Let's solve the problem step by step using the data provided:

The dataset is: $57.6, 75.8, 41, 57, 35.2, 75.8, 51.8, 49, 65.8, 75.8$

1. Arithmetic Mean (Average):

The formula for the mean is: $\text{mean} = \frac{\sum \text{values}}{\text{number of values}}$

2. Median:

The median is the middle value when the numbers are arranged in order. If there is an even number of values, the median is the average of the two middle numbers.

3. Mode:

The mode is the value that appears most frequently in the dataset.

I'll now calculate these values.Here are the calculated values for the given dataset:

1. Mean (Arithmetic Average): 58.48
2. Median: 57.3
3. Mode: 75.8 (appears most frequently)

Would you like further clarification on any of these calculations?

Here are 5 related questions to explore further:

1. How is the range of a data set calculated, and what is it for this set?
2. What is the variance and standard deviation of this data set?
3. How does the presence of multiple modes affect data analysis?
4. What is the difference between a mean and a weighted mean?
5. How do outliers affect the median compared to the mean?

Tip: When calculating the median for an even-sized data set, always take the average of the two middle values.