Calculate the Mean of 10, 12, 8: Exploring Average Changes

To solve this problem, we'll determine the initial average of the numbers provided and address the change in the average when a new number is added:

• Step 1: Calculate the initial average.
• Step 2: Add the new number to recalculate the average.
• Step 3: Compare the old and new averages.

Step 1: Calculate the initial average of 10, 12, and 8:
- First, find the sum of the numbers: $10 + 12 + 8 = 30$.
- There are 3 numbers, so divide the sum by 3 to get the average: $\frac{30}{3} = 10$.

Step 2: Add the number 11 (which is larger than the initial average) to the group and recalculate the average:
- The new sum is $30 + 11 = 41$ with a total of 4 numbers.
- The new average becomes $\frac{41}{4} = 10.25$.

Step 3: Compare the averages:
- The initial average is 10.
- The new average is 10.25, which is higher than 10.

Therefore, adding a number larger than the initial average results in an increased average. So, the average will increase when 11 is added.

The correct answer to the question is: Average 10, the average will increase.