Is The Trimmed Mean Resistant To Changes In The Extreme Values For The Givenã¢â‚¬â€¹ Data?

Statistical Glossary

Trimmed Mean:

The trimmed mean is a family of measures of fundamental trend . The -trimmed hateful of of values is computed by sorting all the values, discarding % of the smallest and % of the largest values, and computing the of the remaining values.

For case, to calculate the -trimmed mean for a fix of values , steps are the following:

Thus the -trimmed mean of 5 values is x.

In contrast to the arithmetic hateful , the trimmed mean is a robust measure of cardinal trend. For example, a small fraction of anomalous measurements with abnormally large divergence from the center may alter the hateful value essentially. At the same fourth dimension, the trimmed mean is stable in respect to presence of such abnormal extreme values, which get "trimmed" abroad.

For example, in the set of 5 values discussed in a higher place, supplant one value past a large number, say, "12" by "1000". Then compute the mean of the five values, and the -trimmed hateful. The replacement does not touch the trimmed mean (because the extreme value is discarded on footstep 2), merely it changes the mean significantly - from 10 to 207.

The trimmed mean, as a family of measures, includes the arithmetic hateful and the median as the most extreme cases. The trimmed hateful with the minimal degree of trimming ( %) coincides with the hateful; the trimmed mean with the maximal degree of trimming ( %) coincides with the median.

One pop instance of a trimmed mean is judges´ scores in gymnastics, where the extreme scores are often discarded before computing the score for a particular performance.

See too Mean values (comparison) and the online short course Basic Concepts in Probability and Statistics

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