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Winsorized Mean Calculator

Enter a data set and a tail percentage to compute the winsorized mean.

Result

5.50
1

How it is calculated

The numbers, separated by spaces or commas, are sorted. With n values and a tail percentage p, the tool computes k = floor(n × p / 100), the number of values to replace at each end. The k smallest values are set equal to the next value up, the (k+1)-th smallest, and the k largest are set equal to the next value down. The mean of the full adjusted list is then Σx / n, with the same n as before. The percentage is per tail and must be from 0 up to but not including 50, and at least two values are needed. Because k is rounded down, a small percentage on a short list gives k = 0 and the plain mean.

Worked example

Data: 1 2 3 4 5 6 7 8 9 100, with 10 % per tail. n = 10, so k = floor(10 × 10 / 100) = 1. The lowest value 1 is replaced by 2, and the highest value 100 is replaced by 9. The adjusted list is 2 2 3 4 5 6 7 8 9 9, whose sum is 55. The winsorized mean is 55 / 10 = 5.50, with 1 value replaced in each tail. The plain mean of the original data is 14.50, which the single outlier pulled upwards.

Try this example →

Common mistakes

  • Expecting a small percentage to change anything on a short list. With 10 values, 5 % gives k = floor(0.5) = 0, so nothing is replaced and you get the plain mean.
  • Entering the total percentage for both tails. The percentage applies to each tail, so 10 means 10 % at the bottom and 10 % at the top.
  • Confusing this with a trimmed mean. Here the extreme values are replaced and still counted in n, rather than removed, so the divisor does not shrink.
  • Entering 0.1 for 10 %. The field takes a percentage, so 10 means 10 %.
  • Typing a decimal comma such as 2,5. A comma separates numbers in the list, so it would be read as two numbers.

About this calculator

The winsorized mean, named after statistician Charles Winsor, tames the effect of extreme values in a data set without discarding any of them: a chosen percentage of the most extreme values at each tail is replaced with the nearest value still inside the kept range, and only then is the ordinary mean calculated on this adjusted data set.

This sets it apart from a trimmed mean, which removes extreme values entirely rather than replacing them. Winsorizing keeps the original sample size intact while still reducing the influence that a handful of outliers or measurement errors would otherwise have on the average. It's used in robust statistics whenever analysts want a measure of central tendency that's less sensitive to outliers than the plain mean but still uses every data point, such as in survey data cleaning, sports statistics, and financial return analysis.

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