Why do adjacent bins differ so widely in histograms?

Looking at the tutorial "Histogram Measurements with NI High-Speed Digitizers", we see that neighboring histogram levels differ by a factor of 3 or more, even though the overall curve is as expected.
I have the same problem in my application in the UNCC Adaptive Optics Lab. Why does this occur?

Short answer - you are probably seeing small number statistics in action. Long answer - most histograms are generated to find the mean and standard deviation of a random process. If the number of points in any particular bin is random, the one sigma variation of the number of hits in each bin is the square root of the number of hits in that bin. So, if you want a smooth curve, you need lots of hits. For example, assume you have a histogram that has a width at the 1/e point of four bins. The peak is 10 hits high. The next bin is 3 hits. The next over from that 4. This represents a Gaussian with a true peak height of 7.3 and a 1 sigma variation in the hits for each bin. There is about a 5% chance of this occurring. Take the same underlying random phenomenon a
nd take a histogram with a true height of 7300 hits and then apply the same one sigma variation to each bin. You get a sequence of 7385, 5610, and 2737 - much smoother.
You need to do this sort of calculation for any histogram you generate. Then you need to determine if the results are interesting physics or just random chance. Nobel prizes have hinged on this very question.
You need to determine whether or not you expect a Gaussian curve. If you are taking the voltage histogram of the tops of two square waves, you should get two sharp spikes. Depending upon the width of your bins, you may or may not get tails on the spikes. If you are capturing the whole pulse, you would not expect a Gaussian peak shape due to ringing at the edges of the pulse.
So, remember what you are measuring, analyze the statistics, and look for the underlying phenomenon. Good luck! Have fun!
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