Trimmed Mean

Trimmed Mean

A trimmed mean is an average calculated after removing a specified percentage of the highest and lowest values from a data set. By excluding extreme observations (outliers) at both tails, the trimmed mean reduces the influence of erratic or skewed values and often gives a more representative measure of central tendency.

How it works

• Sort the data in ascending order.
• Choose a trimming percentage. Commonly this is expressed per tail (for example, a 3% trimmed mean removes the lowest 3% and the highest 3%).
• Drop that percentage of observations from each end of the sorted list.
• Compute the arithmetic mean of the remaining values.

Example conventions:
– If you specify a total trimming of 40%, you remove 20% from the bottom and 20% from the top.
– Small samples may require rounding the count of observations to remove (e.g., remove one value per tail).

Example

Scores: 6.0, 8.1, 8.3, 9.1, 9.9

• Ordinary mean: (6.0 + 8.1 + 8.3 + 9.1 + 9.9) / 5 = 8.28
• Trim by 40% total (remove lowest 20% and highest 20% → drop 6.0 and 9.9)
• Trimmed mean: (8.1 + 8.3 + 9.1) / 3 = 8.50

The trimmed mean (8.50) reduces outlier bias present in the ordinary mean (8.28).

Uses

• Economic statistics: Central banks and research institutions use trimmed means to report inflation measures (based on CPI or PCE) because trimming volatile price movements (often food and energy) yields a smoother, more informative trend.
• Scoring and judging: Competitions such as figure skating and gymnastics sometimes discard extreme judges’ scores before averaging to limit the impact of biased or anomalous ratings.

When to use a trimmed mean

• Data contain outliers or heavy tails that distort the ordinary mean.
• You want a summary measure less sensitive to extreme, infrequent values.
• You need a robust comparison across time or groups where volatility is common.

Limitations

• Choosing the trimming percentage is often ad hoc and can affect results.
• Trimming discards data, which may remove meaningful information if extremes are genuine.
• Not appropriate for very small samples, where removing observations can overly distort the dataset.

Alternatives

• Median: fully robust to outliers (equivalent to an extreme trimmed mean).
• Winsorized mean: replaces extreme values with the nearest remaining values instead of discarding them, reducing the influence of outliers while retaining sample size.

A trimmed mean is a simple, effective tool for obtaining a more robust average when extreme values would otherwise skew the ordinary mean. Use it when you need to reduce outlier influence while still reflecting the bulk of the data.