Binomial mean

In this study, we propose a new mean, which we call the "binomial mean." The binomial mean is calculated by multiplying each observation in a data set ordered from smallest to largest by a binomial coefficient and dividing the sum of the products by the sum of the binomial coefficients. Therefore, as with parametric means, the calculation is made using all observations in the data set. Since the binomial coefficients grow from the extremes towards the middle, the binomial mean reduces the effect of outliers in the data set, as in nonparametric means. The properties of binomial averaging in terms of statistical measurement quality such as unbiasedness, efficiency, minimal adequacy and consistency were analyzed. A comparison of the mean and variance of the median, binomial mean and arithmetic mean results of each of the 5000 samples generated from continuous distributions with different characteristics was made. Comparison of both probability distributions and median, binomial mean, arithmetic mean and variance estimates of variables belonging to different datasets were made. The results are given in tables and graphs. While it gives lower results than other averages for low observations, it gives lower results than the median in terms of variance estimation. In highly skewed distributions, it is better positioned at the center of the distribution than other means. It is more efficient than the median in the presence of extreme outliers. According to these results, the binomial mean can be used as an alternative mean to nonparametric means in the interpretation of data sets in studies to be conducted in the field of statistics.