1. The problem involves calculating sums related to a dataset: specifically, \(\sum X^2 - \sum X\), \(\sum (x - \text{mean})\), and \(\sum (x - \text{mean})^2\). 2. First, understand the terms: - \(\sum X\) is the sum of all data points. - \(\sum X^2\) is the sum of the squares of all data points. - The mean (average) is \(\bar{x} = \frac{\sum X}{n}\), where \(n\) is the number of data points. - \(\sum (x - \bar{x})\) is the sum of deviations from the mean. - \(\sum (x - \bar{x})^2\) is the sum of squared deviations from the mean, also known as the total sum of squares. 3. Important rules: - The sum of deviations from the mean is always zero: \(\sum (x - \bar{x}) = 0\). - The sum of squared deviations \(\sum (x - \bar{x})^2\) measures variance. 4. To compute these: - Calculate \(\sum X\) by adding all midterm or final scores. - Calculate \(\sum X^2\) by squaring each score and summing. - Compute the mean \(\bar{x}\). - Calculate \(\sum (x - \bar{x})\) which should be zero. - Calculate \(\sum (x - \bar{x})^2 = \sum X^2 - n \bar{x}^2\). 5. Without the actual data values, the exact numerical answers cannot be computed here, but the formulas and steps to calculate them from the dataset are provided. This approach helps analyze the distribution and variability of exam scores.