To find the mean (average) of a set of numbers, follow these steps:

1. Add up all the numbers:
   $25 + 20 + 24 + 23 + (-19) + (-10) + 21 = 84$

2. Count how many numbers there are:
   There are 7 numbers.

3. Divide the sum by the number of numbers:
   $\frac{84}{7} = 12$

Thus, the mean is $12$.

Let me know if you'd like more details or have any questions. Here are 5 related questions:

1. How would you calculate the median of this data set?
2. What is the range of these numbers?
3. What is the mode of this data set?
4. How would the mean change if you added another number to the set?
5. How do positive and negative values affect the mean?

Tip: The mean is sensitive to extreme values, also known as outliers.