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.

It is difficult to understand exactly how and what to automate.

Perhaps this will help.

Create a concrete example

f = RandomReal[{0, 5}, 6];
unsort = Table[i = RandomInteger[6]; 
y = RandomReal[{0, 10}]; {f[[i]], y}, {1300}];
sort = Sort[unsort]

Now group together all lists which have the same first element

splitsort = Split[sort, First[#1] == First[#2] &]

Now examine the first set of items which share the first element

splitsort[[1]]

Perhaps this will be useful

For[n = 1, n <= Length[splitsort], n++,
 Print["The ", n, "'th group with the same first element is: ", splitsort[[n]]]
 ]

If this is still not sufficient then can you provide the simplest clearest description of what you need as a result? Perhaps with that it will be possible to get closer to what you want to accomplish.

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.