Trimmed Mean Calculator Formula
Understand the math behind the trimmed mean calculator. Each variable explained with a worked example.
Formulas Used
Trimmed Mean (drop highest & lowest)
trimmed_mean = trimmed_sum / 3Regular Mean
regular_mean = full_meanDifference
difference = full_mean - trimmed_sum / 3Variables
| Variable | Description | Default |
|---|---|---|
v1 | Smallest Value | 2 |
v2 | Value 2 | 10 |
v3 | Value 3 | 12 |
v4 | Value 4 | 14 |
v5 | Largest Value | 98 |
full_mean | Derived value= (v1 + v2 + v3 + v4 + v5) / 5 | calculated |
trimmed_sum | Derived value= v2 + v3 + v4 | calculated |
How It Works
How the Trimmed Mean Works
Approach
1. Sort the values from smallest to largest 2. Remove a fixed percentage from each end (here, one value from each end) 3. Average the remaining values
Trimmed Mean = Sum of remaining values / Count of remaining values
This technique protects the average from outliers while still using most of the data. A common choice is a 20% trimmed mean, which removes the top and bottom 20% of observations.
Worked Example
Data: 2, 10, 12, 14, 98. Compute the trimmed mean removing one value from each end.
- 01Sorted values: 2, 10, 12, 14, 98
- 02Remove lowest (2) and highest (98)
- 03Remaining: 10, 12, 14
- 04Trimmed Mean = (10 + 12 + 14) / 3 = 12
- 05Compare: Regular Mean = 136 / 5 = 27.2 (heavily influenced by 98)
Frequently Asked Questions
What percentage should I trim?
Common choices are 5%, 10%, or 20% from each end. Higher trim percentages provide more resistance to outliers but discard more data.
How does the trimmed mean relate to the median?
The median is the extreme case of trimming: you remove everything except the middle value(s). The trimmed mean sits between the ordinary mean and the median in terms of robustness.
Is the trimmed mean used in practice?
Yes. It is used in Olympic scoring (dropping highest and lowest judges), inflation measurement (the Federal Reserve Bank of Cleveland publishes a trimmed-mean CPI), and robust statistical analysis.
Ready to run the numbers?
Open Trimmed Mean Calculator