1. **State the problem:** We need to determine which battery brand is the most consistent based on the battery life measurements given for each brand. 2. **Understanding consistency:** Consistency in this context means the battery life measurements have the least variation or spread. A common way to measure this is by calculating the standard deviation or variance of the data for each brand. 3. **Formula for variance:** $$\text{Variance} = \frac{1}{n}\sum_{i=1}^n (x_i - \bar{x})^2$$ where $x_i$ are the data points, $\bar{x}$ is the mean of the data points, and $n$ is the number of data points. 4. **Calculate the mean for each brand:** - Brand A: $\bar{x}_A = \frac{8.3 + 7.6 + 7.6 + 7.6 + 6.9}{5} = \frac{37.99999999999999}{5} = 7.6$ - Brand B: $\bar{x}_B = \frac{8.4 + 8.4 + 7.2 + 7 + 7}{5} = \frac{38}{5} = 7.6$ - Brand C: $\bar{x}_C = \frac{8.5 + 8.4 + 7.1 + 7.1 + 7.1}{5} = \frac{38.2}{5} = 7.64$ - Brand D: $\bar{x}_D = \frac{8.6 + 8.6 + 8.6 + 8.5 + 7.2}{5} = \frac{41.5}{5} = 8.3$ 5. **Calculate variance for each brand:** - Brand A: $$\frac{(8.3-7.6)^2 + (7.6-7.6)^2 + (7.6-7.6)^2 + (7.6-7.6)^2 + (6.9-7.6)^2}{5} = \frac{0.49 + 0 + 0 + 0 + 0.49}{5} = \frac{0.98}{5} = 0.196$$ - Brand B: $$\frac{(8.4-7.6)^2 + (8.4-7.6)^2 + (7.2-7.6)^2 + (7-7.6)^2 + (7-7.6)^2}{5} = \frac{0.64 + 0.64 + 0.16 + 0.36 + 0.36}{5} = \frac{2.76}{5} = 0.552$$ - Brand C: $$\frac{(8.5-7.64)^2 + (8.4-7.64)^2 + (7.1-7.64)^2 + (7.1-7.64)^2 + (7.1-7.64)^2}{5} = \frac{0.7396 + 0.5776 + 0.2916 + 0.2916 + 0.2916}{5} = \frac{2.192}{5} = 0.4384$$ - Brand D: $$\frac{(8.6-8.3)^2 + (8.6-8.3)^2 + (8.6-8.3)^2 + (8.5-8.3)^2 + (7.2-8.3)^2}{5} = \frac{0.09 + 0.09 + 0.09 + 0.04 + 1.21}{5} = \frac{1.52}{5} = 0.304$$ 6. **Interpretation:** The brand with the smallest variance is the most consistent. Brand A has variance 0.196, Brand D has 0.304, Brand C has 0.4384, and Brand B has 0.552. 7. **Conclusion:** Brand A is the most consistent battery brand because it has the lowest variance in battery life measurements. **Final answer:** Brand A is the most consistent.