Binomial mean

This study introduces the binomial mean, a novel central tendency measure computed by weighting each ordered observation with a binomial coefficient and dividing the sum of these weighted values by the total coefficients. Like parametric means, it uses all observations, but because binomial coefficients rise toward the centre and fall at extremes, the binomial mean mitigates outlier influence—similar to nonparametric approaches. Key statistical properties (unbiasedness, efficiency, consistency, sufficiency) are examined. Performance is compared with the median and arithmetic mean using 5,000 simulated samples from normal, gamma, and beta distributions with varying characteristics, and real-world datasets. Results show the binomial mean yields lower values in small samples and provides better variance estimation than the median. In highly skewed distributions, it aligns more closely with the centre and demonstrates greater efficiency than the median under extreme outliers. These findings support the binomial mean as a robust alternative to traditional nonparametric means.