Glossary of statistical terms
Statistical Glossary
Trimmed Mean:The trimmed mean is a family of measures of central tendency . The trimmed mean 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 example, to calculate the trimmed mean for a set of values , steps are the following:

Step 1. Sort the values: .

Step 2. Discard 20\% of the largest values  i.e. one (20% of 5) largest value (12); discard 20\% of the smallest values  i.e. one smallest value (8). Now we have a set of 3 values:

Step 3. Compute the mean of the 3 values: the mean value of is 10.
Thus the trimmed mean of 5 values is 10.
In contrast to the arithmetic mean , the trimmed mean is a robust measure of central tendency. For example, a small fraction of anomalous measurements with abnormally large deviation from the center may change the mean value substantially. At the same time, the trimmed mean is stable in respect to presence of such abnormal extreme values, which get "trimmed" away.
For example, in the set of 5 values discussed above, replace one value by a large number, say, "12" by "1000". Then compute the mean of the 5 values, and the trimmed mean. The replacement does not affect the trimmed mean (because the extreme value is discarded on step 2), but it changes the mean significantly  from 10 to 207.
The trimmed mean, as a family of measures, includes the arithmetic mean and the median as the most extreme cases. The trimmed mean with the minimal degree of trimming ( %) coincides with the mean; the trimmed mean with the maximal degree of trimming ( %) coincides with the median.
One popular example 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 also Mean values (comparison) and the online short course Basic Concepts in Probability and Statistics
Want to learn more about this topic?
Statistics.com offers over 100 courses in statistics from introductory to advanced level. Most are 4 weeks long and take place online in series of weekly lessons and assignments, requiring about 15 hours/week. Participate at your convenience; there are no set times when you must to be online. Ask questions and exchange comments with the instructor and other students on a private discussion board throughout the course.
Introductory Statistics Course :
Statistics.com offers a full sequence of introductory courses in statistics, plus a single course that is a survey of basic topics. These courses have been developed and taught by leading textbook authors and authorities on teaching statistics with the needs of the introductory student in mind. Our goal is real understanding, not cookbook learning, and even the most anxious novice (as well as the expert!) will benefit from our rich array of courses that provide a bit of repetition and overlap, as well as multiple perspectives on a sometimes difficult topic.
Promoting better understanding of statistics throughout the world
To celebrate the International Year of Statistics in 2013, we started a program to provide a statistical term every week, delivered directly to your inbox. The Word of the Week program proved to be quite popular, and continues. The Institute for Statistics Education offers an extensive glossary of statistical terms, available to all for reference and research. Make it your New Year's resolution to improve your own statistical knowledge! Sign up here. Rather not have more email? Simply bookmark our home page and check our “Stats Word of the Week” feature.Want to be notified of future courses?
Yes
STUDENT COMMENTS...