What is a trimmed mean?
The trimmed mean uses most of your values while reducing the influence of the most extreme observations. It therefore often moves closer to the median than the ordinary mean does, especially when the data contains strong outliers.
Trimmed Mean = mean of the values remaining after removing k% from each end Why use a trimmed mean?
A trimmed mean reduces the influence of unusually low or high values by removing observations from both ends of an ordered dataset before calculating the average. It can be useful when a dataset contains extreme values that would otherwise have a large effect on the ordinary mean. For another way to describe the spread of data and identify potential outliers, see the IQR Calculator. Unlike a trimmed mean, the Mean Absolute Deviation Calculator measures how far values typically lie from the mean without removing observations.
Worked example
Take the data set 1, 2, 3, 4, 5, 6, 7, 100 with a 12.5% trim:
- Sort the data. It's already in order here.
- Work out how many values to remove from each end: 12.5% of 8 values is 1, so one value comes off each end.
- Remove the lowest value (1) and the highest value (100).
- Average what's left: 2 + 3 + 4 + 5 + 6 + 7 = 27, and 27 ÷ 6 = 4.5.
The 12.5% trimmed mean is 4.5. The ordinary mean of the same data is 16 — a figure larger than seven of the eight values in the set, dragged there entirely by the single reading of 100. The trimmed mean of 4.5 is much less influenced by the single extreme value of 100.
Note that both ends are trimmed, not just the high one. This symmetric rule reduces the influence of unusually low and high observations without choosing which individual values to remove after seeing the results.
How many values actually get removed?
A percentage rarely divides a data set evenly, so there's a convention: multiply the number of values by the trim percentage and round down. Trimming 25% of 10 values gives 2.5, so two values come off each end, not two and a half.
This is the convention used by SciPy's trim_mean and R's
mean(x, trim=), and it's what this calculator implements.
Other methods can handle fractional trimming differently, including methods that interpolate at the boundaries, so two calculators or textbooks can produce different results from the same trim percentage.
One consequence catches people out: on a small data set, a small trim percentage removes nothing at all. A 10% trim of 5 values works out at 0.5 per end, which rounds down to zero, so the result is just the ordinary mean. The calculator says so explicitly rather than quietly returning an untrimmed figure.
Choosing a trim percentage
- 5% or 10% — light trimming. Common for data you expect to be broadly clean, where you want protection against the occasional bad reading without discarding much.
- 20% or 25% — heavier trimming, removing a larger share of observations from both ends.
- 0% — no trimming at all, which returns the ordinary arithmetic mean.
- Approaching 50% — as the trim rises, fewer and fewer central values survive, and the result closes in on the median. A full 50% trim from each end would remove everything, so the calculator stops just short of it.
Where trimmed means are used
In judged competitions, a scoring system may discard the highest and lowest judges' scores before averaging the rest. Economists use trimmed-mean measures of price changes to reduce the influence of unusually large price movements when measuring underlying inflation. The common thread is deciding the rule before seeing the data, which makes the method systematic and reproducible.
Frequently asked questions
Is a trimmed mean the same as a trimmed average?
Yes. They're two names for the same calculation. “Trimmed mean” is the standard statistical term, while “trimmed average” is a more everyday way of describing the same idea.
Does the trim percentage apply to each end or in total?
For this calculator, the trim percentage applies to each end. A 10% trimmed mean removes 10% from the bottom and 10% from the top, so 20% of the data is discarded in total and 80% is averaged.
Why did my trim percentage remove nothing?
Because the number of values it works out to is below one, and the count is rounded down. A 10% trim of 8 values is 0.8 per end, which rounds to zero. Either raise the percentage or accept that the data set is too small for a trim that light to bite.
Is a trimmed mean the same as just deleting outliers?
No, and the difference matters. Deleting outliers means looking at your data and deciding which points to discard, which invites bias. A trimmed mean fixes the rule in advance and applies it symmetrically to both ends, whether or not the values it removes look unusual. On perfectly well-behaved data, a trimmed mean still trims.
What's the difference between a trimmed mean and a winsorized mean?
A trimmed mean discards the extreme values. A winsorized mean keeps them in the data set but replaces each one with the nearest surviving value, so the count stays the same. Winsorizing pulls extremes in; trimming removes them.