1. **Problem Statement:** We have daily customer counts for two branches over 10 days. We need to find the mean and standard deviation for each branch, then use the coefficient of variation (CV) to determine which branch has more consistent customer flow. 2. **Formulas:** - Mean: $$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$ - Standard deviation (sample): $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ - Coefficient of variation: $$CV = \frac{s}{\bar{x}} \times 100\%$$ 3. **Calculate for Branch X:** - Data: 105, 98, 115, 120, 102, 110, 118, 99, 112, 108 - Mean: $$\bar{x}_X = \frac{105 + 98 + 115 + 120 + 102 + 110 + 118 + 99 + 112 + 108}{10} = \frac{1087}{10} = 108.7$$ - Calculate squared deviations: - $(105 - 108.7)^2 = 13.69$ - $(98 - 108.7)^2 = 114.49$ - $(115 - 108.7)^2 = 39.69$ - $(120 - 108.7)^2 = 127.69$ - $(102 - 108.7)^2 = 44.89$ - $(110 - 108.7)^2 = 1.69$ - $(118 - 108.7)^2 = 86.49$ - $(99 - 108.7)^2 = 94.09$ - $(112 - 108.7)^2 = 11.29$ - $(108 - 108.7)^2 = 0.49$ - Sum of squared deviations: $13.69 + 114.49 + 39.69 + 127.69 + 44.89 + 1.69 + 86.49 + 94.09 + 11.29 + 0.49 = 534.5$ - Standard deviation: $$s_X = \sqrt{\frac{534.5}{10 - 1}} = \sqrt{59.39} \approx 7.71$$ 4. **Calculate for Branch Y:** - Data: 95, 100, 92, 88, 110, 105, 98, 102, 97, 101 - Mean: $$\bar{x}_Y = \frac{95 + 100 + 92 + 88 + 110 + 105 + 98 + 102 + 97 + 101}{10} = \frac{988}{10} = 98.8$$ - Calculate squared deviations: - $(95 - 98.8)^2 = 14.44$ - $(100 - 98.8)^2 = 1.44$ - $(92 - 98.8)^2 = 46.24$ - $(88 - 98.8)^2 = 116.64$ - $(110 - 98.8)^2 = 125.44$ - $(105 - 98.8)^2 = 38.44$ - $(98 - 98.8)^2 = 0.64$ - $(102 - 98.8)^2 = 10.24$ - $(97 - 98.8)^2 = 3.24$ - $(101 - 98.8)^2 = 4.84$ - Sum of squared deviations: $14.44 + 1.44 + 46.24 + 116.64 + 125.44 + 38.44 + 0.64 + 10.24 + 3.24 + 4.84 = 361.6$ - Standard deviation: $$s_Y = \sqrt{\frac{361.6}{10 - 1}} = \sqrt{40.18} \approx 6.34$$ 5. **Calculate Coefficient of Variation (CV):** - For Branch X: $$CV_X = \frac{7.71}{108.7} \times 100\% \approx 7.09\%$$ - For Branch Y: $$CV_Y = \frac{6.34}{98.8} \times 100\% \approx 6.42\%$$ 6. **Interpretation:** - The CV measures relative variability; lower CV means more consistency. - Branch Y has a lower CV (6.42%) compared to Branch X (7.09%), so Branch Y has more consistent customer flow. **Final answers:** - Branch X mean = 108.7, standard deviation = 7.71 - Branch Y mean = 98.8, standard deviation = 6.34 - Branch Y is more consistent based on CV.