To find the arithmetic mean of the given data set, follow these steps:

1. Sum all the values in the data set.
2. Divide the sum by the total number of values.

Given data set: $116, 122.8, 101.4, 133.9, 133.9, 91.2, 119.2, 133.9, 113.8, 104.5$

Step 1: Calculate the sum of all values. $116 + 122.8 + 101.4 + 133.9 + 133.9 + 91.2 + 119.2 + 133.9 + 113.8 + 104.5$

$= 116 + 122.8 + 101.4 + 133.9 + 133.9 + 91.2 + 119.2 + 133.9 + 113.8 + 104.5$

$= 1170.6$

Step 2: Divide the sum by the number of values (which is 10). $\text{Mean} = \frac{1170.6}{10} = 117.06$

So, the arithmetic mean of the data set is: $\text{Mean} = 117.06$

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What is the median of the given data set?
2. How do you calculate the variance of this data set?
3. What is the standard deviation of the given data set?
4. How does the presence of an outlier affect the arithmetic mean?
5. How do you find the mode of this data set?
6. What is the range of this data set?
7. How would you interpret the skewness of this data set?
8. How can you visualize this data set using a histogram?

Tip: To quickly check your arithmetic calculations, use a calculator or spreadsheet software to ensure accuracy, especially with larger data sets.