The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number.

Answer Details

The problem tells us that we have a set of 10 numbers, and that the average (or mean) of all those numbers is 56. However, we also know that if we exclude the 10th number from the set and find the average of the remaining 9 numbers, the result is 55. To find the value of the 10th number, we need to use a little bit of algebra. Let's call the sum of the first nine numbers "S". We know that the average of those nine numbers is 55, so: S / 9 = 55 If we multiply both sides of the equation by 9, we get: S = 495 Now we can use the fact that the average of all ten numbers is 56 to find the 10th number. The sum of all ten numbers is: 10 x 56 = 560 We already know that the sum of the first nine numbers is 495, so we can subtract that from the total to get the value of the 10th number: 560 - 495 = 65 Therefore, the 10th number in the set is 65.