Calculating IQR from stem leaf plot with Even number of scores with step by step illustration

1. - Mr Kim

2. Finding IQR for even number of scores

3. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

4. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
First, find the Median by
crossing off the scores

5. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Now, start by crossing
off the Smallest Number

6. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
2
Now, start by crossing
off the Smallest Number

7. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

8. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Now cross off the
Biggest Number

9. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
47
Now cross off the
Biggest Number

10. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

11. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Cross off the scores in
the directions shown

12. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“In”

13. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“Out”

14. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“In”

15. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Notice there is
nothing in the 30’s

16. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
So skip to the next
score

17. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“Out”

18. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“In”

19. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“Out”

20. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“In”

21. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“Out”

22. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Stop here

23. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Always stop at “Out”

24. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Put a line between the
two scores

25. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Put a line between the
two scores

26. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

27. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
12
11

28. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
So the Median (Q2) is in
between 11 and 12
which is …
12
11

29. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
So the Median (Q2) is in
between 11 and 12
which is 11.5
11
12

30. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
So the Median (Q2) is in
between 11 and 12
which is 11.5
11+12
2
11
=11.5
12

31. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

32. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Now find the Lower and
Upper Quartile by dividing
the Stem-Leaf Plot in two

33. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
**It is very important to
divide the sides properly

34. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
To do this, count the
scores from the start
until you reach the Line

35. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

36. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

37. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

38. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

39. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

40. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

41. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Stop here!

42. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Now put a Border around
the scores that you just
counted

43. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

44. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Now put a Border around
the other side

45. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

46. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
This is how you correctly
divide the sides

47. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Now find the Median for
both sides of the scores by
crossing off each side at a
time

48. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
We will start with
this side

49. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Remember the
directions

50. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“In”

51. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“Out”

52. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“In”

53. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
“Out”

54. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Stop here!

55. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7

56. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
43

57. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
So the Lower Quartile (Q1)
is between 3 and 4
which is …
43

58. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
43
So the Lower Quartile (Q1)
is between 3 and 4
which is 3.5

59. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
43
So the Lower Quartile (Q1)
is between 3 and 4
which is 3.5
3+4
2
= 3.5

60. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5

61. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
Now cross off the
other side

62. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
Remember the
directions

63. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
“In”

64. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
“Out”

65. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
“In”

66. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
“Out”

67. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
Stop here!

68. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5

69. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
2320

70. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
So the Upper Quartile (Q3)
is between 20 and 23
which is …
2320

71. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
So the Upper Quartile (Q3)
is between 20 and 23
which is 21.5
2320

72. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
So the Upper Quartile (Q3)
is between 20 and 23
which is 21.5
2320
20+23
2
= 21.5

73. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
Upper Quartile:
21.5

74. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
So, the Interquartile Range is
Upper Quartile:
21.5

75. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
So, the Interquartile Range is
Upper Quartile:
21.5

76. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
Upper Quartile:
21.5
So, the Interquartile Range is
21.5 –

77. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
Upper Quartile:
21.5
So, the Interquartile Range is
21.5 –

78. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
Upper Quartile:
21.5
So, the Interquartile Range is
21.5 – 3.5

79. 0 2 2 3 4 6
1 1 2
2 0 0 3
3
4 5 7
Lower Quartile:
3.5
Upper Quartile:
21.5
So, the Interquartile Range is
21.5 – 3.5 = 18
Our Final Answer!