A trimmed mean is the mean of a dataset that has been calculated after removing a specific percentage of the smallest and largest values from the dataset.
To calculate a X% trimmed mean, you can use the following steps:
Step 1: Order each value in a dataset from smallest to largest.
Step 2: Remove the values in the bottom X% and top X% of the dataset.
Step 3: Calculate the mean of the remaining values.
The following examples show how to calculate a trimmed mean in practice.
Example 1: Calculate a 10% Trimmed Mean
Suppose we have the following dataset:
Dataset: 4, 8, 12, 15, 9, 6, 14, 18, 12, 9
Here is how to calculate the 10% trimmed mean for the dataset:
Step 1: Order each value in a dataset from smallest to largest.
Ordered Dataset: 4, 6, 8, 9, 9, 12, 12, 14, 15, 18
Step 2: Remove the values in the bottom 10% and top 10% of the dataset.
There are 10 total values in the dataset. Thus, 10% * 10 = 1. This means we need to remove the one smallest value and one largest value from the dataset:
Trimmed Dataset: 6, 8, 9, 9, 12, 12, 14, 15
Step 3: Calculate the mean of the remaining values.
10% trimmed mean = (6+8+9+9+12+12+14+15) / 8 = 10.625
The 10% trimmed mean is 10.625.
Example 2: Calculate a 20% Trimmed Mean
Suppose we have the following dataset:
Dataset: 22, 25, 29, 11, 14, 18, 13, 13, 17, 11, 8, 8, 7, 12, 15, 6, 8, 7, 9, 12
Here is how to calculate the 20% trimmed mean for the dataset:
Step 1: Order each value in a dataset from smallest to largest.
Ordered Dataset: 6, 7, 7, 8, 8, 8, 9, 11, 11, 12, 12, 13, 13, 14, 15, 17, 18, 22, 25, 29
Step 2: Remove the values in the bottom 20% and top 20% of the dataset.
There are 20 total values in the dataset. Thus, 20% * 20 = 4. This means we need to remove the four smallest values and four largest values from the dataset:
Trimmed Dataset: 8, 8, 9, 11, 11, 12, 12, 13, 13, 14, 15, 17
Step 3: Calculate the mean of the remaining values.
20% trimmed mean = (8+8+9+11+11+12+12+13+13+14+15+17) / 12 = 11.9167
The 20% trimmed mean is 11.9167.
Bonus Resource: Trimmed Mean Calculator
If you have an extremely large dataset and do not want to calculate a trimmed mean by hand, feel free to use this Trimmed Mean Calculator.
For example, here’s how to use this calculator to find the 20% trimmed mean from the previous dataset:
Notice that the 20% trimmed mean matches the value that we calculated by hand.