A proof coin (the word "mint" is usually not used in conjunction with the term) is a coin specially made for clarity of design. A proof coin started out being much like a proof print of a photograph; it was used to prove that the design elements were situated correctly, and looked good enough to be produced. Today most governments' mints produce sets of proof coins for collectors. A US proof coin is made from dies that are sandblasted (albeit usually with glass beads for the "sand") and then polished. The dies are polished every 5-15 coins, and replaced frequently before the die is worn. Each coin is hand-fed into the press using tongs or gloved hands; the coin is then struck at least twice. The resulting coin has a mirror-finish field or background, with frosted devices (or raised areas). Proof dies can, in some cases, be recycled for use with standard-issue coins, although some proof coins have slightly different designs from standard-issue coins. (For example, the 1-cent coin has an almost-joined "AM" in "AMERICA" for a circulation coin, but a different spacing for the proof coin.) If your coin is dated 1968 or later, proof coins are relatively easy to identify because they all have an "S" mint mark on them. The only possible confusion would be if the coin is a cent from 1968-74 or a nickel from 1968-70, when San Francisco struck those denominations for circulation as well as for inclusion in proof sets. All other S mint coins from 1968 onward are proofs only.
Earlier proofs were struck at Philadelphia so they're more difficult to identify unless they're in their original packaging.
Proof coins sometimes find their way into circulation when a set is broken open. That can happen if a set is stolen and the thief doesn't know what he has; sometimes small children will open Mommy's or Daddy's proof sets to get at the "shiny coins". Unfortunately if a proof coin has been spent, its value is significantly reduced.
About $2.00 for average proof coins
The current value of a 1950 proof set is $750.
If they are reproductions made by a company other than the U.S. Mint, they are not legal tender. If you are talking about U.S. Proof coins, those can be worth significantly more than face value depending on their precious metal content and their rarity.
A proof coin is a coin that is made to test the mint and ensure that the coin is of proper quality before mass production. Generally, a proof is not circulated, but they are sometimes sold to collectors.
1975 Proof sets are valued at $11.00.
NO, they do not. That's the simple answer.
It's not a Proof set, no Proof coins were were struck in 1965-1967. The set is a "Special Mint Set" that has coins with semi-proof like surfaces with less design details. Issue price was $4.00 average retail value is $15.00.
The 1994-S Clad Proof set (5 coins) with all original packaging has a current retail value of $8.00. Issue price was $12.50.
Your 1884 Trade Dollar is a copy or fake with little or no value. There are only 10 known 1884 Trade Dollars and there all Proof coins
Issue price was $11.00, current value is $8.00
Current retail value is $54.00
All Proof coins are sold by the Royal Mint in sealed protective packaging to protect the condition and finish of the coin(s). Proof coins may also come with a certificate of aunthenticity. Apart from that, Proof coins have a very high quality finish and are priced well beyond the face value of the coin. Proof coins are most unlikely to be found in loose change due to their high value.