How to find the median from frequency table with odd and even number of scores with step by step illustrations

1. - Mr Kim

2. Finding the median with even number of
scores

3. Score, x Frequency, f
10 6
11 4
12 10
13 11
14 5

4. Score, x Frequency, f
10 6
11 4
12 10
13 11
14 5
Here is a
Frequency
Table

5. Score, x Frequency, f
10 6
11 4
12 10
13 11
14 5
To find the Median,
a cf column must be
added and filled in

6. Score, x Frequency, f Cumulative
Frequency, cf
10 6
11 4
12 10
13 11
14 5
To find the Median,
a cf column must be
added and filled in

7. Score, x Frequency, f Cumulative
Frequency, cf
10 6
11 4
12 10
13 11
14 5

8. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4
12 10
13 11
14 5

9. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4
12 10
13 11
14 5

10. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4
12 10
13 11
14 5

11. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10
13 11
14 5

12. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10
13 11
14 5

13. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10
13 11
14 5

14. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11
14 5

15. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11
14 5

16. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5

17. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5

18. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36

19. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36

20. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
This is how many scores
there are in total

21. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
Notice how it’s an even
number

22. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
To find the Median
Divide this by 2

23. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
36 ÷ 2=

24. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
36 ÷ 2= 18

25. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
36 ÷ 2= 18
**If you have an even number you
have to look for that place score
and the one after as well

26. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
36 ÷ 2= 18
So look for the 18th score and…
**If you have an even number you
have to look for that place score
and the one after as well

27. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
36 ÷ 2= 18
So look for the 18th score and 19th score
**If you have an even number you
have to look for that place score
and the one after as well

28. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
So, under the cf column look
for the first number that is 18
or more

29. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36

30. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18 or more?

31. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
No.

32. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36

33. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18 or more?

34. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
No.

35. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36

36. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18 or more?

37. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
Yes!

38. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
So 18th score is in that row
Yes!

39. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
So 18th score is in that row
Yes!

40. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12

41. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
Now, under the cf column
look for the 19th score

42. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
19 or more?

43. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
No.

44. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
19 or more?

45. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
No.

46. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
19 or more?

47. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
Yes!

48. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
So 19th score is …
Yes!

49. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
So 19th score is also 12
Yes!

50. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
19th score: 12

51. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
19th score: 12
So the Median is in between
12 and 12 which is …

52. Score, x Frequency, f Cumulative
Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
18th score: 12
19th score: 12
So the Median is in between
12 and 12 which is 12
Our Final Answer!

53. Finding the median with odd number of
scores

54. Score, x Frequency, f
0 7
1 9
2 3
3 6
4 22

55. Score, x Frequency, f
0 7
1 9
2 3
3 6
4 22
Here is another
Frequency
Table

56. Same steps as before,
a cf column must be
added and filled in
Score, x Frequency, f
0 7
1 9
2 3
3 6
4 22

57. Score, x Frequency, f Cumulative
Frequency, cf
0 7
1 9
2 3
3 6
4 22
Same steps as before,
a cf column must be
added and filled in

58. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9
2 3
3 6
4 22

59. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9
2 3
3 6
4 22

60. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3
3 6
4 22

61. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3
3 6
4 22

62. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6
4 22

63. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22

64. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47

65. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47

66. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
This is how many scores
there are in total

67. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
Notice how it’s an odd
number

68. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
To find the Median
Divide this by 2

69. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
47 ÷ 2=

70. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
47 ÷ 2= 23.5

71. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
47 ÷ 2= 23.5
If you round this number up to
the next number you get…

72. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
47 ÷ 2= 23.5
If you round this number up to
the next number you get 24

73. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
47 ÷ 2= 23.5
If you round this number up to
the next number you get 24
**If you have an odd number you
look for that place score only

74. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
47 ÷ 2= 23.5
So look for the 24th score only
**If you have an odd number you
look for that place score only

75. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47

76. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
24 or more?

77. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
No.

78. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
24 or more?

79. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
No.

80. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
24 or more?

81. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
No.

82. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
24 or more?

83. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
Yes!

84. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
Yes!
So the Median is the score in
that row

85. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
Yes!
So the Median is the score in
that row

86. Score, x Frequency, f Cumulative
Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
So the Median is 3
Our Final Answer!