# Winsorized Mean

## 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 "kth" 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 ).