Calculating IQR from c.f histogram polygon with step by step illustration

1. - Mr Kim

2. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f

3. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
This is a Cumulative
Frequency Histogram
Polygon

4. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
x
1. Find the Upper Quartile

5. 3 4 5 6 7
0
5
10
15
20
25
30
8
Upper Quartile:
c.f
x

4
3

6. 3 4 5 6 7
0
5
10
15
20
25
30
8
Upper Quartile:
c.f
x

4
3
For Upper Quartile,
always
Multiply by
4
3

7. 3 4 5 6 7
0
5
10
15
20
25
30
8
Upper Quartile:
c.f
x

4
3
Locate the highest column

8. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
Upper Quartile:
c.f
x

4
3

9. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
Upper Quartile:
c.f
x

4
3

10. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
Upper Quartile:
c.f
x

4
3

11. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
Upper Quartile:
c.f
x
30
4
3


12. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
Upper Quartile:
5.22
30
4
3


c.f

13. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
Upper Quartile:
c.f
x
5.22
30
4
3


Locate 22.5 on the c.f axis

14. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
Upper Quartile:
c.f
x
5.22
30
4
3


Locate 22.5 on the c.f axis

15. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
x
Draw a horizontal line from the
dot until it hits the Polygon

16. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
x
Draw a horizontal line from the
dot until it hits the Polygon

17. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
x
Now draw a Vertical line all the
way down to the Score

18. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
x

19. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
x

20. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
x
Upper Quartile: 8

21. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
x
Upper Quartile: 8
2. Now find the Lower Quartile

22. 3 4 5 6 7
0
5
10
15
20
25
30
8
Lower Quartile:
c.f
x

4
1
Upper Quartile: 8

23. 3 4 5 6 7
0
5
10
15
20
25
30
8
Lower Quartile:
c.f
x

4
1
Upper Quartile: 8
For Lower Quartile,
always
Multiply by
4
1

24. 3 4 5 6 7
0
5
10
15
20
25
30
8
Lower Quartile:
c.f
x

4
1
Upper Quartile: 8

25. 3 4 5 6 7
0
5
10
15
20
25
30
8
Lower Quartile:
c.f
x

4
1
Upper Quartile: 8
Remember the highest
column was 30

26. 3 4 5 6 7
0
5
10
15
20
25
30
8
Lower Quartile:
c.f
x
30
4
1

Upper Quartile: 8

27. 3 4 5 6 7
0
5
10
15
20
25
30
8
Lower Quartile:
c.f
x
5.7
30
4
1


Upper Quartile: 8

28. 3 4 5 6 7
0
5
10
15
20
25
30
8
Lower Quartile:
c.f
x
5.7
30
4
1


Upper Quartile: 8
Locate 7.5 on the c.f axis

29. 3 4 5 6 7
0
5
10
15
20
25
30
8
Lower Quartile:
c.f
x
5.7
30
4
1


Upper Quartile: 8
Locate 7.5 on the c.f axis

30. 3 4 5 6 7
0
5
10
15
20
25
30
8
c.f
x
Upper Quartile: 8
Horizontal line

31. 3 4 5 6 7
0
5
10
15
20
25
30
8
c.f
x
Upper Quartile: 8
Horizontal line

32. 3 4 5 6 7
0
5
10
15
20
25
30
8
c.f
x
Upper Quartile: 8

33. 3 4 5 6 7
0
5
10
15
20
25
30
8
c.f
x
Upper Quartile: 8
The arrow is pointing exactly
half way between 5 and 6

34. 3 4 5 6 7
0
5
10
15
20
25
30
8
c.f
x
Upper Quartile: 8
So, the Lower Quartile (𝑄1) is
5.5

35. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Upper Quartile: 8
Lower Quartile:
5.5

36. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Upper Quartile: 8
Lower Quartile:
5.5
So, the Interquartile Range is:

37. x3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
c.f
Upper Quartile: 8
Lower Quartile:
5.5
So, the Interquartile Range is:

38. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Upper Quartile: 8
Lower Quartile:
5.5
So, the Interquartile Range is:
8 -

39. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Upper Quartile: 8
Lower Quartile:
5.5
So, the Interquartile Range is:
8 -

40. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Upper Quartile: 8
Lower Quartile:
5.5
So, the Interquartile Range is:
8 – 5.5

41. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Upper Quartile: 8
Lower Quartile:
5.5
So, the Interquartile Range is:
8 – 5.5 = 2.5
Our Final Answer!

42. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f

43. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
The Median (Q2 ) can be found
from the graph as well

44. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Median:

2
1

45. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Median:

2
1
For the Median,
always
Multiply by
2
1

46. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Median:

2
1

47. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Median:
30
2
1


48. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Median:
15
30
2
1



49. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Median:
15
30
2
1


Locate 15 on the c.f axis

50. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Median:
15
30
2
1


Locate 15 on the c.f axis

51. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f

52. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f

53. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
Look where the arrow is
pointing

54. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
The Median is just below 7,
by estimation it is 6.8

55. 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
x
c.f
So the Median is 6.8
Our Final Answer!