Table of Contents
To calculate the mean from a frequency table, you need to add up all the values in the table multiplied by their respective frequencies, and divide this total by the sum of the frequencies. As an example, if a frequency table showed the values 1, 2, 3, 4, 5, and 6, each occurring once, the mean would be calculated by adding 1 + 2 + 3 + 4 + 5 + 6 and dividing by 6, resulting in a mean of 3.5.
You can calculate the mean of a frequency table by using the following formula:
Mean = Σfx / Σf
where:
- Σ: A fancy symbol that means “sum”
- f: The frequency of a particular value
- x: The value in the frequency table
The following examples show how to use this formula in practice.
Example 1: Mean Number of Wins
The following frequency table shows the total number of wins for 30 soccer teams in a certain league:
We can use the following formula to calculate the mean number of wins:
- Mean = (0*2 + 1*3 + 2*7 + 3*8 + 4*7 + 5*3) / (2 + 3 + 7 + 8 + 7 + 3)
- Mean = (0 + 3 + 14 + 24 + 28 + 15) / (30)
- Mean = (84) / (30)
- Mean = 2.8
The mean number of wins is 2.8.
Example 2: Mean Number of Pets
The following frequency table shows the total number of pets owned by 20 different families in a certain neighborhood:
We can use the following formula to calculate the mean number of pets owned:
- Mean = (0*2 + 1*10 + 2*4 + 3*3 + 4*1) / (2 + 10 + 4 + 3 + 1)
- Mean = (0 + 10 + 8 + 9 + 4) / (20)
- Mean = (31) / (20)
- Mean = 1.55
The mean number of pets owned is 1.55.
Example 3: Mean Household Size
The following frequency table shows the household size of 40 different households in a particular area:
We can use the following formula to calculate the mean household size:
- Mean = (1*2 + 2*4 + 3*14 + 4*13 + 5*4 + 6*2 + 7*1) / (2 + 4 + 14 + 13 + 4 + 2+1)
- Mean = (2 + 8 + 42 + 52 + 20 + 12 + 7) / (40)
- Mean = (143) / (40)
- Mean = 3.575
The mean household size is 3.575.