Question

what is the purpose of trimming the mean?

Answer 1

A trimmed mean is a method of taking an average that removes a small specific percentage of the largest and smallest values before calculating the mean. After removing the specified outlier observations, the trimmed mean is found using the standard way to calculate meaan . The use of a trimmed mean helps eliminate the influence of data points on the tails that may unfairly affect the usual mean.

For example : Let us calculate the 10% Trimmed mean for the given data

12 16 18 20 22 24 25 25 26 30

Now removing 10% of the bottom as well as top values

Average = 16 + 18 + 20 + 22 + 24 + 25 + 25 + 26 / 8 = 22

Puprpose of trimmed mean : It reduces the effects of outliers on the calculated average. This method is best preffered for data with large, erratic deviations or extremely skewed distributions. If the underlying distribution is symmetric the trimmed mean of a sample is likely to produce an unbiased estimator for either the mean or the median.