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    <p>Here's your first 2 questions:</p> <pre><code> myhist &lt;- hist(x,prob=FALSE,col="gray",xlim=c(0,100)) dens &lt;- density(x) axis(side=1, at=seq(0,100, 20), labels=seq(0,100,20)) lines(dens$x,dens$y*(1/sum(myhist$density))*length(x)) </code></pre> <p>The histogram has a bin width of 5, which is also equal to <code>1/sum(myhist$density)</code>, whereas the <code>density(x)$x</code> are in small jumps, around .2 in your case (512 even steps). <code>sum(density(x)$y)</code> is some strange number definitely not 1, but that is because it goes in small steps, when divided by the x interval it is approximately 1: <code>sum(density(x)$y)/(1/diff(density(x)$x)[1])</code> . You don't need to do this later because it's already matched up with its own odd x values. Scale 1) for the bin width of <code>hist()</code> and 2) for the frequency of x <code>length(x)</code>, as DWin says. The last axis tick became visible after setting the <code>xlim</code> argument.</p> <p>To do your problem 2, set up a plot with the correct dimensions (<code>xlim</code> and <code>ylim</code>), with <code>type = "n"</code>, then draw 3 lines for the densities, scaled using something similar to the density line above. Think however about whether you want those semi continuous lines to reflect the heights of imaginary bars with bin width 5... You see how that might make the density lines exaggerate the counts at any particular point?</p> <p><img src="https://i.stack.imgur.com/P6BQv.png" alt="enter image description here"></p>
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    1. COThanks. I've decided against using frequency on y-axis for the density overlay plots.
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    2. CO@user1202664 probably a good idea
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