Truncated Mean Calculator

Input a dataset and a trimming percentage to easily compute the Truncated Mean (also called the Trimmed Mean).

Calculate the Truncated Mean

Result

What Is the Truncated Mean?

The truncated mean is a method of calculating the average by removing a specified percentage of the highest and lowest values in the dataset. This reduces the impact of outliers, making the mean more representative of the central tendency of the data. The steps to calculate the trimmed mean are:

Sort the Data: Arrange the values in ascending order.
Determine the Trim Amount: Calculate the number of values to trim from both ends of the dataset based on the trimming percentage.
Remove Extreme Values: Exclude the smallest and largest values based on the trim amount.
Calculate the Mean: Compute the average of the remaining data.

Examples

Example 1: Dataset = [5, 7, 12, 15, 16, 19, 22], Trimming Percentage = 20%, Calculate the trimmed mean.

Solution:

1. Sort the data:

Already sorted as [5, 7, 12, 15, 16, 19, 22].

2. Trim amount:

20% trimming means removing 1 value from each end.

3. Remove extreme values:

Exclude 5 (smallest) and 22 (largest). Remaining data: [7, 12, 15, 16, 19].

4. Calculate the mean:

\( \frac{7 + 12 + 15 + 16 + 19}{5} = 13.8 \)

Result: The trimmed mean is 13.8.

Example 2: Dataset = [5, 8, 10, 11, 15, 20, 22, 24, 27, 30], Trimming Percentage = 10%, Calculate the trimmed mean.

Solution:

1. Sort the data:

Already sorted as [5, 8, 10, 11, 15, 20, 22, 24, 27, 30]

2. Trim amount:

10% trimming means removing 1 value from each end.

3. Remove extreme values:

Exclude [5] and [30]. Remaining data: [8, 10, 11, 15, 20, 22, 24, 27].

4. Calculate the mean:

\( \frac{8 + 10 + 11 + 15 + 20 + 22 + 24 + 27}{8} = \frac{137}{8} \approx 17.13 \)

Result: The trimmed mean is approximately 17.13.