1. **State the problem:** Find the sample standard deviation of the data set $\{17, 3, 5, 21, 45, 16\}$.\n\n2. **Calculate the mean:** The mean $\bar{x}$ is given by $$\bar{x} = \frac{17 + 3 + 5 + 21 + 45 + 16}{6} = \frac{107}{6} \approx 17.83.$$\n\n3. **Calculate each squared deviation from the mean:**\n\n$$(17 - 17.83)^2 = (-0.83)^2 = 0.6889,$$\n$$(3 - 17.83)^2 = (-14.83)^2 = 219.8689,$$\n$$(5 - 17.83)^2 = (-12.83)^2 = 164.6089,$$\n$$(21 - 17.83)^2 = 3.17^2 = 10.0489,$$\n$$(45 - 17.83)^2 = 27.17^2 = 738.1489,$$\n$$(16 - 17.83)^2 = (-1.83)^2 = 3.3489.$$\n\n4. **Sum the squared deviations:**\n$$0.6889 + 219.8689 + 164.6089 + 10.0489 + 738.1489 + 3.3489 = 1136.7134.$$\n\n5. **Compute the sample variance:** divide by $n-1=5$ because it's a sample,\n$$s^2 = \frac{1136.7134}{5} = 227.3427.$$\n\n6. **Find the sample standard deviation:**\n$$s = \sqrt{227.3427} \approx 15.08.$$\n\n**Final answer:** The sample standard deviation is approximately **15.08**, which corresponds to option C.