Are Population Numbers Accurate?

They reduce populations when coins are cracked out and labels are returned.

Thanks for the link -- in that example, the detail for the auctioned item is at https://www.pcgs.com/auctionprices/...941791892459 where there is a certification number shown, but it gives a "not found" when clicked. The original item at the auction site is at https://auctions.stacksbowers.com/l...k-ms-65-pcgs but there is no slab or certification number shown there to confirm it. That auction ended in June 2010.

However, looking at the MS66 example, that one went for auction in January 2016, and it appears to be the same coin: https://coins.ha.com/itm/a/1231-4876.s -- there's a mark on Jefferson's cheek behind his eye and another in front of his eye, and a white spot in the center of the top field on the reverse.

In this case, it looks like this coin was a 65 then later resubmitted/graded as 66. The auction listings just show the sales for each grade, which is useful to know for historical pricing, even if the same coin.

Brandmeister: Key is labels are returned.

If you crack and trash, or paste the label in the back of the album, it's still in the population.

Populations can be wildly out. When they create a new variety the population of that variety only includes those graded after they recognise that variety. For example in 2017 for the Australian 1953 florin they recognised the Large Denticle variety and the Small Denticle variety. But in the population report all the pre 2017 graded '53s are counted as Small. Worse yet their identification skills are abysmal as I know of 2 Large in Small slabs and 3 Medium in Large slabs and they include Medium with Small as they don't recognise the Mediums as from a different hub to the Small.
In my collection I have a similar problem with 1926 sixpences and 1952 pennies so it appears to be a standard problem whenever new varieties are recognised.