1. The problem asks for the greatest amount the average mechanic makes during the year based on monthly earnings data. 2. To find the greatest amount, we look for the maximum value in the given monthly earnings. 3. The earnings for each month are approximately: January $1500$, February $1630$, March $1600$, April $1680$, May $1700$, June $1690$, July $1770$, August $1830$, September $1930$, October $1880$, November $1900$, December $1840$. 4. Among these values, the maximum is $1930$ in September. 5. Therefore, the greatest amount the average mechanic makes during the year is $1930$.