## What Is a Trimmed Mean?

A trimmed mean (similar to an adjusted mean) is a method of averaging that removes a small designated percentage of the largest and smallest values before calculating the mean. After removing the specified outlier observations, the trimmed mean is found using a standard arithmetic averaging formula. The use of a trimmed mean helps eliminate the influence of outliers or data points on the tails that may unfairly affect the traditional mean.

Trimmed means are used in reporting economic data in order to smooth the results and paint a more realistic picture.

A trimmed mean is also known as a truncated mean.

## The Basics of a Trimmed Mean

The trimmed mean looks to reduce the effects of outliers on the calculated average. This method is best suited for data with large, erratic deviations or extremely skewed distributions.

A trimmed mean is stated as a mean trimmed by x%, where x is the sum of the percentage of observations removed from both the upper and lower bounds. The trimming points are often arbitrary in that they follow rules of thumb rather than some optimized method of setting those thresholds.

## Trimmed Means and Inflation Rates

A trimmed mean may be used in place of a traditional mean when determining inflation rates from the Consumer Price Index (CPI) or personal consumption expenditures (PCE). The levels that are trimmed from each tail may not be equitable, as these values are instead based on historical data to reach the best fit between the trimmed mean inflation rate and the inflation rate’s core.

The core of the CPI or PCE refers to the selected products minus prices associated with food or energy. Food and energy costs are generally considered the most volatile, also referred to as noisy, items within the data. Shifts in the non-core area are not necessarily indicative of overall inflationary activities.

When the data points are organized, they are placed in ascending order based on those prices that fell the most, to the prices that rose the most. Specific percentages are removed from the tails to help lower the effect of volatility on the overall CPI changes.

Trimmed means are used in the Olympics to remove extreme scoring from possibly biased judges who may impact an athlete's average score.

### Inflation Comparisons With Trimmed Means

Providing a trimmed mean inflation rate along with other measures provides a basis for comparison, allowing for a more thorough analysis of the inflation rates being experienced. This comparison may include the traditional CPI, the core CPI, a trimmed mean CPI, and a median CPI.

### Key Takeaways

• A trimmed mean is a method of averaging that removes a small designated percentage of the largest and smallest values before calculating the mean.
• Using a trimmed mean helps eliminate the influence of outliers or data points on the tails that may unfairly affect the traditional mean.
• Trimmed means are used in reporting economic data in order to smooth the results and paint a more realistic picture.
• Providing a trimmed mean inflation rate along with other measures provides a basis for comparison.

## Theoretical Example of a Trimmed Mean

For example, imagine that a figure skating competition produces the following scores: 6.0, 8.1, 8.3, 9.1, 9.9. A mean trimmed at 40% would equal 8.5. First we obtain the arithmetic mean based on the calculation:

﻿\begin{aligned} &\frac{ 8.1 + 8.3 + 9.1 }{ 3 } = 8.28 \\ \end{aligned}﻿

To trim the mean by 40%, we remove the lowest 20% and the highest 20% of values, eliminating the scores of 6.0 and 9.9. As shown by this example, trimming the mean can reduce the effects of outlier bias in a sample and has the effect of increasing the reported average by 0.22 points.