In case you have all intermediate steps, i.e., full data for number (which is suspect based on your axis labelled iterations), you best use the every
option
plot "data.csv" every 10 with linespoints
Otherwise, I would use awk
inside your script for simplicity
plot "<awk '$1%10==0' data8" with linespoints
The probably with your original script, is that the points are shown, but with value infinity. It is a feature that these lines are not shown.