1. **State the problem:** We have a data set: 16, 24, 12, 22, 28, 32, 26, 40, 18, 30, 38. We want to find the percentage of values that lie within one standard deviation of the mean. 2. **Calculate the mean ($\mu$):** $$\mu = \frac{16 + 24 + 12 + 22 + 28 + 32 + 26 + 40 + 18 + 30 + 38}{11} = \frac{286}{11} = 26$$ 3. **Calculate the standard deviation ($\sigma$):** First, find each squared deviation from the mean: $$(16-26)^2 = 100, (24-26)^2 = 4, (12-26)^2 = 196, (22-26)^2 = 16, (28-26)^2 = 4, (32-26)^2 = 36, (26-26)^2 = 0, (40-26)^2 = 196, (18-26)^2 = 64, (30-26)^2 = 16, (38-26)^2 = 144$$ Sum of squared deviations: $$100 + 4 + 196 + 16 + 4 + 36 + 0 + 196 + 64 + 16 + 144 = 776$$ Variance ($\sigma^2$): $$\frac{776}{11} = 70.545$$ Standard deviation ($\sigma$): $$\sqrt{70.545} \approx 8.4$$ 4. **Determine the interval within one standard deviation:** $$[\mu - \sigma, \mu + \sigma] = [26 - 8.4, 26 + 8.4] = [17.6, 34.4]$$ 5. **Count values within this interval:** Values in the data set within [17.6, 34.4] are: 24, 22, 28, 32, 26, 30, 18 (7 values). 6. **Calculate the percentage:** $$\frac{7}{11} \times 100 \approx 63.6\%$$ **Final answer:** C. 63.6%