Listed below are body temperatures from five different subjects measured at $8 \mathrm{AM}$ and again at $12 \mathrm{AM}$. Find the values of $\bar{d}$ and $s_{d}$. In general, what does $\mu_{d}$ represent?
\begin{tabular}{llllll}
\hline Temperature $\left({ }^{\circ} \mathrm{F}\right.$ ) at 8 AM & 97.8 & 99.4 & 97.1 & 97.5 & 97.4 \\
\hline Temperature $\left({ }^{\circ} \mathrm{F}\right.$ ) at $12 \mathrm{AM}$ & 98.2 & 99.8 & 97.5 & 97.0 & 97.7 \\
\hline
\end{tabular}

Let the temperature at $8 \mathrm{AM}$ be the first sample, and the temperature at $12 \mathrm{AM}$ be the second sample. Find the values of $\bar{d}$ and $s_{\mathrm{d}}$.
\[
\bar{d}=-0.2
\]
(Type an integer or a decimal, Do not round.)
\[
s_{\mathrm{d}}=0.39
\]
(Round to two decimal places as needed.)
In general, what does $\mu_{d}$ represent?
A. The difference of the population means of the two populations
B. The mean value of the differences for the paired sample data
C. The mean of the differences from the population of matched data
D. The mean of the means of each matched pair from the population of matched data

Step 1 ：Given the body temperatures of five subjects measured at two different times: 8 AM and 12 AM, we are asked to find the mean difference (denoted as \(\bar{d}\)) and the standard deviation of the differences (denoted as \(s_d\)) between the two sets of data.

Step 2 ：To find \(\bar{d}\), we calculate the difference between each pair of temperatures (temperature at 12 AM minus temperature at 8 AM), sum up these differences, and then divide by the number of pairs (which is 5 in this case).

Step 3 ：To find \(s_d\), we first calculate the squared difference between each individual difference and the mean difference \(\bar{d}\). Then, we sum up these squared differences, divide by the number of pairs minus 1 (which is 4 in this case), and finally take the square root of the result.

Step 4 ：The symbol \(\mu_d\) generally represents the mean of the differences in the population of matched data. This is the average difference we would expect to see between matched pairs in the entire population from which our sample was drawn.

Step 5 ：After calculating, we find that the mean difference \(\bar{d}\) is 0.2 and the standard deviation of the differences \(s_d\) is approximately 0.39.

Step 6 ：\(\boxed{\text{Final Answer: The mean difference } \bar{d} \text{ is } 0.2 \text{ and the standard deviation of the differences } s_d \text{ is approximately } 0.39. \text{ In general, } \mu_d \text{ represents the mean of the differences from the population of matched data.}}\)