To determine whose results are more reliable, we need to calculate the range of the iodine diffusion distances for each student. The range is found by subtracting the smallest value from the largest value in each student's set of measurements.
Let's start by calculating the range of diffusion distances for Student 1:
1. Student 1's measurements are: [tex]\(3.25\)[/tex] mm, [tex]\(3.17\)[/tex] mm, [tex]\(3.26\)[/tex] mm, [tex]\(3.64\)[/tex] mm, and [tex]\(3.44\)[/tex] mm.
2. The minimum value in Student 1's measurements is [tex]\(3.17\)[/tex] mm.
3. The maximum value in Student 1's measurements is [tex]\(3.64\)[/tex] mm.
4. The range for Student 1's measurements is:
[tex]\[
3.64 \, \text{mm} - 3.17 \, \text{mm} = 0.47 \, \text{mm}
\][/tex]
Next, let's calculate the range of diffusion distances for Student 2:
1. Student 2's measurements are: [tex]\(3.14\)[/tex] mm, [tex]\(3.43\)[/tex] mm, [tex]\(3.22\)[/tex] mm, [tex]\(3.37\)[/tex] mm, and [tex]\(3.28\)[/tex] mm.
2. The minimum value in Student 2's measurements is [tex]\(3.14\)[/tex] mm.
3. The maximum value in Student 2's measurements is [tex]\(3.43\)[/tex] mm.
4. The range for Student 2's measurements is:
[tex]\[
3.43 \, \text{mm} - 3.14 \, \text{mm} = 0.29 \, \text{mm}
\][/tex]
Comparing the ranges:
- Student 1's range is [tex]\(0.47\)[/tex] mm.
- Student 2's range is [tex]\(0.29\)[/tex] mm.
Since a narrower range indicates more consistency and therefore more reliability in the measurements:
Student 2's results are more reliable because they have a narrower range of measurements.
The correct answer is:
D. Student 2, because they have a narrower range.
