If we have the data:

5, 8, 15, 7, 10, 22, 3, 1, 15

What is the mode?

To find the mode, we need to identify the number that appears most frequently in the data set. Here are the given numbers:

\[ 5, 8, 15, 7, 10, 22, 3, 1, 15 \]

### Step-by-Step Calculation

1. Count the frequency of each number:
   - 5 appears 1 time
   - 8 appears 1 time
   - 15 appears 2 times
   - 7 appears 1 time
   - 10 appears 1 time
   - 22 appears 1 time
   - 3 appears 1 time
   - 1 appears 1 time

2. Identify the number with the highest frequency:
   - 15 appears the most frequently (2 times).

### Conclusion

The mode of the data set is \( 15 \), as it appears more frequently than any other number.

If you have any questions or need further details, feel free to ask!

Here are some related questions for further exploration:
1. What are the mean and median of this data set?
2. How would the mode change if another 15 was added to the data set?
3. What if 15 appeared only once? What would be the mode then?
4. Can a data set have more than one mode? How does that work?
5. How does the presence of multiple modes affect the interpretation of data?
6. What is the range of this data set?
7. How would the measures of central tendency change if we included additional values?
8. How can outliers affect the mode in a larger data set?

**Tip:** When there is no number that repeats, the data set has no mode. If every number appears with the same frequency, each number is considered a mode.

Learn how to find the mode of a data set using a step-by-step example problem. This problem covers basic statistics and measures of central tendency. Suitable for students in Grades 6-8.

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