The formula to calculate the trimmed mean is:
\[ \mu = \frac{\sum X_i}{n} \]
Where:
A trimmed mean is defined as the mean of a trimmed data set. It is calculated by removing a specified percentage of the smallest and largest values from the data set and then computing the mean of the remaining values. This method helps to reduce the effect of outliers on the mean.
Example 1:
Trimmed Data Set: 3, 4, 5, 6, 7, 8
Using the formula:
\[ \mu = \frac{3 + 4 + 5 + 6 + 7 + 8}{6} = 5.5 \]
The trimmed mean (μ) is 5.5.
Example 2:
Trimmed Data Set: 20, 30, 40, 50, 60, 70, 80, 90
Using the formula:
\[ \mu = \frac{20 + 30 + 40 + 50 + 60 + 70 + 80 + 90}{8} = 55 \]
The trimmed mean (μ) is 55.
