To correctly represent the data shown on the stem-and-leaf plot as a data table, we need to understand how a stem-and-leaf plot works. Each "stem" (the values in the left column) represents the leading digit(s) of the numbers, and each "leaf" (the values in the right column) represents the following digits. We combine each stem with its corresponding leaves to form full numbers.
Let's break it down step-by-step:
1. Stem 0 with Leaves 2 and 6:
- 0 combined with 2 gives us 02, which is just 2.
- 0 combined with 6 gives us 06, which is just 6.
2. Stem 1 with Leaves 1, 3, and 5:
- 1 combined with 1 gives us 11.
- 1 combined with 3 gives us 13.
- 1 combined with 5 gives us 15.
3. Stem 2 with Leaf 5:
- 2 combined with 5 gives us 25.
4. Stem 3 with Leaf 1:
- 3 combined with 1 gives us 31.
5. Stem 4 with Leaf 0:
- 4 combined with 0 gives us 40.
6. Stem 5 with Leaf 1:
- 5 combined with 1 gives us 51.
After gathering all these numbers, let's list them:
- 2
- 6
- 11
- 13
- 15
- 25
- 31
- 40
- 51
To arrange these numbers in ascending order:
[tex]\[2, 6, 11, 13, 15, 25, 31, 40, 51\][/tex]
Therefore, the data table that correctly represents the data shown on the stem-and-leaf plot is:
[tex]\[
\[2, 6, 11, 13, 15, 25, 31, 40, 51\][/tex]
\]
