You can find the median value of a frequency table by using the following steps:

Step 1: Arrange all of the individual values from smallest to largest.

Step 2: Identify the value directly in the middle of the ordered list.

• If there are an odd number of values, the median is the value directly in the middle.
• If there are an even number of values, the median is the average of the middle two values.

The following examples show how to find the median value of a frequency table in practice.

Example 1: Median from Frequency Table (Odd Number of Values)

The following frequency table shows the total number of wins for 17 soccer teams in a certain league:

We can use the following steps to find the median value in this frequency table:

Step 1: Arrange all of the individual values from smallest to largest.

Values: 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6

Step 2: Identify the value directly in the middle of the ordered list.

Values: 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6

The median value is 2.

Example 2: Median from Frequency Table (Even Number of Values)

The following frequency table shows the household size of 20 different households in a particular area:

Step 1: Arrange all of the individual values from smallest to largest.

Values: 1, 1, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8

Step 2: Identify the value directly in the middle of the ordered list.

Values: 1, 1, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8

There are two values located directly in the middle: 4 and 4.

Thus, the median value is the average of these two values: (4 + 4) / 2 = 4.