A culled coin, or simply a "cull", refers to a coin that is in such bad shape that it has been removed from an otherwise circulated group of coins. Such a coin might be bent, cut, holed, or otherwise damaged.
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I suggest you get a good coin book and search for your coin in there.
The most expeditious way to get a coin graded is to locate a coin shop nearby - present the coin to the owner for grading. If he/she is uncomfortable to do so, he/she will refer you to a numismatist (experienced coin collector).
a Coin Toss
The coin would float.
If that is a private mint coin, it is probably the weight of the coin.