# How do I display a histogram with normalized counts?

I have some data corresponding to real number distances: {200.04053, 200.232123, 156.3242,...}, and I would like to bin these values and display them as a histogram where the heights of each bar in the histogram are normalized so that the sum of all the bin heights is equal to one. The objective here is for me to be able to use FindDistributionParameters to determine, well, appropriate distribution parameters, and then to overlay the PDF of this suggested distribution on my actual data. Is there an easy way to do this?

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Add the argument "Probability" to the Histogram command. To be precise, if list is your list of data, then

Histogram[list,Automatic,"Probability"]


should do the trick. The Automatic argument specifies the bin size.

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Why does this appear to be dwarfed by the PDF of something like an InverseGaussianDistribution? Is that simply because of the long RHS tail for my data? –  Telomer Apr 15 '13 at 2:25
E.g. ::: Show[Histogram[DATA, Automatic, "Probability"], Plot[PDF[InverseGaussianDistribution[30.11455031212564, 17898.020946792625], x], {x, 25, 50}, Filling -> Axis, PlotRange -> All]] (I'm not claiming that this is the right distribution) –  Telomer Apr 15 '13 at 2:26
I'm afraid I don't understand what you mean by "dwarfed"? That said, I'm not a statistician, so even if I understood your question, I probably couldn't provide you with a satisfactory answer. –  David Skulsky Apr 15 '13 at 2:34
Sorry, I fooled myself into thinking that the bins weren't summing to one, but that's not the case. Thanks for your great answer! –  Telomer Apr 15 '13 at 2:39