Thanks for the answer Gustavo, I solved with this:

ascisse = Table[sort[[i]][[1]], {i, 1, npunti}];

ascisse2 = DeleteDuplicates[ascisse];

nscisse2 = Length[ascisse2];

vettoreord = Table[{}];

For[i = 1, i < nscisse2 + 1, i++,

riga = Cases[sort, {ascisse2[[i]], , }];

ordinateriga = Table[riga[[i]][[2]], {i, 1, Length[riga]}];

psi = Table[riga[[i]][[3]], {i, 1, Length[riga]}];

mediaord = Mean[ordinateriga];

vettoreord = Append[vettoreord, mediaord]];

The problem was that some abscissa were assosiated to more ordinates. Really thank you for yours advice.

Thanks for your answer. This procedure works, but my problem is to automate the calculation in a loop. In fact I need more or less 1300 extraction for all the different values ??that assumes the first component of each element of the table. These values also include numbers with long decimal points.

Perhaps you can adapt something like this

First create come concrete data to see how this works

In[1]:= sort = RandomInteger[{0, 5}, {6, 2}]

Out[1]= {{5, 3}, {4, 3}, {2, 2}, {5, 2}, {4, 3}, {2, 1}}

Now suppose you want to pick out the items that begin with a 4

In[2]:= table = Cases[sort, {4, __}]

Out[2]= {{4, 3}, {4, 3}}

If this isn't enough and you can provide a simple clear description of what you need to accomplish then perhaps someone can take a moment to show you how to translate it into Mathematica.

Be careful with this if your data is going to include numbers with decimal points. It might work, but it might require other approaches to make sure that it correctly matches numbers which might display the same on the screen, but have very very tiny differences in the values that may not be visible.