Alpha-Trimmed Mean

An alternative to Arithmetic Mean which is more robust against Outlier where the lower and upper $\alpha$ percent are being truncated. $\alpha \in [0,1/2)$ k=\lfloor n\alpha \rfloor$$$$\bar{x} = \frac{1}{n-2k}(x_{k+1} + ... + x_{n-k})

• Order data
• discard lowest and highest $\alpha$ percent
• Compute Arithmetic Mean on remaining data
• 50% trimmed mean corresponds to Median