Table of Contents
- What Is a Trimmed Mean?
- Key Takeaways
- Understanding a Trimmed Mean
- Trimmed Means and Inflation Rates
- Fast Fact
- Providing a Basis for Comparison
- Example of a Trimmed Mean
- How Are Trimmed Means Used?
- Where Are Trimmed Means the Best Fit?
- How Does the Trimmed Mean Help Determine the Inflation Rate?
- The Bottom Line
What Is a Trimmed Mean?
Let me explain what a trimmed mean is. It's a statistical measure of central tendency where you exclude a specified percentage of the highest and lowest values from your data set before computing the average.
You calculate a trimmed mean by first removing a small percentage of the highest and lowest values. Once those extreme values are out, you compute the average using the standard method. This approach reduces the impact of unusual data points and provides a clearer, more accurate picture, especially in economic data reporting. You'll see trimmed means used to smooth results and give a more realistic view.
Key Takeaways
Here's what you need to remember: A trimmed mean removes a small designated percentage of the largest and smallest values before calculating the average. By doing this, it eliminates the influence of outliers or data points on the tails that could unfairly skew the traditional mean. I use trimmed means in reporting economic data to smooth the results and paint a more realistic picture. Providing a trimmed mean inflation rate, along with other measures, gives you a basis for comparison.
Understanding a Trimmed Mean
A mean is just the mathematical average of two or more numbers, but the trimmed mean reduces the effects of outliers on that calculated average. You should use a trimmed mean for data with large, erratic deviations or extremely skewed distributions.
We state a trimmed mean as one 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, following rules of thumb rather than some optimized method. For instance, a 3% trimmed mean removes the lowest and highest 3% of values, leaving you to calculate the mean from the remaining 94% of data.
This makes a trimmed mean a more realistic representation of your data set, as you've removed the few erratic outliers that could otherwise skew the information. You might also hear it called a truncated mean.
Trimmed Means and Inflation Rates
You can use a trimmed mean in place of a traditional mean when determining inflation rates from the Consumer Price Index (CPI) or personal consumption expenditures (PCE). The CPI and PCE price index measure prices of baskets of goods in an economy to identify inflation, which means rising price trends.
The levels trimmed from each tail may not be equal; they're based on historical data to best fit between the trimmed mean inflation rate and the core inflation rate.
The core of the CPI or PCE refers to selected products minus prices associated with food or energy. Food and energy costs are the most volatile, or noisy, items in the data. Shifts in non-core areas aren't necessarily indicative of overall inflationary activities.
When you organize the data points, place them in ascending order from prices that fell the most to those that rose the most. Remove specific percentages from the tails to lower the effect of volatility on overall CPI changes.
Fast Fact
Trimmed means are used in the Olympics to remove extreme scoring from possibly biased judges who may impact an athlete’s average score.
Providing a Basis for Comparison
By providing a trimmed mean inflation rate along with other measures, you get a basis for comparison, allowing for a more thorough analysis of the inflation rates being experienced. This might include the traditional CPI, the core CPI, a trimmed mean CPI, and a median CPI.
Example of a Trimmed Mean
Take this example: a figure skating competition with scores of 6.0, 8.1, 8.3, 9.1, and 9.9.
The regular mean is ((6.0 + 8.1 + 8.3 + 9.1 + 9.9) / 5) = 8.28.
To trim the mean by a total of 40%, remove the lowest 20% and highest 20%, eliminating 6.0 and 9.9.
Then calculate the mean as (8.1 + 8.3 + 9.1) / 3 = 8.50.
So, the 40% trimmed mean is 8.5 versus 8.28, reducing outlier bias and increasing the reported average by 0.22 points.
How Are Trimmed Means Used?
Trimmed means are used in reporting economic data. They help smooth the results and present a more realistic picture.
Where Are Trimmed Means the Best Fit?
Trimmed means are best suited for data with large, erratic deviations or extremely skewed distributions.
How Does the Trimmed Mean Help Determine the Inflation Rate?
Providing a trimmed mean inflation rate, along with other measures, gives you a basis for comparison, allowing for a more thorough analysis of the inflation rates being experienced.
The Bottom Line
A trimmed mean is a method of averaging that removes a small designated percentage of the largest and smallest values before calculating the mean. It helps eliminate the influence of outliers or data points on the tails that may unfairly affect the mean.
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