1. **State the problem:** We are given a sample of false fire alarm counts: 8, 6, 15, 6, and an unknown value. We need to compute the sample standard deviation using the given table and information. 2. **Identify the mean ($\bar{x}$) and missing values:** The table shows squared deviations from the mean, but the mean is unknown. The squared deviations given are 0, 4, (missing), 4, and 9. 3. **Use the squared deviations to find the mean:** The squared deviation for the first value is $(8 - \bar{x})^2 = 0$, which implies $8 - \bar{x} = 0$ so $\bar{x} = 8$. 4. **Check other squared deviations with $\bar{x} = 8$:** - For $x_2 = 6$, $(6 - 8)^2 = (-2)^2 = 4$ matches the table. - For $x_4 = 6$, same calculation, 4. - For $x_5$, squared deviation is 9, so $(x_5 - 8)^2 = 9$ which means $x_5 - 8 = \pm 3$, so $x_5 = 11$ or $5$. 5. **Find the missing $x_3$ and its squared deviation:** We know $x_3 = 15$ from the problem statement. Calculate $(15 - 8)^2 = 7^2 = 49$. 6. **Calculate the average (mean) of the sample:** $$\bar{x} = \frac{8 + 6 + 15 + 6 + 11}{5} = \frac{46}{5} = 9.2$$ 7. **Calculate each squared deviation from the mean 9.2:** - $(8 - 9.2)^2 = (-1.2)^2 = 1.44$ - $(6 - 9.2)^2 = (-3.2)^2 = 10.24$ - $(15 - 9.2)^2 = 5.8^2 = 33.64$ - $(6 - 9.2)^2 = 10.24$ - $(11 - 9.2)^2 = 1.8^2 = 3.24$ 8. **Sum of squared deviations:** $$1.44 + 10.24 + 33.64 + 10.24 + 3.24 = 58.8$$ 9. **Calculate variance:** Sample variance formula is $$s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} = \frac{58.8}{5 - 1} = \frac{58.8}{4} = 14.7$$ 10. **Calculate sample standard deviation:** $$s = \sqrt{14.7} \approx 3.83$$ **Final answer:** The sample standard deviation is approximately **3.83**.