Introduction to calculating interquartile range

1. - Mr Kim

2. Finding IQR for even number of scores

3. 12 13 21 28 29 31 31 32 33 34 38 39

4. 12 13 21 28 29 31 31 32 33 34 38 39
Here are some
random scores

5. 12 13 21 28 29 31 31 32 33 34 38 39
**Make sure the scores are
in Ascending Order first!

6. 12 13 21 28 29 31 31 32 33 34 38 39
**Make sure the scores are
in Ascending Order first!

7. 12 13 21 28 29 31 31 32 33 34 38 39
**Make sure the scores are
in Ascending Order first!
This means the scores
are written from
smallest to largest

8. 21 39 12 31 31 28 29 32 38 34 33 13
For example this is not in
Ascending Order

9. 21 39 12 31 31 28 29 32 38 34 33 13
For example this is not in
Ascending Order
Because the scores are
not written from
smallest to largest

10. 12 13 21 28 29 31 31 32 33 34 38 39

11. 12 13 21 28 29 31 31 32 33 34 38 39
First, find the Median by
crossing off the scores

12. 12 13 21 28 29 31 31 32 33 34 38 39
Start with the smallest
score

13. 12 13 21 28 29 31 31 32 33 34 38 39

14. 12 13 21 28 29 31 31 32 33 34 38 39
Now cross off the
largest score

15. 12 13 21 28 29 31 31 32 33 34 38 39

16. 12 13 21 28 29 31 31 32 33 34 38 39
Now cross off the next
smallest score

17. 12 13 21 28 29 31 31 32 33 34 38 39

18. 12 13 21 28 29 31 31 32 33 34 38 39
Now cross off the next
largest score

19. 12 13 21 28 29 31 31 32 33 34 38 39

20. 12 13 21 28 29 31 31 32 33 34 38 39
Next smallest score

21. 12 13 21 28 29 31 31 32 33 34 38 39

22. 12 13 21 28 29 31 31 32 33 34 38 39
Next largest score

23. 12 13 21 28 29 31 31 32 33 34 38 39

24. 12 13 21 28 29 31 31 32 33 34 38 39
Continue crossing off in
that order

25. 12 13 21 28 29 31 31 32 33 34 38 39
“In”

26. 12 13 21 28 29 31 31 32 33 34 38 39
“Out”

27. 12 13 21 28 29 31 31 32 33 34 38 39
“In”

28. 12 13 21 28 29 31 31 32 33 34 38 39
“Out”

29. 12 13 21 28 29 31 31 32 33 34 38 39
Stop here

30. 12 13 21 28 29 31 31 32 33 34 38 39
Always stop at “Out”

31. 12 13 21 28 29 31 31 32 33 34 38 39
If you continue, you will
cross off all the scores.
You don’t want that!

32. 12 13 21 28 29 31 31 32 33 34 38 39

33. 12 13 21 28 29 31 31 32 33 34 38 39
The Median (Q2) is in between
31 and 31 which is…

34. 12 13 21 28 29 31 31 32 33 34 38 39
The Median (Q2) is in between
31 and 31 which is 31

35. 12 13 21 28 29 31 31 32 33 34 38 39
Now, put a line between
those two scores

36. 12 13 21 28 29 31 31 32 33 34 38 39

37. 12 13 21 28 29 31 31 32 33 34 38 39
Now find the Median for
both sides of the scores

38. 12 13 21 28 29 31 31 32 33 34 38 39
Start with this side

39. 12 13 21 28 29 31 31 32 33 34 38 39
Remember to cross off in
the order: “In” “Out”

40. 12 13 21 28 29 31 31 32 33 34 38 39
“In”

41. 12 13 21 28 29 31 31 32 33 34 38 39
“Out”

42. 12 13 21 28 29 31 31 32 33 34 38 39
“In”

43. 12 13 21 28 29 31 31 32 33 34 38 39
“Out”

44. 12 13 21 28 29 31 31 32 33 34 38 39
Stop here

45. 12 13 21 28 29 31 31 32 33 34 38 39

46. 12 13 21 28 29 31 31 32 33 34 38 39
The Lower Quartile (Q1) is in
between 21 and 28 which is…

47. 12 13 21 28 29 31 31 32 33 34 38 39
The Lower Quartile (Q1) is in
between 21 and 28 which is…
21

48. The Lower Quartile (Q1) is in
between 21 and 28 which is…
12 13 21 28 29 31 31 32 33 34 38 39
2821

49. The Lower Quartile (Q1) is in
between 21 and 28 which is…
12 13 21 28 29 31 31 32 33 34 38 39
2
2821

50. The Lower Quartile (Q1) is in
between 21 and 28 which is…
12 13 21 28 29 31 31 32 33 34 38 39
5.24
2
2821



51. 12 13 21 28 29 31 31 32 33 34 38 39
The Lower Quartile (Q1) is in
between 21 and 28 which is
24.5

52. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5

53. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5

54. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Now cross off this side
of the scores

55. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
“In”

56. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
“Out”

57. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
“In”

58. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
“Out”

59. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Stop here

60. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5

61. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
The Upper Quartile (Q3) is in
between 33 and 34 which is
…

62. The Upper Quartile (Q3) is in
between 33 and 34 which is
…
12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
33

63. The Upper Quartile (Q3) is in
between 33 and 34 which is
…
12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
3433

64. The Upper Quartile (Q3) is in
between 33 and 34 which is
…
12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
2
3433

65. The Upper Quartile (Q3) is in
between 33 and 34 which is
…
12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
5.33
2
3433



66. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
The Upper Quartile (Q3) is in
between 33 and 34 which is
33.5

67. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Upper Quartile:
33.5

68. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Upper Quartile:
33.5
Interquartile Range=
Upper Quartile – Lower Quartile

69. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Upper Quartile:
33.5
Interquartile Range=
Upper Quartile – Lower Quartile

70. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Upper Quartile:
33.5
Interquartile Range=
Upper Quartile – Lower Quartile
33.5 -

71. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Upper Quartile:
33.5
Interquartile Range=
Upper Quartile – Lower Quartile
33.5 -

72. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Upper Quartile:
33.5
Interquartile Range=
Upper Quartile – Lower Quartile
33.5 – 24.5

73. 12 13 21 28 29 31 31 32 33 34 38 39
Lower Quartile:
24.5
Upper Quartile:
33.5
Interquartile Range=
Upper Quartile – Lower Quartile
33.5 – 24.5 = 9 Our Final Answer!

74. Finding IQR for odd number of scores

75. 16 31 37 39 42 44 56 58 60 63 71
Here are some
random scores

76. 16 31 37 39 42 44 56 58 60 63 71
Same steps as before.
Find the Median by crossing
off the scores

77. 16 31 37 39 42 44 56 58 60 63 71
**Make sure the scores are
in Ascending Order first!

78. 16 31 37 39 42 44 56 58 60 63 71
“In”

79. 16 31 37 39 42 44 56 58 60 63 71
“Out”

80. 16 31 37 39 42 44 56 58 60 63 71
“In”

81. 16 31 37 39 42 44 56 58 60 63 71
“Out”

82. 16 31 37 39 42 44 56 58 60 63 71
“In”

83. 16 31 37 39 42 44 56 58 60 63 71
“Out”

84. 16 31 37 39 42 44 56 58 60 63 71
“In”

85. 16 31 37 39 42 44 56 58 60 63 71
“Out”

86. 16 31 37 39 42 44 56 58 60 63 71
“In”

87. 16 31 37 39 42 44 56 58 60 63 71
“Out”

88. 16 31 37 39 42 44 56 58 60 63 71
Stop here

89. 16 31 37 39 42 44 56 58 60 63 71
So the Median (Q2) is 44

90. 16 31 37 39 42 44 56 58 60 63 71
Put 2 lines around the
Median

91. 16 31 37 39 42 44 56 58 60 63 71

92. 16 31 37 39 42 44 56 58 60 63 71
Now find the Median for
both sides of the scores

93. 16 31 37 39 42 44 56 58 60 63 71
Start with this side

94. 16 31 37 39 42 44 56 58 60 63 71
“In”

95. 16 31 37 39 42 44 56 58 60 63 71
“Out”

96. 16 31 37 39 42 44 56 58 60 63 71
“In”

97. 16 31 37 39 42 44 56 58 60 63 71
“Out”

98. 16 31 37 39 42 44 56 58 60 63 71
Stop here

99. 16 31 37 39 42 44 56 58 60 63 71
The Lower Quartile (Q1) is 37

100. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37

101. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37

102. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
Now cross off this side
of the scores

103. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
“In”

104. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
“Out”

105. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
“In”

106. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
“Out”

107. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
Stop here

108. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
The Upper Quartile (Q3) is 60

109. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
Upper Quartile:
60

110. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
Upper Quartile:
60
Interquartile Range=
Upper Quartile – Lower Quartile

111. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
Upper Quartile:
60
Interquartile Range=
Upper Quartile – Lower Quartile
60 -

112. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
Upper Quartile:
60
Interquartile Range=
Upper Quartile – Lower Quartile
60 - 37

113. 16 31 37 39 42 44 56 58 60 63 71
Lower Quartile:
37
Upper Quartile:
60
Interquartile Range=
Upper Quartile – Lower Quartile
60 – 37 = 23 Our Final Answer!