I think I understand what you are trying to do but you are going about it the wrong way. i believe you wish to get the average result (whatever type) for a given face or geometry. When I see the images you posted I see that you are using the result measure command but are viewing the post-processed results and therein lies your problem.
When you are viewing post-processed results you should use the "Identify Results" command on the Results tab in the Post Processing section.
When using this command you can see I have set the Pick to "Feature Face" and this selects all the elements on that face. In this case i am measuring the Von-Mises Stress - Elemental. In the dialog box you see the average value for that face is 71.99MPa. Remember this value.
Now let's get out of the post-processor and select the results measure manager icon in the Home tab under the Solution section. You then created and I create here a new result measure and I will name the expression "Avg_Stress"
If we then go back to the Result Measure Manager dialog you will see:
And what you see is the same value of 71.99MPa for the average von mises elemental - stress.
So what does this mean?
Well as I said above when in the post-processor, the right way to get results is to use "Identify Results" but when you aren't you can use the "result measure". But what's the difference? The difference is that you can do much more with a result measure. The value is stored in an expression, and similarly many can be stored (hence the Result Measure Manager dialog). More importanly, this value can be manipulated and you can start to combine them and do many things with them, essentially creating derived results.
You can read more about this in the help section: Working with Results
So bottom line, use the Identify Results command. But I will concede that the use of "Results Measure" can be confusing as I can see how you would think based on the command name that this measures the result! I think this is something worth mentioning to development, and I will do so.
Let me know if you have any other questions,
Yes, you've given me the best possible explanation one could give!
Thanks for this help.
The problem was that Result measure doesn't measure or allow us to select the face for doing that analysis.
But it was solved with identify Results option.