title: Plotting normalized histograms in gnuplot
body: <p>I am having a set of data (one column) available from my <a href="https://www.dropbox.com/sh/b5lxgzckv3cn3wb/AABwvr8Q7XWh6xKK_2qf-fpJa?dl=0" rel="nofollow noreferrer">dropbox</a>. In the dropbox, there is also a gnuplot code that produces the following figures.:
  <a href="https://i.stack.imgur.com/TueYH.png" rel="nofollow noreferrer">Not normalized histogram for velocities</a> and <a href="https://i.stack.imgur.com/5Cbjn.png" rel="nofollow noreferrer">Not normalized distribution for the radius</a>. What I would like to do are the following</p>
  
  <ol>
  <li>Normalize both histogram using gnuplot</li>
  <li>to make the radius graph as nice as the velocities and magnify both if possible.</li>
  </ol>
  
  <p>I am facing this problem since a week since I am not used with histograms in gnuplot, so your help will be greatly appreciated. Here is the gnuplot code:</p>
  
  <pre><code>reset
  set terminal pngcairo 
  set output 'r_distr_3ev.png'
  set key off
  set border 3
  
  set boxwidth 0.05 absolute
  set style fill solid 1.0 noborder
  
  bin_width = 0.005;
  
  bin_number(x) = floor(x/bin_width)
  
  rounded(x) = bin_width * ( bin_number(x) + 0.00025 )
  
  plot 'data_prob_distr_funct_radius_3eV.dat' using (rounded($1)):(1) 
  smooth frequency with boxes
  
  
  reset
  set terminal pngcairo 
  set output 'v_distr_3ev.png'
  set key off
  set border 3
  
  set boxwidth 0.05 absolute
  set style fill solid 1.0 noborder
  
  bin_width = 0.1;
  
  bin_number(x) = floor(x/bin_width)
  
  rounded(x) = bin_width * ( bin_number(x) + 0.5 )
  
  plot 'data_prob_distr_funct_veloci_3eV.dat' using (rounded($3)):(1) 
  smooth frequency with boxes
  </code></pre>
  
  <p>Here is a sample of data (file is too long to be posted fully). However, need to edit the data sources on the plot commands.</p>
  
  <pre><code> # radius                        # Velocities
  1.432710516747764062         0.518383911504932460
  1.415400787912409752         0.117744310428800222
  1.420463215076467778         0.083766261830559782
  1.437922410272506557         0.309560054349534541
  1.420463215076467778         0.268622745024368170
  1.438756837417662471         0.203390900905284472
  1.418356121124933145         0.518346867895466801
  1.438756837417662471         0.182812150806309304
  1.421657988632006209         0.299301056216330852
  1.432074613018175180         0.293967535681474712
  1.421657988632006209         0.183613746565735064
  1.412588932829508259         0.501168210407462289
  1.416512172894701438         0.179507944624779481
  1.412588932829508259         0.029653108171494944
  1.417995684224648612         0.234379565912604448
  1.417914885270917580         0.255589209064060963
  1.417995684224648612         0.539792616529789826
  1.408834060670934862         0.256331796703176962
  1.423042784959195561         0.082132902455306064
  1.408834060670934862         0.198595146234998993
  1.432298354037856436         0.255681807316227472
  1.406168218647184665         0.595524682621352608
  1.432298354037856436         0.150127810412636647
  1.431591815111461719         0.271379130577297567
  1.422276604689641788         0.367863070449541862
  1.431591815111461719         0.135432525011420862
  1.431551259009345989         0.138525547190355175
  1.400408991855918162         0.626963309755715237
  1.431551259009345989         0.294435076616490321
  1.425580611910310047         0.527847978352356417
  </code></pre>
  
  <p>Cheers</p>