This is supposed to be an extension to my answer for your other question drawing duplicated points in gnuplot with small margin:
You need to have the first column interpreted as time data. For this you need
set xdata time
set timefmt '%Y-%m-%d'
In order to set the point color, it is best to define a palette and then use linecolor palette, which sets the point color based on its value in the palette.
So, using the explanations from drawing duplicated points in gnuplot with small margin the final script is:
reset
filename = 'data.dat'
stats filename using 4 nooutput
set xdata time
set timefmt '%Y-%m-%d'
set format x '%Y-%m'
rand_x(x) = x + 60*60*24*7 * (rand(0) - 0.5)
rand_y(y) = y + (rand(0) - 0.5)
plot for [i=0:int(STATS_max)-1] filename \
using (rand_x(timecolumn(1))):(i < $4 ? rand_y($2) : 1/0):3 pointtype 7 linecolor palette notitle
Some other things you must have in mind are:
- The
stats call must come before set xdata time, because the statistics don't work with time data.
- When calculating with time data in the
using statement, one needs to use the timecolumn function (as opposed to column or $.. in generic cases). This gives the time as a timestamp (i.e. in seconds).
- For that reason you need two different random functions for
x and y, because of the very different scalings. Here, I used a 'jitter' of one week (60*60*24*7 seconds) on the time axis.
The result with 4.6.4 is:

Some remarks to your question about learning gnuplot: Try to solve your questions by yourself and then post more concrete questions! Browse through the gnuplot demos to see what is possible, look which feature or plotting style is used, look them up in the documentation, what options/settings are offered? Play around with those demos and try to apply that to your data sets etc. In the end its all about practice (I've been using gnuplot for 12 years...).