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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.

\begin{tabular}{|c|c|c|}
\hline
[tex]$1^{\text {st }}$[/tex] Nap & [tex]$2^{\text {nd }}$[/tex] Nap & [tex]$3^{\text {rd }}$[/tex] Nap \\
\hline
Mean [tex]$=83$[/tex] & Mean [tex]$=52$[/tex] & Mean [tex]$=39$[/tex] \\
SD [tex]$=9$[/tex] & SD [tex]$=6$[/tex] & SD [tex]$=11$[/tex] \\
\hline
\end{tabular}

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

A. The [tex]$2^{\text {nd }}$[/tex] nap is the least consistent in duration because its standard deviation is the lowest.
B. The [tex]$3^{\text {rd }}$[/tex] nap is the least consistent in duration because its standard deviation is the highest.
C. The [tex]$3^{\text {rd }}$[/tex] nap is the least consistent in duration because its mean is the lowest.
D. The [tex]$1^{\text {st }}$[/tex] nap is the least consistent in duration because its mean is the highest.

Sagot :

GinnyAnsweridn
To determine which nap is the least consistent in duration, we need to consider the standard deviation (SD) associated with each nap. Standard deviation is a measure of the dispersion or variability around the mean. Higher standard deviation indicates more variability and thus less consistency.

Let's analyze the standard deviations provided:

- For the 1st nap: [tex]\( \text{SD} = 9 \)[/tex]
- For the 2nd nap: [tex]\( \text{SD} = 6 \)[/tex]
- For the 3rd nap: [tex]\( \text{SD} = 11 \)[/tex]

Higher values of standard deviation indicate less consistency because the durations are more spread out from the mean.

Among the three naps, the 3rd nap has the highest standard deviation of 11. This means the 3rd nap has the most variability in duration and is, therefore, the least consistent.

So, the correct statement is:
B. The [tex]\(3^{\text{rd}}\)[/tex] nap is the least consistent in duration because its standard deviation is the highest.
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