Post on 17-Feb-2017
Finding: The Median from Frequency Table
1- Mr Kim
Example 1Finding the median with even number of
scores
Score, x Frequency, f
10 6
11 4
12 10
13 11
14 5
Score, x Frequency, f
10 6
11 4
12 10
13 11
14 5 Here is a Frequency
Table
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
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
Score, x Frequency, f Cumulative Frequency, cf
10 6
11 4
12 10
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4
12 10
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4
12 10
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4
12 10
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
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
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
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 MedianDivide this by 2
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
36 ÷ 2=
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
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
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
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
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
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 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?
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
No.
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 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?
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
No.
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 3618 or more?
Score, x Frequency, f Cumulative Frequency, cf
10 6 6
11 4 10
12 10 20
13 11 31
14 5 36Yes!
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!
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!
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
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
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?
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.
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?
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.
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?
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!
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!
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!
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
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 …
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!
Example 2Finding the median with odd number of
scores
Score, x Frequency, f
0 7
1 9
2 3
3 6
4 22
Score, x Frequency, f
0 7
1 9
2 3
3 6
4 22 Here is another
Frequency Table
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
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
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9
2 3
3 6
4 22
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9
2 3
3 6
4 22
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3
3 6
4 22
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3
3 6
4 22
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6
4 22
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
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
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
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 MedianDivide this by 2
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
47 ÷ 2=
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
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…
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
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
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
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
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?
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
No.
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?
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47
No.
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 4724 or more?
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47No.
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?
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47Yes!
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47Yes!
So the Median is the score in that row
Score, x Frequency, f Cumulative Frequency, cf
0 7 7
1 9 16
2 3 19
3 6 25
4 22 47Yes!
So the Median is the score in that row
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 3Our Final Answer!