The arithmetic mean of a set is the sum of all the values divided by the total number of values. The arithmetic mean is usually called the average.
A set of nine numbers that has a mean of 10 must total 90
90/9 = 10
A set of 10 numbers that has a mean of 12 must total 120
120/10 = 12
Thus, the difference between the set of 10 numbers and the set of nine numbers is
120 – 90 = 30
Answer: the number that was added to the set was 30.