Answered

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

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



Answer :

GinnyAnswer
To determine the reliability of the reaction time data gathered by the four students, we need to analyze how consistent their reaction times are across different trials. A common measure of this consistency is the standard deviation. The lower the standard deviation, the more reliable and consistent the data is.

Here are the individual reaction times for each student:

- 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]

Next, we calculate the standard deviation for each student’s reaction times. The standard deviation values are as follows:

- Student 1: 0.00687 (approximately)
- Student 2: 0.02794 (approximately)
- Student 3: 0.03131 (approximately)
- Student 4: 0.05416 (approximately)

Now we order the students based on the ascending order of their standard deviations, from most reliable to least reliable:

1. Student 1 (standard deviation: 0.00687)
2. Student 2 (standard deviation: 0.02794)
3. Student 3 (standard deviation: 0.03131)
4. Student 4 (standard deviation: 0.05416)

Therefore, the students ordered from most to least reliable data are:

1. Student 1
2. Student 2
3. Student 3
4. Student 4

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