Provided you are taking random
samples from a normal
population of a continuous
variable, the arithmetic mean ( )
has the smallest variance and most power. It is the best linear unbiased function of its parameter, the maximum likelihood estimator, the least squares estimator, and the minimax estimator - in other words, it has the smallest risk of being wildly wrong. It is also unbiased, sufficient, consistent, impartial and regular. It, and its immediate relatives (such as the sum, the difference between means, and the linear regression slope) are also by far and away the most heavily studied, best understood, and most used statistics.