Select the correct answer.

A mother tracks the duration of her baby's three daily naps for a few weeks. The mean time (in minutes) and the standard deviation (SD) for each nap are recorded in the table below.

| Nap | Mean | SD |
|------------------|------|-----|
| 1st Nap | 83 | 9 |
| 2nd Nap | 52 | 6 |
| 3rd Nap | 39 | 11 |

Use the information in the table to select the true statement:

A. The 2nd nap is the least consistent in duration because its standard deviation is the lowest.
B. The 1st nap is the least consistent in duration because its mean is the highest.
C. The 3rd nap is the least consistent in duration because its standard deviation is the highest.
D. The 3rd nap is the least consistent in duration because its mean is the lowest.



Answer :

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.