The arithmetic mean of the last 9 numbers of a data set is 56. The mean reduces by 7 when one of the terms is excluded from the data. What is the number that is not included?

Step 1: Calculate the total sum of the last 9 numbers. The arithmetic mean is the sum of the numbers divided by the count of the numbers. So, the total sum of the last 9 numbers is 56 * 9 = 504.

Step 2: Calculate the total sum of the last 8 numbers. The mean reduces by 7 when one of the terms is excluded, so the new mean is 56 - 7 = 49. The total sum of the last 8 numbers is 49 * 8 = 392.

Step 3: Find the number that is not included. The number that is not included is the difference between the total sum of the last 9 numbers and the total sum of the last 8 numbers. So, the number that is not included is 504 - 392 = 112.