How to use the robust center calculator
- Paste your values, separated by commas, spaces or new lines. At least three are needed.
- Set the trim from each end as a percent. The default of 10% removes the lowest 10% and highest 10% of the values for the trimmed mean.
- Read the headline median and the stats for the trimmed mean, winsorized mean, plain mean and the median absolute deviation.
- Look at the table of differences from the mean to see how much each estimate moves when an extreme value is handled differently.
Formula
trimmed mean = mean of the values left after dropping floor(p n) from each end
winsorized mean = mean after replacing those values with the nearest kept value
MAD = median of |x - median| scaled MAD = 1.4826 x MAD
p is the trimming share and n the number of values. The scale factor 1.4826 makes the MAD match the standard deviation for data that follow a normal curve. The median is the middle value, or the average of the two middle values.
Ten values with one extreme
Take 12, 14, 15, 15, 16, 17, 18, 19, 21 and 95. The mean is 24.2, pulled upward by the 95. The median is 16.5. Trimming 10% removes one value from each end, leaving eight values whose mean is 16.875. Winsorizing replaces the 12 with 14 and the 95 with 21, and the mean becomes 17. The MAD is 2, which scales to 2.9652, while the ordinary standard deviation of 25.01 is inflated by the 95.
The three robust estimates agree closely with each other (16.5, 16.875 and 17) and none of them is near 24.2. That agreement is what you look for: it tells you the bulk of the data sit around 17 and a single point is responsible for the larger mean.
Choosing between them
The median ignores everything except the middle and is the most resistant to extremes, but it uses little of the information in the rest of the data. The trimmed mean keeps most of the values and so is more efficient when there are only a few outliers. The winsorized mean keeps the sample size and limits the pull of extremes rather than discarding them.
Robust estimates are most useful when you cannot be sure a strange value is an error. They do not remove the need to look at the data. To flag the strange points themselves, use the Outlier Calculator.
Limits
With few values the trimming share rounds down to zero values, and then the trimmed and winsorized means equal the mean; the page tells you so. The MAD is zero when more than half the values are the same. Standard summary numbers such as the standard deviation and quartiles are on the Descriptive Statistics Calculator.
More statistics tools
For score scales, sampling, runs and waiting times, try the Standard Score Converter, Stratified Sample Allocation Calculator and Streak Probability Calculator.
Assumptions and limits
- The values are numbers on one scale, and each one is a separate observation.
- The number trimmed from each end is the share you enter times the count, rounded down.
- The scale factor 1.4826 assumes normal data when comparing the MAD with a standard deviation.
- Nothing is removed from the list you typed. Trimming and winsorizing happen only inside the calculation.
- The example values are an illustration. Replace them with your own.
Frequently asked questions
Is it fair to drop the top and bottom values?
It is a standard technique when stated openly, and this page shows the plain mean beside it. Report what you did. Removing values only because they spoil a hoped-for result is not fair.
What is the difference between trimming and winsorizing?
Trimming deletes the extreme values, so fewer values are averaged. Winsorizing replaces them with the nearest kept value, so the count stays the same but the extremes cannot pull as hard.
Why does the median absolute deviation matter?
It measures spread without being thrown off by outliers, unlike the standard deviation, which squares each distance. It is a good partner for the median.
How much should I trim?
Ten to twenty percent from each end is common, but there is no single right answer. A larger trim is more resistant and less efficient, with 50% reaching the median itself.