Median from Frequency TablesIn 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
Example: The following is a frequency table of the score obtained in a mathematics quiz. Find the median score.
Solution: Number of scores = 3 + 4 + 7 + 6 + 3 = 23 (odd number) Since the number of scores is odd, the median is at the To find out the 12 th position, we need to add up the frequencies as shown:
The 12th position is after the 7th position and before the 14th 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 Example: The table is a frequency table of the scores obtained in a competition. Find the median score.
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
To find out the 25th position and 26th position, we add up the frequencies as shown:
The score at the 25th position is 2 and the score at the 26th position is 3. The median is the average of the scores at 25th and 26th positions =
The following video shows how to find the mean, mode and median from a frequency table for both discrete and grouped data
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