If for a sample size of 10, $\sum_{i=1}^{10}(x_i - 5)^2 = 350$ and $\sum_{i=1}^{10}(x_i - 6) = 20$, then the variance is
Step-by-Step Solution
Key Concept: Extracting the sum and sum of squares from expanded expressions involving deviations, then applying the variance formula
We have $\sum_{i=1}^{10}(x_i - 6) = 20$, so $\sum x_i = 80$. From $\sum_{i=1}^{10}(x_i^2 - 10x_i + 25) = 350$, we get $\sum x_i^2 - 10(80) + 250 = 350$, which gives $\sum x_i^2 = 900$. Then $\text{variance} = \frac{\sum x_i^2}{n} - (\bar{x})^2 = \frac{900}{10} - 8^2 = 90 - 64 = 26$.
Correct Answer: 26