To determine the students' reliability based on their reaction times, we need to calculate the standard deviation for each student's data. A lower standard deviation indicates more consistent (reliable) reaction times.
The data for each student is as follows:
- Student 1: [0.42, 0.43, 0.41, 0.42, 0.41, 0.42]
- Student 2: [0.44, 0.41, 0.47, 0.39, 0.46, 0.42]
- Student 3: [0.35, 0.43, 0.38, 0.39, 0.42, 0.44]
- Student 4: [0.41, 0.52, 0.57, 0.46, 0.55, 0.49]
Here are the standard deviations for each student:
- Student 1: [tex]\(0.006871842709362774\)[/tex]
- Student 2: [tex]\(0.027938424357067015\)[/tex]
- Student 3: [tex]\(0.031313823713426565\)[/tex]
- Student 4: [tex]\(0.0541602560309064\)[/tex]
We need to arrange the students from the most reliable to the least reliable data. Reliability is inversely related to the standard deviation: a lower standard deviation corresponds to higher reliability. Therefore, the order from most to least reliable based on their standard deviations is:
1. Student 1 (with the standard deviation of [tex]\(0.006871842709362774\)[/tex])
2. Student 2 (with the standard deviation of [tex]\(0.027938424357067015\)[/tex])
3. Student 3 (with the standard deviation of [tex]\(0.031313823713426565\)[/tex])
4. Student 4 (with the standard deviation of [tex]\(0.0541602560309064\)[/tex])
So the correct order from most to least reliable data is:
A. Student 3, Student 2, Student 1, Student 4 is incorrect.
B. Student 2, Student 1, Student 4, Student 3 is incorrect.
C. Student 4, Student 1, Student 2, Student 3 is incorrect.
The correct answer is:
D. Student 1, Student 2, Student 3, Student 4
