Seven students on an intramural team weigh \( 198 \mathrm{lb}, 201 \mathrm{lb}, 193 \mathrm{lb}, 204 \mathrm{lb} \), \( 191 \mathrm{lb}, 210 \mathrm{lb} \) and 182 lb . What is the standard deviation of the weights of these students? The standard deviation is \( \square \). (Round to the nearest tenth.)

To calculate the standard deviation of the weights of the seven students, we'll follow these steps: 1. **List of Weights:** \[ 198\ \text{lb},\ 201\ \text{lb},\ 193\ \text{lb},\ 204\ \text{lb},\ 191\ \text{lb},\ 210\ \text{lb},\ 182\ \text{lb} \] 2. **Calculate the Mean:** \[ \text{Mean} = \frac{198 + 201 + 193 + 204 + 191 + 210 + 182}{7} = \frac{1379}{7} = 197\ \text{lb} \] 3. **Determine the Deviations from the Mean and Square Them:** \[ \begin{align*} 198 - 197 &= 1 &\Rightarrow 1^2 &= 1 \\ 201 - 197 &= 4 &\Rightarrow 4^2 &= 16 \\ 193 - 197 &= -4 &\Rightarrow (-4)^2 &= 16 \\ 204 - 197 &= 7 &\Rightarrow 7^2 &= 49 \\ 191 - 197 &= -6 &\Rightarrow (-6)^2 &= 36 \\ 210 - 197 &= 13 &\Rightarrow 13^2 &= 169 \\ 182 - 197 &= -15 &\Rightarrow (-15)^2 &= 225 \\ \end{align*} \] 4. **Sum of Squared Deviations:** \[ 1 + 16 + 16 + 49 + 36 + 169 + 225 = 512 \] 5. **Calculate the Variance:** - **Population Variance:** \[ \sigma^2 = \frac{512}{7} \approx 73.1429 \] - **Sample Variance (if treating the data as a sample):** \[ s^2 = \frac{512}{6} \approx 85.3333 \] 6. **Calculate the Standard Deviation:** - **Population Standard Deviation:** \[ \sigma = \sqrt{73.1429} \approx 8.6\ \text{lb} \] - **Sample Standard Deviation:** \[ s = \sqrt{85.3333} \approx 9.2\ \text{lb} \] **Final Answer:** The standard deviation is **8.6** lb.