To determine the arithmetic mean of the given set of numbers, follow these steps:

1. Add all the numbers together: $8 + 11 + 7 + 10 + 8 + 11 + 7 + 9 + 7 + 7 + 8 + 7 + 7 = 107$

2. Count the number of elements in the set: $\text{There are 13 numbers in the set.}$

3. Divide the sum by the number of elements: $\text{Arithmetic Mean} = \frac{107}{13} \approx 8.23$

So, the arithmetic mean of the given set of numbers is approximately 8.23.

Would you like further details or have any questions about the solution?

Here are some related questions:

1. What is the difference between arithmetic mean and median?
2. How do you calculate the median of a set of numbers?
3. How does the arithmetic mean differ from the geometric mean?
4. Can the arithmetic mean be lower than the smallest number in a set?
5. How does adding a number to a set affect the arithmetic mean?
6. What is the impact of an outlier on the arithmetic mean?
7. What is the relationship between arithmetic mean and standard deviation?
8. How can the arithmetic mean be used in data analysis?

Tip: In datasets with extreme outliers, the median is often a better measure of central tendency than the arithmetic mean.