The mean is not good in this case, because there are galleries that have an artist with a high rank and several other artists with way lower ranks. I'm thinking about doing a weighted mean, but I don't know how to split the weights to the ranking ranges. Any ideas? Thank you.
How about simply summing the qualities of the artists, where ranks are probably not the best measure for the quality, but if that's all you have...
Isn't it the case that a gallery with ten soso artists is better than one with five soso artists?
Also think about whether a gallery with ten works of a single artist is better than a gallery with five works of the same artist (if you have access to this information).
Maybe just quote the top one and say how many of their works are there. The quantity of art is quite important isn't it?
Summary statistic of all ranks: if you have outliers at the top you may want to use a robust measure. Look up robust statistics on wikipedia. These include the median and trimmed means, or Winsorization.