To find the mode of the given data set, we need to first compile all the individual numbers represented by the stems and leaves, and then identify which number occurs most frequently.
Step-by-Step Solution:
1. Understand the Stem-and-Leaf Plot:
- Each stem represents the tens place of a number.
- Each leaf connected to a stem represents the units place of a number.
2. Convert the Stems and Leaves to Individual Numbers:
- For stem 1 with leaves 6 and 8, the numbers are 16 and 18.
- For stem 2 with leaves 3, 5, and 6, the numbers are 23, 25, and 26.
- For stem 3 with leaves 4, 7, and 7, the numbers are 34, 37, and 37.
- For stem 4 with leaves 0, 1, and 6, the numbers are 40, 41, and 46.
- Additionally, we have individual numbers 6, 37, and 34 directly.
3. Combine All the Numbers:
- Collect all the numbers from the steps above into one list:
[tex]\[
\{16, 18, 23, 25, 26, 34, 37, 37, 40, 41, 46, 6\}
\][/tex]
4. Determine the Mode:
- The mode of a data set is the value that appears most frequently.
- Count the frequency of each number:
- 16: 1 time
- 18: 1 time
- 23: 1 time
- 25: 1 time
- 26: 1 time
- 34: 2 times
- 37: 2 times
- 40: 1 time
- 41: 1 time
- 46: 1 time
- 6: 1 time
5. Identify the Number with the Highest Frequency:
- From the counts above, the numbers 34 and 37 are the most frequent, appearing 2 times each.
6. Select the Mode:
- Since the mode is the highest frequency number, we find that 37 appears most frequently in the dataset.
Therefore, the mode of the dataset is:
[tex]\[
\boxed{37}
\][/tex]
