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Four students all perform the same experiment for the science fair. They test reaction times for pushing a button when a specific color is shown. Their data is as follows:

[tex]\[
\begin{array}{|l|c|c|c|c|c|c|}
\hline
& \text{Trial 1} & \text{Trial 2} & \text{Trial 3} & \text{Trial 4} & \text{Trial 5} & \text{Trial 6} \\
\hline
\text{Student 1} & 0.42 & 0.43 & 0.41 & 0.42 & 0.41 & 0.42 \\
\hline
\text{Student 2} & 0.44 & 0.41 & 0.47 & 0.39 & 0.46 & 0.42 \\
\hline
\text{Student 3} & 0.35 & 0.43 & 0.38 & 0.39 & 0.42 & 0.44 \\
\hline
\text{Student 4} & 0.41 & 0.52 & 0.57 & 0.46 & 0.55 & 0.49 \\
\hline
\end{array}
\][/tex]

Put the students in order from most to least reliable data.

A. Student 3, Student 2, Student 1, Student 4
B. Student 2, Student 1, Student 4, Student 3
C. Student 4, Student 1, Student 2, Student 3

Sagot :

GinnyAnsweridn
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
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