There are essentially two types of rarity: absolute (a coin that is rare in all grades; an example of this would be an 1842-O half eagle) and conditional (a coin that is rare based mainly on grade; an example of this would be an MS63 1892-O eagle). What can we learn about rarity based on distribution--i.e., if the number of coins known for an issue is 300, in what grade range are these coins found? The answers are interesting. It is fairly obvious why a coin is an absolute rarity. Generally, the best reason for this is low mintage. Obviously, a Proof gold coin from the 1870's with a mintage of 25-35 is going to be rare; even if the survival rate is 50% or so, you are still not talking about many coins. But many issues have an uncommonly low survival rate to to heavy use in commerce and a high degree of meltings. Examples of this include No Motto half eagles and eagles from the Philadelphia mint. It is not uncommon for issues of these types to have fewer than a dozen known in Uncirculated even with original mintages of 200,000 to 500,000 or more coins. Let's use current PCGS population statistics to look at a specific example: the 1849 eagle; an issue with an original mintage that tops out at 653,618.
To date, a total of 361 1849 eagles have been graded by PCGS. The breakdown is as follows:
Mint State= 30 coins About Uncirculated= 128 coins Extremely Fine= 149 coins Very Fine and below= 54 coins
Breaking this down further, we see that around 8% of all 1849 eagles graded by PCGS are Uncirculated while close to 80% grade Extremely Fine and About Uncirculated. Given the fact that the Uncirculated numbers are inflated by resubmissions, the percentage of 1849 eagles that grade MS60 and above is probably less than 5%.
There are, of course, coins with high mintage figures that are actually quite rare due to excessive meltings. A good example of this is the 1819 half eagle. There were 51,723 of these made but nearly all were melted by 1834 due to a change in the weight of gold coins which made these old tenor issues worth more than face value. Today there are, at most, thirty known 1819 half eagles. And the grade distribution of this issue is bizarre with virtually every known example grading MS60 or better.
Why is this the case? In addition to the heavy meltings above, a little history will show that this type barely circulated at all. Five dollars was a lot of money in 1819 and since the half eagle was the largest denomination made in the United States, these coins were basically storehouses of value. For the entire Capped Head Left half eagle type of 1813-1829, only two or three dates are seen with any degree of frequency in circulated grades and only one (the 1813) is more readily available in circulated grades than in higher grades.
Remember the 1849 eagle that I just mentioned above? There are some coins that are almost exactly the opposite when it comes to grade distribution. There are, for example, many gold dollars from the 1880's that are virtually unknown in circulated grades but common in Uncirculated. Let's look at the 1886 as an example.
A total of 5,000 business strikes were made. The most current PCGS numbers show a total of 354 examples having been graded. Of these, 331 (or 93.5%) have been graded MS60 or better. In theory, an 1886 gold dollar in AU55 is rarer than one in MS65 (although, of course, the MS65 is still worth considerably more).
Why is this the case? A little basic research shows that, by the late 1870's, the gold dollar denomination had been made redundant by the new Morgan dollars. Mintages were small and the demand was even smaller. The gold dollars didn't circulate and there were enough dealers and hoarders saving them that Gems (MS65 and finer) are plentiful.
What this means is that the 1886 gold dollar is a coin that is much less rare than its low mintage would suggest and hundreds are known in high grades (PCGS alone has graded 61 in MS65 or higher). If you were to graph the grade distribution of this issue, it would skew well towards higher grades. If you were to graph the distribution of the 1849 eagle, it would skew towards lower grades with most survivors grading EF-AU and very few in the Uncirculated grades.