I want to create a plot like this with gnuplot:

I have different data points for a fixed moment in time. I want to group these data points around the representing x value. These datapoints come from different data files which look like this:
9 0.333
9 0.308
9 0.289
15 0.356
15 0.836
15 0.364
15 0.347
0 0.386
0 0.318
0 0.347
0 0.322
12 0.351
12 0.314
12 0.314
Currently I plot the data using a loop like this:
set xtics (0, 3, 6, 9, 12, 15, 18, 21)
plot for [i=1:15] sprintf('file_%i.dat', i) using 1:2 with points
but they're overlapping. How can I do this using gnuplot?