PERCENTRANK Entire Column via Array Formula

I need to use the PERCENTRANK function in order to rank an entire column; however, the column includes non-numbers such as the column header as well as numerous #N/A's that are returned via formula when a number is non-existent in a database. I have used the following array formulas in order to force the calculation of the GEOMEAN and AVERAGE of the column:

{=GEOMEAN(IF(ISNUMBER($M:$M),$M:$M,""),IF(ISNUMBER($M:$M),$M:$M,""),IF(ISNUMBER($M:$M),$M:$M,""))}

{=AVERAGE(IF(ISNUMBER($M:$M),$M:$M,""),IF(ISNUMBER($M:$M),$M:$M,""),IF(ISNUMBER($M:$M),$M:$M,""))}

Is there a way to use PERCENTRANK, or one of its brethren, in the same way?

Unfortunately, the #N/As are there by design, as Excel ignores them when drawing charts. If the cell was populated using "", then the charts dive to the zero line, which is not aesthetically pleasing for use in presentation.

In an ideal world, it would also be great if the cells using the formula in the PERCENTRANK column would generate #N/As if another column did not have a number in it, but I have no idea if this is possible.

Thanks for cleaning up my use of the AVERAGE function three times! It was something I cobbled together after searching all over the web and while it worked, it was not efficient, to be sure.

For PERCENTRANK, you are correct that I am copying down the column, ranking each individual numeric entry in column M relative to the entire numeric contents of column M. I would expect each cell to have a different number.

Your solution works perfectly! Many, many thanks!!!