jmc

For simplicity, divide all the percent scores by $10.$ We will account for this later by multiplying by $10.$ The average percent score is equal to the sum of all percent scores divided by the total number of students $(100).$ The sum of all percent scores is $$10\cdot 7+9\cdot 18+8\cdot 35+7\cdot 25+6\cdot 10+5\cdot 3+4\cdot 2=770.$$ Since we divided all the percent scores by $10$ in the beginning, we multiply by $10$ to get that the sum of all percent scores is $770\cdot 10=7700.$ Finally, dividing by the total number of students, we find that the average percent score is $7700/100=\boxed{77}.$