The definition of the Winsorized mean
Winsorized mean is a method of averaging that initially replaces the smallest and largest values with the observations closest to them. This is done to limit the effect of anomalous extreme values, or outliers. However, if the distribution has heavy tails, the effect of removing the largest and smallest values in the distribution will have little impact due to the large number of changes in the distribution. After replacing the values, a simple arithmetic averaging formula to calculate the average winsorized.
Winsorized means are expressed in two ways. A “KTN” winsorized means refers to the replacement of ” to “the smallest and largest observations, where” K ” is an integer. “X%” winsorized mean involves replacing a given percentage of values from both ends of the data.
Breaking down the ‘Winsorized mean’
Winsorized average is less sensitive to outliers because it can replace them with less extreme values. This method of averaging is similar to the average salary; however, instead of trying to resolve these comments would be changed, given the degree of influence.
The Calculation Of The Winsorized Mean
First, let’s calculate the winsorized mean for the following data: 1, 5, 7, 8, 9, 10, 14. Because mean is the winsorized at the first order, we model the smallest and largest values with their nearest observations. Now our data set looks as follows: 5, 5, 7, 8, 9, 10, 10. Taking the arithmetic mean of the new set produces the mean of winsorized 7.71 ( (5+5+7+8+9+10+10) / 7 ).