To determine which nap is the least consistent in duration, we should examine the standard deviation (SD) of each nap. Standard deviation measures the amount of variability or dispersion of a set of values. A higher standard deviation indicates greater inconsistency.
Let's analyze the provided data:
- For the [tex]\(1^{\text{st}}\)[/tex] nap, the standard deviation is 9.
- For the [tex]\(2^{\text{nd}}\)[/tex] nap, the standard deviation is 6.
- For the [tex]\(3^{\text{rd}}\)[/tex] nap, the standard deviation is 11.
The highest standard deviation among these values is 11, which corresponds to the [tex]\(3^{\text{rd}}\)[/tex] nap. This means that the [tex]\(3^{\text{rd}}\)[/tex] nap has the greatest variability and is therefore the least consistent in duration.
Let's go through the options one by one:
A. The [tex]\(2^{\text{nd}}\)[/tex] nap is the least consistent in duration because its standard deviation is the lowest.
- This statement is incorrect because a lower standard deviation indicates higher consistency, not less.
B. The [tex]\(1^{\text{st}}\)[/tex] nap is the least consistent in duration because its mean is the highest.
- This statement is incorrect because the mean does not determine consistency; the standard deviation does.
C. The [tex]\(3^{\text{rd}}\)[/tex] nap is the least consistent in duration because its standard deviation is the highest.
- This statement is correct because the [tex]\(3^{\text{rd}}\)[/tex] nap has the highest standard deviation (11), indicating it is the least consistent.
D. The [tex]\(3^{\text{rd}}\)[/tex] nap is the least consistent in duration because its mean is the lowest.
- This statement is incorrect because the mean does not determine consistency; the standard deviation does.
Therefore, the correct answer is:
C. The [tex]\(3^{\text{rd}}\)[/tex] nap is the least consistent in duration because its standard deviation is the highest.
