With the given info it is impossible to help you. Could you provide more details?
1. Do you manually insert those rows?
2. Which column(s) of the inserted rows would you like to get the average of?
3. When we have the average, what do you want to do with it? Place it in a cell or show it as a message or ...?
These are just some questions that pops up in my head. If there is more relevant info, do inform us.
4. Since you use a code to insert rows, I either have to know that the insertion part of the code is at the bottom (meaning, the inserted part is still selected) or I have to know the code (assuming you don't know how to alter your code).
5. There are 16384 columns and I'm pretty sure you don't use all of them. So how many columns do you use or how many averages do you want? No need to make the code do more than is needed.
6. Which range did you have in mind to place the averages?