What is the relationship between number of samples and appropriate number of discrete frequencies? This question is inspired by an eBird feature that displays the "frequency" of species being reported in a location during a particular time of year.  eBird calls these "bar charts" they look like this:

The year is divided into 48 periods.  For each period and for each species, the height of the bar represents the number of checklists submitted containing the species, divided by the total number of checklists submitted during that period.
I once found an article somewhere on eBird where some additional detail about bar charts was provided.  Despite some effort in searching, I'm unable to find the article now, but I recall reading something along the lines of "in order to show the maximum number of bar sizes, at least 300 checklists must be submitted per period."
I interpreted this to mean that if it is possible to render a finite number of different bar heights, then maybe it isn't necessarily appropriate to just render the bar height that corresponds most closely to the calculated frequency.  Instead, maybe it is more appropriate to determine how many different significant heights are possible (i.e. to chose a fewer number of heights which span the same range), given the total number of observations for a period (and some criteria for significance).  I'm thinking this is similar to using a measuring tape to measure distance and reporting the result in nanometers - the use of too many significant digits implies accuracy that isn't really there.
I do not have a strong statistics background.  I've been reading about some different tests for significance, but so far I've struggled to understand how these tests might be applied to this case.
So my question is twofold:

*

*Is my interpretation of the statement regarding the maximum number of bar sizes and the number of observations correct?

*If so, what is the process for determining how many different heights are appropriate, given a number of observations?  If not correct, what was meant by the statement?

 A: As I understand the problem, it deals with a simple ratio of integers (number of checklists with a particular species divided by the total number of checklists). Integers are infinitely precise, so a ratio of integers is also infinitely precise. If you find that 500 of 1300 checklists contain the species, you could accurately state that exactly 38.461538461% of your observations contained the species. This would be an appropriate statement about your sample, but would not be an appropriate statement to make about the population. Most of the precision in that percentage will be completely dwarfed by variability in your sampling - the 95% confidence interval of that proportion as measured in 1300 samples is between 35.8% and 41.1%, so reporting the proportion to many decimal places is an unnecessarily precise point estimate.
I'm not really sure what is meant by "in order to show the maximum number of bar sizes". A sample size of 300 would yield 301 distinct bar heights, but there's no reason you couldn't estimate frequency from fewer samples. Having more samples also doesn't guarantee  different bar sizes, anyway - you might have 100 species with thousands of samples, each of which appears 40% of the time, resulting in only one single bar size being shown on the plot. The most likely reason I can think of is that they only want to show proportions with sufficient data to have a reasonable estimate of proportion. With 300 samples, a proportion around 50% can vary up or down by about 6%, so perhaps they don't want to show less precise estimates than that. A proportion estimated from only 10 samples might appear identically on the plot with a 50% proportion, but would be expected to vary by as much as 31% up or down. As the sample size gets smaller, point estimates of proportion become increasingly unreliable.
As for bar sizes, I don't think you'd want to adjust estimates to points that are "significantly different". A proportion of 100/1000 isn't significantly different from 101/1000, but that doesn't mean you shouldn't report estimates as you find them. You quickly run into the issue of where to set the reference points - should it be 99/1000, or 100/1000, or 101/1000? You're effectively binning the data, which you generally want to avoid unless you have a good reason to do so. With three values A, B, and C, you might find that B is not significantly different from A or C, but that A and C are significantly different from one another - do you then map B to the value of A or C?
