To find the mean of the given numbers, follow these steps:

1. Sum all the numbers: $13 + 16 + 12 + 14 + 19 + 12 + 14 + 13 + 14 = 127$

2. Count the total number of values: There are 9 numbers.

3. Divide the sum by the number of values to find the mean: $\frac{127}{9} = 14.11$

Thus, the mean of the given numbers is approximately 14.11.

Would you like further clarification or more details?

Here are five related questions to expand on this concept:

1. How do you calculate the median of these numbers?
2. What is the mode of the given data set?
3. How would adding another number to the set affect the mean?
4. What is the range of these numbers?
5. How does the mean compare to the median in this data set?

Tip: The mean is sensitive to extreme values (outliers), so adding very large or small numbers can significantly change it.