Let's solve the arithmetic mean of the given data set correctly.

The data set is: $35.2, \ 47.4, \ 49.2, \ 50.2, \ 64, \ 23.6, \ 30.1, \ 64, \ 64, \ 41.2$

Step 1: Sum of the data points

First, we need to sum all the numbers: $35.2 + 47.4 + 49.2 + 50.2 + 64 + 23.6 + 30.1 + 64 + 64 + 41.2$

Let me calculate the sum.The sum of the data points is $468.9$.

Step 2: Calculate the mean

The formula for the arithmetic mean is:

$\text{mean} = \frac{\text{sum of the data points}}{\text{number of data points}}$

There are 10 data points in this set. Let's now calculate the mean:

$\text{mean} = \frac{468.9}{10} = 46.89$

Thus, the correct mean of this data set is 46.89, not 47.9 as originally provided.

Do you have any questions or need further details? Here are some related questions you might find useful:

1. How is the median of a data set calculated?
2. Can there be more than one mode in a data set?
3. What is the difference between the mean, median, and mode?
4. How do outliers affect the mean of a data set?
5. Can the mean be less than both the median and mode?

Tip: The mean is sensitive to extreme values, so always check for outliers that could distort the result.