1. **Problem:** Compute the mean, median, mode, and standard deviation for the data: 5, 8, 6, 7, 9, 10, 6, 7, 8, 7. 2. **Mean formula:** $$\text{Mean} = \frac{\sum x_i}{n}$$ where $x_i$ are data points and $n$ is the number of data points. 3. **Calculate mean:** $$\sum x_i = 5 + 8 + 6 + 7 + 9 + 10 + 6 + 7 + 8 + 7 = 73$$ $$n = 10$$ $$\text{Mean} = \frac{73}{10} = 7.3$$ 4. **Median:** Sort data: 5, 6, 6, 7, 7, 7, 8, 8, 9, 10. Since $n=10$ (even), median is average of 5th and 6th values: $$\text{Median} = \frac{7 + 7}{2} = 7$$ 5. **Mode:** The most frequent value(s) is 7 (appears 3 times). 6. **Standard deviation formula:** $$s = \sqrt{\frac{1}{n-1} \sum (x_i - \bar{x})^2}$$ 7. **Calculate squared deviations:** $$(5-7.3)^2 = 5.29$$ $$(8-7.3)^2 = 0.49$$ $$(6-7.3)^2 = 1.69$$ $$(7-7.3)^2 = 0.09$$ $$(9-7.3)^2 = 2.89$$ $$(10-7.3)^2 = 7.29$$ $$(6-7.3)^2 = 1.69$$ $$(7-7.3)^2 = 0.09$$ $$(8-7.3)^2 = 0.49$$ $$(7-7.3)^2 = 0.09$$ Sum of squared deviations: $$5.29 + 0.49 + 1.69 + 0.09 + 2.89 + 7.29 + 1.69 + 0.09 + 0.49 + 0.09 = 20.1$$ 8. **Calculate standard deviation:** $$s = \sqrt{\frac{20.1}{10-1}} = \sqrt{\frac{20.1}{9}} = \sqrt{2.2333} \approx 1.494$$ **Final answers:** - Mean = 7.3 - Median = 7 - Mode = 7 - Standard deviation $\approx 1.494$