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To calculate the median from a frequency table, you must first add up all the frequencies and then divide the total by two. This will give you the cumulative frequency up to the median. Then, find the row in the frequency table that contains the median cumulative frequency and the corresponding data value is the median. Examples of this calculation are provided to demonstrate the process.
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.