More precisely, the roundoff error for each dithered number will be a uniformly distributed random variable with mean value of zero, but with a standard deviation formula_12, which is better than the 1/2 standard deviation with the simple predictive methods, but slightly higher than with the simpler stochastic method. However, the sum of "n" rounded numbers will be a random variable with expected error zero, but with standard deviation formula_13 (the total remaining noise) which diverges semi-quadratically and may become easily perceptible, even if the standard deviation of the roundoff error per sample will be formula_14 which slowly converges semi-quadratically to zero. So, this random distribution may still be too high for some applications that are rounding a lot of data.