Given the following confidence intervals for the mean, find the margin of error and the sample mean: 1. $(56.2,84.4)$ 2. $(19.13,29.84)$

Step 1 ：Given the confidence intervals for the mean are $(56.2,84.4)$ and $(19.13,29.84)$.

Step 2 ：The confidence interval is defined as the range in which we are confident that the population mean lies. It is calculated as the sample mean plus or minus the margin of error.

Step 3 ：The margin of error is half the width of the confidence interval. So, for the first interval, the margin of error is \((84.4 - 56.2) / 2 = 14.1\) and for the second interval, the margin of error is \((29.84 - 19.13) / 2 = 5.355\).

Step 4 ：The sample mean is the midpoint of the confidence interval. So, for the first interval, the sample mean is \((56.2 + 84.4) / 2 = 70.3\) and for the second interval, the sample mean is \((19.13 + 29.84) / 2 = 24.485\).

Step 5 ：Final Answer: The margin of error and the sample mean for the first confidence interval $(56.2,84.4)$ are approximately \(\boxed{14.1}\) and \(\boxed{70.3}\) respectively. For the second confidence interval $(19.13,29.84)$, the margin of error and the sample mean are approximately \(\boxed{5.355}\) and \(\boxed{24.485}\) respectively.