Example:
The following is a frequency table of the score obtained in a mathematics quiz. Find the median score.
Score |
0 |
1 |
2 |
3 |
4 |
Frequency |
3 |
4 |
7 |
6 |
3 |
Solution:
Number of scores = 3 + 4 + 7 + 6 + 3 = 23 (odd number)
Since the number of scores is odd,
the median is at the position
To find out the 12 ^{th} position, we need to add up the frequencies as shown:
Score |
0 |
1 |
2 |
3 |
4 |
Frequency |
3 |
4 |
7 |
6 |
3 |
Position |
3 |
3 + 4 = 7 |
7 + 7 =14 |
The 12^{th} position is after the 7^{th} position but before the 14^{th} position. So, the median is 2.
Example:
The table is a frequency table of the scores obtained in a competition. Find the median score.
Scores |
0 |
1 |
2 |
3 |
4 |
Frequency |
11 |
9 |
5 |
10 |
15 |
Solution:
Number of scores = 11 + 9 + 5 + 10 + 15 = 50 (even number)
Since the number of scores is even, the median is at the average of the position and position
To find out the 25^{th} position and 26^{th} position, we add up the frequencies as shown:
Scores |
0 |
1 |
2 |
3 |
4 |
Frequency |
11 |
9 |
5 |
10 |
15 |
Position |
11 |
11 + 9 = 20 |
20 + 5 = 25 |
25 + 10 = 35 |
36 to 50 |
The score at the 25^{th} position is 2 and the score at the 26^{th} position is 3. The median is the average of the scores at 25^{th} and 26^{th} positions =