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In a frequency table, the observations are already arranged in an ascending order. We can obtain the median by looking for the value in the middle position.
Case 1. When the number of observations is odd, then the median is the value at the position.
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.
Case 2. When the number of observations is even, then the median is the average of values at the positions.
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 =
How to find the median from a frequency table (even)
Finding the Median of a frequency table
The following video shows how to find the mean, mode and median from a frequency table for both discrete and grouped data.
Estimating median, quartiles from a grouped frequency table.