you need to know how many files you have, in this num_files=16, and you need to know the total number of columns per file in this tot_num_cols=13. Here I wanted to average colums 1 and 4. Using the paste command which pastes a number of files to the screen side by side and piping to awk the script will output the average of columns 1 and 4 to a file called anewfile.txt
paste filename.* | awk 'BEGIN{num_col=4;num_files=16;timecol=1;tot_num_cols} {c=0; for (j=0;j < num_files;j++){c+=$(timecol+tot_num_cols*j)}}; s="0;" i="0;i < ="num_files;i++){s+="$(num_col+tot_num_cols*i)};" > | anewfile.txt