Statistic analysis and histogram plotting using gnuplot

Given a data file containing a set of data, count how many datas locate in intervals [a1:a2],[a2:a3]... respectively, then plot the result into a histogram. This a common problem in statistics and exactly what we will do in this article.

Firstly, let us see how to map the data into intervals. There is a function "floor(x)" which return the largest integer not greater than its argument. So function floor(x/dx)*dx will map x into one of the intervals [-n*dx:-(n-1)*dx],[-(n-1)*dx:-(n-2)*dx]...[(n-1)*dx:n*dx].

Now we come to count the data number in each interval. In gnuplot there is a smooth option called "frequency". It makes the data monotonic in x. Points with the same x-value are replaced by a single point having the summed y-values. Using this property, we can count the data numbers in the intervals.

At last we plot our result using boxes plot style.

The main idea have introduced. It is time to write the plotting script.

reset
n=100 #number of intervals
max=3. #max value
min=-3. #min value
width=(max-min)/n #interval width
#function used to map a value to the intervals
hist(x,width)=width*floor(x/width)+width/2.0
set term png #output terminal and file
set output "histogram.png"
set xrange [min:max]
set yrange [0:]
#to put an empty boundary around the
#data inside an autoscaled graph.
set offset graph 0.05,0.05,0.05,0.0
set xtics min,(max-min)/5,max
set boxwidth width*0.9
set style fill solid 0.5 #fillstyle
set tics out nomirror
set xlabel "x"
set ylabel "Frequency"
#count and plot
plot "data.dat" u (hist($1,width)):(1.0) smooth freq w boxes lc rgb"green" notitle

We use a data file (download from here) which contains 10000 normally distributed random numbers and get a graph like the follow one.

statistic histogram plotting using gnuplot