Consider the data set below: \[ \begin{array}{llllllllllll} 26 & 33 & 37 & 44 & 46 & 47 & 50 & 52 & 55 & 63 & 67 & 72 \end{array} \] Note: $\sum x^{2}=31,266$ a) Find the five-number summary (Show work.) b) Compute the sample mean and the sample standard deviation (include symbols with answers.)

Step 1 ：Given the data set: \(26, 33, 37, 44, 46, 47, 50, 52, 55, 63, 67, 72\)

Step 2 ：The five-number summary of a data set consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. These values can be calculated using the sorted data set.

Step 3 ：The minimum value is \(26\)

Step 4 ：The first quartile (Q1) is \(42.25\)

Step 5 ：The median (Q2) is \(48.5\)

Step 6 ：The third quartile (Q3) is \(57.0\)

Step 7 ：The maximum value is \(72\)

Step 8 ：So, the five-number summary is \(\boxed{26, 42.25, 48.5, 57.0, 72}\)

Step 9 ：The sample mean is the sum of all the values divided by the number of values. The sample mean is \(49.33\)

Step 10 ：The sample standard deviation is the square root of the variance, which is the average of the squared differences from the mean. The variance is \(187.33\) and the standard deviation is \(13.69\)

Step 11 ：So, the sample mean is \(\boxed{49.33}\) and the sample standard deviation is \(\boxed{13.69}\)