On mean values

New results in the theory of means (mean values) are given. We introduce the weighted means of type I corresponding to the sample, and those of type II corresponding to the set of order statistics. Evolution of ideas on Kemeny distance and Kemeny median is traced. We also propose a computation-friendly variation of Kemeny median, which avoids the “center of the bagel hole” effect. Then we generalize the Kemeny median by virtue of empirical and theoretical means in abstract spaces and prove the laws of large numbers for them.