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A winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean. It involves the calculation of the mean after winsorizing -- replacing given parts of a probability distribution or sample at the high and low end with the most extreme remaining values, typically doing so for an equal amount of both extremes; often 10 to 25 percent of the ends are replaced. The winsorized mean can equivalently be expressed as a weighted average of the truncated mean and the quantiles at which it is limited, which corresponds to replacing parts with the corresponding quantiles.
The winsorized mean is a useful estimator because it is less sensitive to outliers than the mean but will still give a reasonable estimate of central tendency or mean for almost all statistical models. In this regard it is referred to as a robust estimator.
The winsorized mean uses more information from the distribution or sample than the median. However, unless the underlying distribution is symmetric, the winsorized mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median.
- For a sample of 10 numbers (from x1, the smallest, to x10 the largest) the 10% winsorized mean is
- The key is in the repetition of x2 and x9: the extras substitute for the original values x1 and x10 which have been discarded and replaced.
- This is equivalent to a weighted average of 0.1 times the 5th percentile (x2), 0.8 times the 10% trimmed mean, and 0.1 times the 95th percentile (x9).
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