Is there a way of encryption that allows to check what encrypted values are close to their mean? I am looking for a way to allow parties to publicize encrypted values that can only be decrypted by one or a select few other parties, but that allow everyone to check how close they are to the mean of all such publicized values.

This of course would mean that there is some entropy that is lost; the encryption would not be perfect because certain information can be gleaned from the given values.

However, are there schemes in which this is possible? At first I thought it might be possible using Homomorphic Encryption, but as far as I now know, these seems to allow to calculate the mean as encrypted value, but not the process of comparing the other values against it.

Is there a way to do this?
If I understand what you're looking for correctly, that would completely destroy the security.

First off, if an attacker can compute the difference between her value and the mean, it is trivial to find the actual mean. Simply encrypt the number $0$ and then compare it to the mean.

If she can compute the mean of any subset, it's pretty trivial to recover plaintexts: just compute the "mean" of a single ciphertext. Even if you somehow make it work only for subsets of a particular size or something, she can still decrypt an arbitrary ciphertext $c$ like so:

$$ d(c) = (N+1)(\mu(S\cup m)-\mu(S\cup e(0)))$$

Where $e(0)$ is the encrypted $0$, $S$ is some arbitrary subset of the ciphertexts, $N$ is the size of $S$, and $\mu$ is the mean of a subset.