To find the average of a set of numbers, we use the formula:

$\text{Average} = \frac{\text{Sum of the numbers}}{\text{Total count of numbers}}$

Here are the steps:

1. Sum of the numbers: $35.5 + 51.5 + 53.2 + 54.0 + 54.4 + 56.6 + 58.4 + 61.6 + 62.4 + 71.4 = 559$

2. Total count of numbers: There are 10 numbers in the set.

3. Calculate the average: $\text{Average} = \frac{559}{10} = 55.9$

Thus, the average of the numbers is 55.9.

Would you like any further details or have any questions?

Here are five related questions you might find useful:

1. How do you find the median of a set of numbers?
2. How do you calculate the weighted average?
3. What is the mode of a dataset, and how do you find it?
4. How does the mean differ from the median in data interpretation?
5. How can outliers affect the average of a dataset?

Tip: Always check if your dataset contains outliers, as they can significantly affect the average!