Median from Frequency Tables

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.

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:

The 12^th position is after the 7^th position and 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.

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:

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 =

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