Step-by-step Solution:

Step 1: Calculate the sample mean (\( \bar{x} \)). \[ \bar{x} = \frac{14.5 + 15.2 + 16.8 + 17.1 + 15.9 + 16.3 + 14.7}{7} \] \[ \bar{x} = \frac{110.5}{7} \approx 15.7857 \approx 15.79 \] Step 2: Calculate the sample variance (\( s^2 \)). \[ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} \] Sum of squared deviations from the exact mean (110.5/7): \[ \sum (x_i - \bar{x})^2 \approx (-1.29)^2 + (-0.59)^2 + (1.01)^2 + (1.31)^2 + (0.11)^2 + (0.51)^2 + (-1.09)^2 \] \[ \sum (x_i - \bar{x})^2 \approx 1.65 + 0.34 + 1.03 + 1.73 + 0.01 + 0.26 + 1.18 = 6.20 \] \[ s^2 = \frac{6.20}{6} \approx 1.033 \] Step 3: Calculate the sample standard deviation (\( s \)). \[ s = \sqrt{1.033} \approx 1.016 \approx 1.02 \] Thus, the mean is 15.79 and sample standard deviation is 1.02.