One dial from the arithmetic mean to the median, with the whole sweep plotted.
From the mean to the median, continuously
The mean is 18.8 and the 5% trimmed mean is 13.0. One value moved the mean by 5.8.
n = 20, trimming 2 from each end, keeping 16
Trimmed mean = 12.812500
The arithmetic mean is 18.800000 and the median is 12.500000. Trimming 10.0% moved it 5.9875 toward the median.
Trimmed mean
12.812500
extremes discarded
Winsorized mean
12.950000
extremes replaced
Arithmetic mean
18.800000
0% trim
Median
12.500000
50% trim
Breakdown point
10.0%
corruption it survives
Removed from each end
2
of 20
Winsorized SD
6.065216
the scale to pair with it
Midrange
71.000000
(min + max)/2 — breakdown 0
Points are the trimmed mean; the dashed line is the Winsorized mean. Both start at the arithmetic mean and end at the median, and the shape between is what your data’s tails look like.
A 0% trim is the arithmetic mean and a 50% trim is the median — exactly, for odd and even n. So this is one continuous family rather than two rival statistics, and picking a trim fraction is choosing how much of the tails to believe. The 50% case is not an approximation: trimming half the data from each end leaves the middle one or two values, which is the median’s definition. The verification suite checks that equality across 600 random datasets.
Trimmed is 12.812500 and Winsorized is 12.950000. They are not the same statistic. Trimming discards the extreme values; Winsorizing replaces them with the nearest one that survives. Both have the same breakdown point, and the Winsorized version keeps the sample size — which makes its standard error easier to work with and keeps a trace of the direction the extremes pointed. On symmetric data they nearly agree; on skewed data they do not.
Removed from the low end: 2.000, 4.000. From the high end: 25.000, 140.000. Trimming is symmetric by construction — the same count comes off each end regardless of where the outliers actually are — so on one-sided data it discards good observations from the clean side to remove bad ones from the other. That is the price of a method that does not have to decide which points are outliers, and it is why the outlier calculator exists as a separate question.
The breakdown point is 10.0%, and the arithmetic mean’s is zero. One arbitrary value can move the mean anywhere at all; the midrange is worse still, since it depends on nothing but the two extremes — 71.0000 here, against a median of 12.5000. A trim fraction of f survives f of the data being corrupted and fails at the next value, and the median’s 50% is the highest any location estimator can achieve.
What this tool shows
A 0% trim is the arithmetic mean and a 50% trim is exactly the median. So this is one continuous family rather than a third statistic, and the trim fraction is a dial between them. The tool plots the full sweep, computes the Winsorized version alongside — a different number for the same fraction — and reports the breakdown point.
The trimmed mean at any fraction, with the values removed listed
The Winsorized mean beside it, which replaces rather than discards
The full sweep plotted from the mean at 0% to the median at 50%
The breakdown point, which equals the realised trim fraction
The Winsorized standard deviation, which is the scale to pair with it
The midrange, for contrast — the least robust estimator there is
Mean to median Winsorized too Breakdown point Sweep plotted
Updated 12 September 2026 · Works in any browser, no installation
A trimmed mean discards a fixed fraction from each end and averages the rest. It buys resistance to extreme values without going all the way to the median, which discards all the magnitude information — and the fraction you choose is exactly how much corruption the result can survive.
At a glance
Formula shown
Sort the values, remove ⌊f·n⌋ from each end, and average the rest. At f = 0 that is the arithmetic mean; at f = 0.5 it is the median, because trimming half from each side leaves the middle one or two values. The Winsorized mean replaces the trimmed values with the nearest survivor instead of removing them, keeping n the same. The breakdown point — the fraction of arbitrary corruption the estimate survives — is exactly f.
Scenario support
Judged competitions that drop the extreme scores, response times with a few enormous values, survey data with entry errors, any average where a handful of observations should not dominate, and price indices where trimming is the standard construction.
Educational estimate
Planning support from the values you enter — not professional advice.
One family, not three statistics
The mean, the trimmed mean and the median are usually taught as three separate things. Two of them are endpoints of the third.
At f = 0, nothing is removed and the trimmed mean is the arithmetic mean. Trivially, and the tool checks it.
At f = 0.5, trimming half from each end leaves the middle one or two values — which is the median’s definition. Not an approximation to it: the same number, for odd and even n, verified across 600 random datasets.
So the trim fraction is a dial. The plot shows the whole sweep, and its shape is a description of your data’s tails: flat means the extremes were not doing much, steep at the start means they were.
Which reframes the usual argument. “Mean or median?” is a choice between two points on a continuum, and the interesting question is how much of the tails to believe rather than which of two formulas to apply.
The conventional choices are 5%, 10% and 20%. There is no derivation behind them. A 20% trimmed mean is often recommended as a general-purpose default because it is close to optimal over a wide range of tail behaviours, which is a defensible reason and still a judgement.
Trimming is not Winsorizing
Both are called robust means and both are described as “dealing with outliers”. They do different things to them.
Trimming removes the extreme values. The sample gets smaller and the extremes contribute nothing at all.
Winsorizing replaces them with the nearest survivor. The sample size is unchanged and the extremes still count — they just count as the value at the boundary rather than as their own.
So Winsorizing keeps the direction and drops the magnitude. Five enormous values on the high side still pull the Winsorized mean upward, five times over, at the boundary value. A trimmed mean would not know they existed.
The breakdown point is identical. Both survive exactly f of the data being corrupted. The difference is in the variance and in what the number means, not in robustness.
Winsorizing has the easier standard error. Because n is unchanged, the Winsorized standard deviation pairs naturally with the Winsorized mean — which is why Yuen’s t test, the robust two-sample test, uses the Winsorized variance with the trimmed mean rather than either alone.
Both are reported as “trimmed” in practice, which is the reason this tool prints them together. On symmetric data they nearly agree, and on skewed data they do not.
The breakdown point, and why the mean has none
Robustness gets described in adjectives. It has a number, and the number is exact.
The breakdown point is the largest fraction of the data that can be made arbitrarily wrong before the estimate can be dragged anywhere. For a trimmed mean it is exactly the trim fraction.
The arithmetic mean’s breakdown point is zero. One value, moved far enough, moves the mean as far as you like. The tool’s first preset shows a 5.8-unit shift from a single observation.
The median’s is 0.5, which is the maximum possible. No location estimator can do better, because at more than half corrupted the “good” data is the minority and no method can identify it.
The midrange’s is zero, and it is worse than the mean. It depends on nothing but the two extremes — the values most likely to be wrong. On the first preset it gives 71 against a median of 12.5.
A high breakdown point is not free. On clean, normal data the ordinary mean is the most efficient estimator there is, and every robust alternative gives up some precision for insurance. A 20% trimmed mean retains about 90% of the mean’s efficiency under normality — a small premium for a large policy.
Trimming is symmetric, and your outliers may not be
The defining feature of a trimmed mean is that it does not have to decide which points are outliers. That is also its main limitation.
The same count comes off each end, wherever the extremes actually are. On data with one long tail, trimming discards perfectly good observations from the clean side in order to remove bad ones from the other.
Which on skewed data shifts the estimate toward the short tail. That is not a bug: for skewed data the trimmed mean estimates something between the mean and the median, and which of those you wanted is a question about the data rather than the method.
The alternative is to identify the outliers, and that is a different problem. It needs a rule, a rule needs a threshold, and thresholds get chosen after seeing the data. The outlier calculator covers what those rules disagree about.
One-sided trimming exists and is rarely appropriate. Removing only the high tail builds the conclusion into the method, and the result is no longer estimating a centre of anything.
If the skew is the phenomenon, do not trim it away. Incomes, insurance losses and waiting times are genuinely right-skewed, and a trimmed mean of them answers a question about typical cases rather than about the total — which is usually not what a budget needs.
Where trimmed means are the standard
Several fields adopted trimming as a convention long before it had a name in the statistics literature, and the reasons are instructive.
Judged sports drop the highest and lowest score. Diving, gymnastics, figure skating. With seven judges that is a 1/7 trim, and the purpose is not statistical efficiency — it is removing the incentive for a single judge to swing the result.
Trimmed-mean inflation is a published statistic. Several central banks compute one, removing the most extreme price movements each month, because a few volatile categories otherwise dominate a figure that is meant to describe the general trend.
Benchmarking discards the fastest and slowest runs. The extremes there are usually measurement artefacts rather than performance, and trimming removes them without anybody having to decide which runs were contaminated.
Interlaboratory studies use it to set consensus values. A robust mean across labs resists the one lab with a miscalibrated instrument, which is exactly the failure mode the design has to survive.
In each case the point is the same. The extremes are expected to be unrepresentative, and the method removes them by a fixed rule rather than by a judgement made after seeing which way the result went.
Reporting it honestly
A trimmed mean is a defensible statistic and an easy one to use badly, in four specific ways.
State the fraction. “Trimmed mean = 13.0” is not a complete report. A 5% and a 20% trim of the same data are different numbers, and on the first preset they differ by 0.33.
Decide the fraction before looking. Trying 5%, 10% and 20% and reporting the most convenient is the same error a multiple comparison makes, with no correction available.
Say whether you trimmed or Winsorized. The two are reported under the same word and give different numbers.
Report the count removed, not just the percentage. A 10% trim of 23 values removes 2 from each end, which is 8.7% — the floor is standard and the difference is visible in the output rather than left to be inferred.
And do not pair it with an ordinary standard deviation. The SD is not robust, so quoting a trimmed mean beside it gives a centre that resists outliers and a spread that does not. The median absolute deviation or the Winsorized SD above is the matching scale.
Method. The count removed from each tail is ⌊f·n⌋, the standard definition, so the realised fraction is usually slightly below the one requested and the tool reports the count rather than leaving it implied. At f = 0.5 the result is the median, computed as the median rather than as a degenerate average, so the identity holds exactly for odd and even n. The suite verifies that equality across 600 random datasets and that f = 0 gives the arithmetic mean across 300 more, checks the sweep runs monotonically from one to the other on skewed data, and demonstrates the breakdown point directly: corrupting 2 of 20 values leaves a 20% trimmed mean unchanged to machine precision while moving the ordinary mean by fifty million. That engine is verified on every change against 54 assertions. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Mean, Median and ModeAll three centres marked on your own data, every mode rather than just the first, and the mean-median gap read as a direct measure of skew.
OutlierRuns four outlier rules together and says when each is failing — the 3-sigma rule cannot flag anything below n=11, two outliers hide each other, and the quartile convention alone can decide the answer.
Mean Absolute DeviationAll three statistics the acronym MAD names — about the mean, about the median, and the median absolute deviation — plus the ratio to the standard deviation, which is exactly 0.7979 for a normal distribution and so reads as a free shape check.
Standard DeviationSample and population standard deviation, plus variance, mean, median, quartiles, z-scores, outliers, and confidence intervals.
PercentileThe value at any percentile and the percentile rank of any value, with all nine standard methods — and the round trip that shows the two directions are not inverses.
Moving AverageSimple, exponential, weighted and centred moving averages with the lag each one carries — exactly (n−1)/2 periods for a simple average, which is also the reason α = 2/(n+1) is in every EMA formula.
An educational tool. Trimming is symmetric regardless of where the extreme values actually are, so on skewed data it discards good observations from one side; where the skew is the phenomenon rather than contamination, a trimmed mean answers a different question from the one being asked.
Published a trimmed mean calculator built around an identity: a 0% trim IS the arithmetic mean and a 50% trim IS the median, exactly, for odd and even n. So this is one continuous family rather than a third statistic beside two others, and the tool plots the whole sweep between them. Verified across 600 random datasets.
Computes the Winsorized mean alongside, because 'trimmed' is used for both and they are different: trimming discards the extreme values, Winsorizing replaces them with the nearest survivor. Same breakdown point, different number, and on skewed data they diverge.
Reports the breakdown point, which equals the realised trim fraction — and demonstrates it rather than asserting it: corrupting 2 of 20 values leaves a 20% trimmed mean unchanged to machine precision while moving the ordinary mean by fifty million. The midrange is shown for contrast, at 71 against a median of 12.5 on the first preset.
States that trimming is symmetric regardless of where the extremes actually are, so on one-sided data it discards good observations from the clean side — the price of a method that does not have to decide which points are outliers.
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