I'm trying to figure out - when they list mintage figures for individual denominations - does that INCLUDE the quantity in the mint sets?

For example - if the mintage for a 19xx coin is listed as 5,150,150 and the mint set for the same year is listed as 1,150,150 does that mean a total of 6,300,300 coins were minted or only 5,150,150 were minted OUT OF WHICH 1,150,150 was put into mint sets, leaving only 4,000,000 to be put into actual circulation....?

This is a perennial problem for everyone because the Mint is not always consistent in their reporting. In most cases the two figures are separate and not inclusive.

I’m the Red Book’s production editor, which means I coordinate the pricing and other edits and generally ride herd on the process. I also compile the mintages from the Mint’s published figures each year. The short answer is, yes, the single-coin mintages include the set mintages, so you don’t have to add the single coins to the sets to get an additional mintage figure.

Mintages for Proofs are derived a bit differently from those for circulating coins. For each Proof denomination, I figure out which sets it was included in (Proof Sets, Silver Proof Sets, Limited Edition Proof Sets, etc.), then add up the most recent numismatic sales for those sets. For circulating coins, I simply pick up the Mint’s most recently published production figures. The Mint pulls from this supply to make its regular Mint Sets, so the coins in those sets are already accounted for in the numbers the Mint publishes.

In the example above, the total mintage is 5,150,150. If the 19xx coin is a circulation strike, 1,150,150 of the coins went into sets and 4 million went into circulation. If 19xx is Proof, all 5,150,150 went into Proof Sets.