DEFINITION of 'Winsorized Mean'
A method of averaging that initially replaces the smallest and largest values with the observations closest to them. After replacing the values, a simple arithmetic averaging formula is used to calculate the winsorized mean.
Winsorized means are expressed in two ways. A "k^{th}" winsorized mean refers to the replacement of the 'k' smallest and largest observations, where 'k' is an integer. A "X%" winsorized mean involves replacing a given percentage of values from both ends of the data.
BREAKING DOWN 'Winsorized Mean'
The winsorized mean is less sensitive to outliers because it replaces them with less influential values. This method of averaging is similar to the trimmed mean; however, instead of eliminating data, observations are altered, allowing for a degree of influence.
Let's calculate the first winsorized mean for the following data set: 1, 5, 7, 8, 9, 10, 14. Because the winsorized mean is in the first order, we replace the smallest and largest values with their nearest observations. The data set now appears as follows: 5, 5, 7, 8, 9, 10, 10. Taking an arithmetic average of the new set produces a winsorized mean of 7.71 ( (5+5+7+8+9+10+10) / 7 ).

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