Ignoring Specific Values While Selecting Multiple Cells

I have to correct a spreadsheet that takes a bunch of values and creates an average.

=average(N15;N29;N43;N57;N71;N85;N99;N113;N127;N141;N155;N169;N183;
N197;N211;N225;N241;N255;N269;N283;N301;N315;N329;N343;N357)*100%

I didn't create this. Anyway, the problem is that most of these cells will be empty unless a whole bunch of other stuff is filled. These N cells take several values, put them together and create a new one. As time goes by they are filled. While they aren't filled, they'll return the DIV/0 error.

So when that formula I pasted there uses all of these values, it also returns a DIV/0 error because it is getting info from cells that have this error.

I managed to correct that with this
=averageif(N15:N357;"<>#DIV/0!")*100%

It works like a charm save for one problem. When I use averageif I'm forced to use an interval. Along this interval other values show up (it is always a value ranging from 0 to 2). So when the formula works its magic the results are slightly skewed because of this other value that I don't want.

So I figure there must be two ways around this. The first one would be using something like averageif that lets me use several handpicked cells instead of an interval. If I try

=averageif(N15;N29;N43;N57;N71;N85;N99;N113;N127;N141;N155;N169;N183;
N197;N211;N225;N241;N255;N269;N283;N301;N315;N329;N343;N357;"<>#DIV/0!")*100%

It doesn't work, it says I have too many values. So if I could the exact same thing as I did with averageif but keeping all of these values it'd be super nice.

The other solution, less nice but equally effective I guess, is using this same interval but having more than one criteria. The first criteria would still be the one telling it to ignore DIV/0 error, the second criteria would be the one to ignore any values equal or lower than 2.