arithmetic mean

A set of nine numbers has a mean of 10. A tenth number was added to this set, and the mean increased to 12. What was the number that was added to the set?

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.