The document shows the step-by-step process of constructing a cumulative frequency histogram from a frequency table. It begins with a frequency table listing test scores and their frequencies. A cumulative frequency column is added and filled in by summing the frequencies. A grid is created with the scores and cumulative frequencies, and values are plotted on the x and y axes to draw the histogram.

1. - Mr Kim

2. Score, x Frequency, f
2 2
3 5
4 11
5 7
6 10
7 9
8 6

3. Score, x Frequency, f
2 2
3 5
4 11
5 7
6 10
7 9
8 6
This is a
Frequency
Table

4. Score, x Frequency, f
2 2
3 5
4 11
5 7
6 10
7 9
8 6

5. Score, x Frequency, f
2 2
3 5
4 11
5 7
6 10
7 9
8 6
To draw a Cumulative Frequency
Histogram Polygon,
a cf column must be
added and filled in

6. Score, x Frequency, f Cumulative
Frequency, cf
2 2
3 5
4 11
5 7
6 10
7 9
8 6
To draw a Cumulative Frequency
Histogram Polygon,
a cf column must be
added and filled in

7. Score, x Frequency, f Cumulative
Frequency, cf
2 2
3 5
4 11
5 7
6 10
7 9
8 6

8. Score, x Frequency, f Cumulative
Frequency, cf
2 2
3 5
4 11
5 7
6 10
7 9
8 6
The first number is always
the same as the first
frequency number

9. Score, x Frequency, f Cumulative
Frequency, cf
2 2
3 5
4 11
5 7
6 10
7 9
8 6
The first number is always
the same as the first
frequency number

10. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5
4 11
5 7
6 10
7 9
8 6

11. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5
4 11
5 7
6 10
7 9
8 6

12. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5
4 11
5 7
6 10
7 9
8 6

13. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5
4 11
5 7
6 10
7 9
8 6

14. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11
5 7
6 10
7 9
8 6

15. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11
5 7
6 10
7 9
8 6

16. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11
5 7
6 10
7 9
8 6

17. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11
5 7
6 10
7 9
8 6

18. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7
6 10
7 9
8 6

19. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7
6 10
7 9
8 6

20. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7
6 10
7 9
8 6

21. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10
7 9
8 6

22. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10
7 9
8 6

23. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10
7 9
8 6

24. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9
8 6

25. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9
8 6

26. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6

27. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6

28. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50

29. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50

30. Score, x Frequency, f Cumulative
Frequency, cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50
Now that’s complete, time to
start drawing the graph

31. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50

32. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50
Here’s our grid to fill
in the values

33. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
All the Scores go on
the Horizontal axis

34. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x

35. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2

36. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2
Notice how 2 starts
here

37. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2
Not here

38. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2

39. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3

40. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3

41. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4

42. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4

43. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5

44. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6

45. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7

46. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8

47. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
All the cf values go on
the Vertical axis

48. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
Start from 0 and let’s go
up by 10s until we reach …

49. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
Start from 0 and let’s go
up by 10s until we reach
50

50. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10

51. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20

52. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30

53. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40

54. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

55. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
Now start plotting the
Histogram

56. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

57. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
2 is about there just
above 0

58. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
2 is about there just
above 0

59. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
There must be half unit
gap

60. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

61. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

62. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

63. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

64. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

65. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

66. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

67. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

68. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

69. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

70. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
That’s Histogram complete.
Let’s start the Polygon now

71. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
Start by plotting a dot in
the corner

72. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
The dots are placed at the end
of each histogram

73. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

74. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

75. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

76. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

77. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

78. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

79. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
Now, join them up using
straight lines

80. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

81. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

82. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

83. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

84. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

85. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

86. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50

87. x f cf
2 2 2
3 5 7
4 11 18
5 7 25
6 10 35
7 9 44
8 6 50 x
2 3 4 5 6 7 8
cf
0
10
20
30
40
50
And this is how you draw a
Cumulative Frequency
Histogram Polygon!