Particle size distribution/histogram errors.

[RossJJ]

I posted this elsewhere but probably in the wrong topic so have reposted here.

Okay, so I have obtained a particle size distribution of diesel exhaust particles on a SEM. Data has been plotted and fitted with a lognormal distribution. Although it isn't a usual path to take I have been told I must put errors on each bin height. I obviously have an error on each individual particle measurement but I am having issues converting this to an error in the frequency counts/probability.
I tried to take the errors and re-bin the particles with the error added and subtracted but was told I should follow the usual error procedure, such as adding in quadrature or something similar, other than that my supervisor was quite vague.
After many a trawl of articles and suchlike I am coming up blank, mainly because it is rather rare to use errors on a histogram, as a histogram is kind of inherent of the errors, being a distribution and whatnot.
Can anyone help please?

 

[LightHero]

It sounds like your supervisor is asking you to use a method known as propagation of error, or uncertainty propagation. This is a common technique used in statistics when dealing with data that has errors associated with it. The idea is to propagate the errors from the individual measurements up to the final result. In your case, you would need to calculate the uncertainty associated with each bin in the histogram. You can do this by propagating the errors in the individual particle measurements through any calculations you have done to obtain the frequency counts and/or probabilities for each bin. This will give you an estimate of the uncertainty associated with each bin.For more information on propagation of error and how to calculate it, you may want to search online for tutorials or guides on the subject.