Step 1 :Given two sets of temperatures measured at 8 AM and 12 AM, we are asked to find the mean difference and the standard deviation of the differences.
Step 2 :The mean difference, denoted as \(\bar{d}\), is calculated by subtracting each temperature at 8 AM from the corresponding temperature at 12 AM, summing these differences, and then dividing by the number of differences.
Step 3 :The standard deviation of the differences, denoted as \(s_{d}\), is a measure of the amount of variation or dispersion of the set of differences. It is calculated by subtracting each difference from the mean difference, squaring the result, summing these squared results, dividing by the number of differences minus 1, and then taking the square root of the result.
Step 4 :By performing these calculations, we find that the mean difference \(\bar{d}\) is approximately 0.36 and the standard deviation of the differences \(s_{d}\) is approximately 0.37.
Step 5 :Thus, the values of \(\bar{d}\) and \(s_{d}\) are \(\boxed{0.36}\) and \(\boxed{0.37}\) respectively.