1. Listed below are the durations (in hours) of a simple random sample of all flights of a space shuttle program.
$\begin{array}{lllll}78 & 97 & 236 & 198 & 168\end{array}$
(a) Find the mean (Round to the nearest tenths)
(b) Find the median
(c) Find the mode(s)
(d) Find the variance. (Round final answer to the nearest tenths)
(e) Find the standard deviation. (Round final answer to the nearest tenths)

Step 1 ：First, we need to calculate the mean of the given data set. The mean is the sum of all the numbers divided by the count of numbers. In this case, the data set is [78, 97, 236, 198, 168]. So, the mean is \((78 + 97 + 236 + 198 + 168) / 5 = 155.4\).

Step 2 ：Next, we need to find the median of the data set. The median is the middle number in a sorted list of numbers. If the list has an even number of observations, the median is the average of the two middle numbers. In this case, the data set is already sorted and has 5 numbers, so the median is the third number, which is 168.

Step 3 ：Then, we need to find the mode of the data set. The mode is the number that appears most frequently in a data set. In this case, all the numbers appear only once, so there is no mode.

Step 4 ：After that, we need to calculate the variance of the data set. The variance is the average of the squared differences from the mean. In this case, the variance is \((78 - 155.4)^2 + (97 - 155.4)^2 + (236 - 155.4)^2 + (198 - 155.4)^2 + (168 - 155.4)^2) / 5 = 4467.8\).

Step 5 ：Finally, we need to find the standard deviation of the data set. The standard deviation is the square root of the variance. In this case, the standard deviation is \(\sqrt{4467.8} = 66.8\).

Step 6 ：So, the final answers are: (a) The mean of the durations is \(\boxed{155.4}\) hours. (b) The median of the durations is \(\boxed{168}\) hours. (c) Since all the durations appear only once, there is no mode. (d) The variance of the durations is \(\boxed{4467.8}\) hours squared. (e) The standard deviation of the durations is \(\boxed{66.8}\) hours.