Cal11 calculator
Search calculator...

Calculate 15 Percent Trimmed Mean of 11

Reviewed by Calculator Editorial Team

The trimmed mean is a robust measure of central tendency that reduces the influence of extreme values in a dataset. This guide explains how to calculate a 15 percent trimmed mean for 11 numbers, including the formula, step-by-step instructions, and practical applications.

What is a trimmed mean?

A trimmed mean is a statistical measure that removes a specified percentage of the highest and lowest values from a dataset before calculating the arithmetic mean. This process helps reduce the impact of outliers on the final result.

For example, a 15 percent trimmed mean of 11 numbers would remove the lowest 15% and highest 15% of values before calculating the mean of the remaining values.

How to calculate the trimmed mean

To calculate a 15 percent trimmed mean for 11 numbers:

  1. Sort all 11 numbers in ascending order.
  2. Calculate 15% of 11: 15% × 11 = 1.65. Since you can't remove a fraction of a data point, round to the nearest whole number (2).
  3. Remove the 2 lowest and 2 highest values from the sorted list.
  4. Calculate the mean of the remaining 7 values.

Formula

The trimmed mean (TM) is calculated as:

TM = (Sum of remaining values) / (Number of remaining values)

Note: The exact percentage to trim depends on your specific requirements. A common choice is 10-20% for small datasets.

Example calculation

Let's calculate the 15 percent trimmed mean for these 11 numbers: 5, 8, 10, 12, 15, 18, 20, 22, 25, 30, 35.

  1. Sort the numbers: 5, 8, 10, 12, 15, 18, 20, 22, 25, 30, 35
  2. Calculate 15% of 11: 1.65 → round to 2
  3. Remove the 2 lowest (5, 8) and 2 highest (30, 35) values
  4. Remaining values: 10, 12, 15, 18, 20, 22, 25
  5. Calculate the mean: (10+12+15+18+20+22+25)/7 = 120/7 ≈ 17.14

The 15 percent trimmed mean for this dataset is approximately 17.14.

When to use a trimmed mean

A trimmed mean is particularly useful when:

  • Your dataset contains outliers that might skew the results
  • You want a more robust measure of central tendency than the arithmetic mean
  • You're working with small datasets where extreme values could significantly affect the result

However, be aware that trimming data removes information and may not be appropriate for all statistical analyses.

FAQ

How does trimming affect the mean?

Trimming removes extreme values, which can make the trimmed mean less sensitive to outliers than the regular mean. However, it also reduces the sample size, which may affect the precision of your estimate.

What percentage should I trim?

The percentage to trim depends on your specific dataset and research question. Common choices range from 10% to 20% for small datasets. Larger datasets may use smaller trim percentages.

Is the trimmed mean always better than the regular mean?

Not necessarily. The trimmed mean is more robust to outliers but loses information by removing data points. Choose based on your specific needs and the characteristics of your dataset.