1. **State the problem:** We are given a data set of total fat amounts in grams: $$\{25, 21, 23, 17, 22, 16, 18, 20, 22, 17, 17, 17, 16, 21, 24, 16, 24, 21, 16, 17\}$$ We need to find the standard deviation of this data set, rounded to the nearest tenth. 2. **Recall the formula for standard deviation:** $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ where $n$ is the number of data points, $x_i$ are the data values, and $\bar{x}$ is the mean. 3. **Calculate the mean $\bar{x}$:** Sum all values: $$25 + 21 + 23 + 17 + 22 + 16 + 18 + 20 + 22 + 17 + 17 + 17 + 16 + 21 + 24 + 16 + 24 + 21 + 16 + 17 = 386$$ Number of data points $n = 20$ Mean: $$\bar{x} = \frac{386}{20} = 19.3$$ 4. **Calculate each squared deviation $(x_i - \bar{x})^2$ and sum them:** \begin{align*} (25 - 19.3)^2 &= 32.49 \\ (21 - 19.3)^2 &= 2.89 \\ (23 - 19.3)^2 &= 13.69 \\ (17 - 19.3)^2 &= 5.29 \\ (22 - 19.3)^2 &= 7.29 \\ (16 - 19.3)^2 &= 10.89 \\ (18 - 19.3)^2 &= 1.69 \\ (20 - 19.3)^2 &= 0.49 \\ (22 - 19.3)^2 &= 7.29 \\ (17 - 19.3)^2 &= 5.29 \\ (17 - 19.3)^2 &= 5.29 \\ (17 - 19.3)^2 &= 5.29 \\ (16 - 19.3)^2 &= 10.89 \\ (21 - 19.3)^2 &= 2.89 \\ (24 - 19.3)^2 &= 22.09 \\ (16 - 19.3)^2 &= 10.89 \\ (24 - 19.3)^2 &= 22.09 \\ (21 - 19.3)^2 &= 2.89 \\ (16 - 19.3)^2 &= 10.89 \\ (17 - 19.3)^2 &= 5.29 \end{align*} Sum of squared deviations: $$\sum (x_i - \bar{x})^2 = 190.8$$ 5. **Calculate the variance:** $$s^2 = \frac{190.8}{20 - 1} = \frac{190.8}{19} = 10.0421$$ 6. **Calculate the standard deviation:** $$s = \sqrt{10.0421} = 3.17$$ 7. **Round to the nearest tenth:** $$3.2$$ **Final answer:** The standard deviation of the data set is **3.2 grams**.