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The table shows the maze-completion times, in seconds, of two sets of mice in an experiment.

Maze-Completion Times (seconds)
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Group A & 52 & 41 & 45 & 58 & 49 & 55 & 44 & 54 & 48 & 50 \\
\hline
Group B & 45 & 62 & 40 & 43 & 57 & 52 & 48 & 60 & 41 & 55 \\
\hline
\end{tabular}

Which statement is true about the variability of the group times?

A. The times in Group A have a greater standard deviation.
B. The times in Group A have a greater median.
C. The times in Group B have a greater interquartile range.
D. The times in Group B have a greater mean.

Sagot :

GinnyAnsweridn
To determine which statement is true about the variability of the group times, we'll examine four key statistical measures: standard deviation, median, interquartile range (IQR), and mean for both groups. Let's list out the findings:

1. Standard Deviation:
- Group A: [tex]\(5.32\)[/tex]
- Group B: [tex]\(8.03\)[/tex]

Conclusion: The standard deviation of Group B is greater than that of Group A, indicating that the times in Group B are more spread out around the mean.

2. Median:
- Group A: [tex]\(49.5\)[/tex] seconds
- Group B: [tex]\(50.0\)[/tex] seconds

Conclusion: The median maze-completion time for Group B is slightly higher than that for Group A.

3. Interquartile Range (IQR):
- Group A: [tex]\(7.75\)[/tex] seconds
- Group B: [tex]\(13.0\)[/tex] seconds

Conclusion: The IQR of Group B is greater than that of Group A, suggesting that Group B's times have a wider spread in the middle 50% of the data.

4. Mean:
- Group A: [tex]\(49.6\)[/tex] seconds
- Group B: [tex]\(50.3\)[/tex] seconds

Conclusion: The mean maze-completion time for Group B is higher than that for Group A.

Given these findings, the correct statements about the variability of the group times are:
- The times in Group B have a greater standard deviation.
- The times in Group B have a greater interquartile range.
- The times in Group B have a greater mean.

The statement that says "The times in Group A have a greater median" is not true. Therefore, the correct statements are:

- The times in Group B have a greater standard deviation.
- The times in Group B have a greater interquartile range.
- The times in Group B have a greater mean.

Hence, the most accurate specific statement about the variability of the group times is:
- The times in Group B have a greater interquartile range.
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