Trimmed Mean Calculator

Understanding the trimmed mean calculator — concept and principle

A trimmed mean is the average you get after removing a fixed percentage of the smallest and largest values. It sits between the ordinary mean, which uses every value, and the median, which uses only the middle one. It is used when a few extreme values could distort the average, such as judges' scores or trimmed-mean inflation measures.

How it is calculated

1. Sort the n values.
2. Compute the number to drop from each end: c = ⌊n × t/100⌋, where t is the trim percentage per end. The calculator rounds down, so it never removes more than you asked.
3. Keep the values from position c + 1 to n − c and average them: trimmed mean = (sum of kept values) ÷ (n − 2c).

The result is in the same unit as the data. A 10% trim per end is a common choice; 25% per end gives the interquartile mean.

The principle

The ordinary mean has a breakdown point of zero: one sufficiently extreme value can move it anywhere. Trimming c values from each side means an outlier must outnumber the trimmed values before it can affect the result, so the estimate becomes robust. If the data are symmetric, the trimmed mean estimates the same centre as the mean and median, while losing little efficiency when there are no outliers.

Worked example

1. Data: 12, 15, 11, 19, 22, 15, 18, 25, 14, 16, sorted to 11, 12, 14, 15, 15, 16, 18, 19, 22, 25 (n = 10). Trim 10% from each end.
2. c = ⌊10 × 10/100⌋ = 1, so drop 11 and 25.
3. Kept values: 12, 14, 15, 15, 16, 18, 19, 22. Values used: 8.
4. Sum = 131, so trimmed mean = 131 ÷ 8 = 16.375.
5. Ordinary mean = 167 ÷ 10 = 16.7.

How to read the result

Compare the trimmed mean with the ordinary mean. Here the ordinary mean is 0.325 higher, because the largest value (25) is further from the centre than the smallest (11): the data have a slight right skew. A large gap suggests outliers or strong skew; a near-zero gap suggests a roughly symmetric data set.

Common mistakes

• Entering the total trim (20%) when the field asks for the trim from each end (10%).
• Expecting a trim on a small sample to remove anything: with n = 9 and 10%, c = ⌊0.9⌋ = 0 and nothing is dropped.
• Using a trimmed mean to hide inconvenient data rather than to resist genuine errors.

Frequently asked questions

Is a trimmed mean the same as a winsorized mean?

No. Winsorizing replaces the extreme values with the nearest kept value instead of deleting them, so n stays the same.

What trim percentage should I use?

5–25% per end is typical. 10% is a common default; 25% per end gives the interquartile mean, and trimming almost 50% approaches the median.

How does Excel compute it?

Excel's TRIMMEAN takes the total percentage to exclude and rounds the number removed down to an even number, so TRIMMEAN(data, 0.2) matches a 10% per-end trim here.

Sources: Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press. · Microsoft Support, TRIMMEAN function documentation.