14.5
 15th value =
47 seconds
The lower quartile, Q1, is the 1/4th value:
n/4 = 29/4 = 7.25
 8th value =
44 seconds
The upper quartile, Q3, is the 3/4th value:
3n/4 = 3x29/4 = 21.75
 22nd value =
54 seconds
not whole -so round up
to whole

72. Example - drawing a stem and leaf
Answer (b):- find the median, quartiles and inter-quartile range
Completion times 3 4 5 6 7 8 2
(1)
(17)
(6)
(4)
The median is the middle value:
n/2 = 29/2 = 14.5
 15th value =
47 seconds
The lower quartile, Q1, is the 1/4th value:
n/4 = 29/4 = 7.25
 8th value =
44 seconds
The upper quartile, Q3, is the 3/4th value:
3n/4 = 3x29/4 = 21.75
 22nd value =
54 seconds
The inter quartile range = Q3 – Q1 = 54 – 44 = 10 seconds

73. Note:
you are more likely to be required to interpret a stem and leaf diagram than to have to draw one
the textbook examples use a stem consisting of one digit. More digits are possible.
The range of values should not be too great - otherwise the values may need to be rounded so that the number of stems does not become too large
Stem and leaf diagrams can be drawn back to back for comparisons – much like bar charts.