Trimmed Mean CalculatorFree online math calculator — instant results, no sign-up
Calculate a mean after removing a percentage from each tail.
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About the Trimmed Mean Calculator
The Trimmed Mean Calculator finds an average after removing a specified percentage of values from both the low and high ends of a sorted dataset. The trim percentage applies to each tail separately, reducing the influence of extreme values. With the default values 1, 2, 3, 4, 100 and a 20% trim per tail, it removes 1 and 100 and returns a trimmed mean of 3.
- Values
- Enter the numerical observations to average, such as the default 1, 2, 3, 4, 100, using the same measurement units for all values.
- Trim per tail (%)
- Enter the percentage of observations to remove from each end of the sorted data, with the default 20 meaning 20% from the lowest end and 20% from the highest end.
Formula and method
k = floor(n × p / 100); m = n − 2k; trimmed mean = (Σ from i = k + 1 to n − k of x_(i)) / m. For the default inputs: k = floor(5 × 20 / 100) = 1, m = 5 − 2 = 3, and trimmed mean = (2 + 3 + 4) / 3 = 3.
- nThe number of observations in the original dataset.
- pThe trim percentage applied separately to each tail.
- kThe whole number of observations removed from each tail.
- floorThe operation that rounds down to the nearest integer.
- mThe number of observations remaining after trimming.
- x_(i)The observation in position i after sorting the values from smallest to largest.
- iThe position index in the sorted dataset.
- ΣThe sum of the retained observations over the indicated positions.
Sort the observations in ascending order. Multiply the observation count by the trim percentage divided by 100, then round down to obtain the number removed from each tail. Remove that many observations from both ends and calculate the arithmetic mean of the remaining values. For 1, 2, 3, 4, 100 at 20% per tail, remove one observation from each end, leaving 2, 3, 4; their sum is 9 and their mean is 3.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Values1, 2, 3, 4, 100
- Trim per tail (%)20
Results
- Trimmed mean3
How to use the Trimmed Mean Calculator
- 1Enter the observations in Values; the default dataset is 1, 2, 3, 4, 100.
- 2Set Trim per tail (%) to the percentage to remove from each end; use 20 for the default example.
- 3Run the calculation to sort the data and determine the whole-number trim count.
- 4Check the retained observations: the default example removes 1 and 100, leaving 2, 3, 4.
- 5Read the trimmed mean: the default result is 3, expressed in the same units as the input values.
Reading your result
The Trimmed mean result is the arithmetic average of the observations left after trimming, not the average of the full dataset. For the default inputs, this output is 3. Any supporting trim count should be read as a count per tail: one value is removed from each end, two are removed in total, and three remain. The 20% setting therefore removes 40% of the observations in total in this example.
Limitations
This documentation uses whole-observation trimming with the trim count rounded down; fractional weighting or other rounding conventions can produce different results. Use a trim percentage from 0% up to, but not including, 50%, and supply at least one valid numerical observation. Small datasets may lose no observations at low trim percentages because of rounding. Trimming removes observations by rank, not by whether they are proven errors, and can discard meaningful extreme values. All observations are equally weighted, and the result alone does not describe variability or uncertainty.
Common questions
Does a 20% trim remove 20% of the dataset in total?+
No. This calculator applies 20% to each tail separately. With the five default observations, it removes one lowest value and one highest value, removing 40% of the dataset in total.
Why is the default trimmed mean 3 even though the dataset contains 100?+
After sorting 1, 2, 3, 4, 100, the 20% trim removes 1 and 100. Only 2, 3, 4 contribute to the result, so the trimmed mean is (2 + 3 + 4) / 3 = 3.
What happens when the trim percentage implies a fraction of an observation?+
Under the rounding-down convention, the calculator removes floor(n × p / 100) whole observations from each tail. The actual percentage removed can therefore be smaller than the requested percentage.
Is the trimmed mean always the same as the median?+
No. The trimmed mean averages all retained observations, whereas the median identifies the center of the sorted dataset. They both equal 3 for the default inputs, but that agreement is not guaranteed for other datasets.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.