Result:
Understanding the Trimmed Mean
The trimmed mean is calculated by removing a specified percentage of the smallest and largest values from the data set before averaging the remaining values. This method reduces the impact of outliers, providing a more stable measure of central tendency.
Formula: \( \text{Trimmed Mean} = \frac{\sum x_{\text{trimmed}}}{n_{\text{trimmed}}} \)
Real-Life Example
Consider a set of test scores: 45, 55, 65, 78, 82, 91, and 96. With a 20% trim, you remove the lowest 20% and highest 20% of scores. For a data set of 7 values, 20% of 7 is approximately 1 value from each end.
After trimming:
- Removed lowest score: 45
- Removed highest score: 96
- Remaining values: 55, 65, 78, 82, and 91
Calculation: \( \frac{55 + 65 + 78 + 82 + 91}{5} = 74.2 \)
The trimmed mean score is 74.2, providing a more robust average by reducing the influence of the lowest and highest outliers.