ALL U.S. coins have the word LIBERTY on them and in 1878 many of them had a picture of Miss Liberty as well, so a "Liberty coin" is a bit like saying "what kind of car has a windshield and headlights"?
Please determine what the coin's denomination is and whether there is a small mintmark somewhere on the back - S, O, or CC - then post a new question with those details.
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The Liberty head design was used on over several different coins in 1878. Please post a new question with the coin's denomination, with the wording "What is the value of an 1878 US (coin denomination)?" e.g. What is the value of an 1878 US silver dollar? or What is the value of an 1878 US 10 dollar gold piece.
Please recompose your inquiry to include exactly what you desire to know about the coin.
The coin is a 1878 Morgan silver dollar and is common with values of $17.00-$31.00 in average circulated condition
The most common type of 1878 Morgan sells for $17.00-$30.00 in circulated grades
Assuming the coin IS a Morgan dollar, the most common type for this date has values of $18.00 to $40.00 depending on the condition of the coin.