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

Formula for Arithmetic Mean:

$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$

Data Set:

$125, 164, 183, 154, 132, 129, 524, 476, 165, 133$

Step 1: Calculate the sum of all data points

$125 + 164 + 183 + 154 + 132 + 129 + 524 + 476 + 165 + 133 = 2085$

Step 2: Count the number of data points

There are $10$ numbers in the data set.

Step 3: Calculate the mean

$\text{Mean} = \frac{2085}{10} = 208.5$

Final Answer:

The arithmetic mean of the data set is 208.5.

Would you like a deeper explanation or further calculations?

Here are 5 related questions you might explore:

1. What is the median of this data set?
2. How does the presence of extreme values (e.g., 524 and 476) affect the mean?
3. What is the range of this data set?
4. Can you calculate the standard deviation for this data set?
5. What is the mode of this data set?

Tip: When calculating a mean, always consider if outliers (extreme values) skew the result significantly.