1. **State the problem:** We are given a frequency table of resting heart rates for 60 patients and need to find the standard deviation of the data set and interpret its meaning. 2. **Recall the formula for standard deviation for grouped data:** $$\sigma = \sqrt{\frac{\sum f(x - \bar{x})^2}{N}}$$ where $f$ is frequency, $x$ is the heart rate, $\bar{x}$ is the mean, and $N$ is total frequency. 3. **Calculate the mean $\bar{x}$:** $$\bar{x} = \frac{\sum f x}{N}$$ Calculate $\sum f x$: $$1\times60 + 3\times65 + 4\times70 + 12\times75 + 8\times80 + 15\times85 + 9\times90 + 5\times95 + 3\times100 = 60 + 195 + 280 + 900 + 640 + 1275 + 810 + 475 + 300 = 4935$$ Total frequency $N = 60$ So, $$\bar{x} = \frac{4935}{60} = 82.25$$ 4. **Calculate $\sum f (x - \bar{x})^2$:** Calculate each squared deviation times frequency: - $(60 - 82.25)^2 \times 1 = 22.25^2 \times 1 = 495.06$ - $(65 - 82.25)^2 \times 3 = 17.25^2 \times 3 = 297.56 \times 3 = 892.69$ - $(70 - 82.25)^2 \times 4 = 12.25^2 \times 4 = 150.06 \times 4 = 600.25$ - $(75 - 82.25)^2 \times 12 = 7.25^2 \times 12 = 52.56 \times 12 = 630.75$ - $(80 - 82.25)^2 \times 8 = 2.25^2 \times 8 = 5.06 \times 8 = 40.50$ - $(85 - 82.25)^2 \times 15 = 2.75^2 \times 15 = 7.56 \times 15 = 113.44$ - $(90 - 82.25)^2 \times 9 = 7.75^2 \times 9 = 60.06 \times 9 = 540.56$ - $(95 - 82.25)^2 \times 5 = 12.75^2 \times 5 = 162.56 \times 5 = 812.81$ - $(100 - 82.25)^2 \times 3 = 17.75^2 \times 3 = 315.06 \times 3 = 945.19$ Sum these: $$495.06 + 892.69 + 600.25 + 630.75 + 40.50 + 113.44 + 540.56 + 812.81 + 945.19 = 5071.25$$ 5. **Calculate the standard deviation:** $$\sigma = \sqrt{\frac{5071.25}{60}} = \sqrt{84.52} = 9.19$$ 6. **Interpretation:** The standard deviation of approximately 9.19 means that the typical heart rate varies from the mean heart rate by about 9.19 beats per minute on average. **Note:** The closest answer choice is the one with standard deviation 9.27 and interpretation about typical variation from the mean. **Final answer:** The standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.