https://file.aiquickdraw.com/mathbot/file/1725892838097k4bjdzc4.jpg

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.

What is the arithmetic mean of the following data set: 35.2, 47.4, 49.2, 50.2, 64, 23.6, 30.1, 64, 64, 41.2?

Learn how to calculate the mean, median, and mode of the data set: 35.2, 47.4, 49.2, 50.2, 64, 23.6, 30.1, 64, 64, 41.2. The correct mean is 46.89, not 47.9, with a median of 48.3 and a mode of 64. This lesson is suitable for Grades 5-8 and covers key statistical concepts.

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