1. **Problem 21:** Solve for $\bar{X}$ when $\sum X = 1800$ and $n = 80$. Formula: $$\bar{X} = \frac{\sum X}{n}$$ Explanation: $\bar{X}$ is the mean (average) of the data set, calculated by dividing the sum of all values by the number of values. Calculation: $$\bar{X} = \frac{1800}{80} = 22.5$$ 2. **Problem 22:** Solve for $\sum (X - \bar{X})^2$ when $n = 1501$ and $S^2 = 10$. Given: $$S^2 = \frac{\sum (X - \bar{X})^2}{n - 1}$$ Let $A = \sum (X - \bar{X})^2$. Rearranged formula: $$A = S^2 \times (n - 1)$$ Calculation: $$A = 10 \times (1501 - 1) = 10 \times 1500 = 15000$$ 3. **Problem 23:** Given $X_1=0$, $X_2=4$, $X_3=1$, $X_4=5$, $X_5=8$, $X_6=6$, $X_7=2$, $X_8=5$, find: A. $\sum_{i=1}^4 X_i$ Explanation: Sum the first four values. Calculation: $$\sum_{i=1}^4 X_i = X_1 + X_2 + X_3 + X_4 = 0 + 4 + 1 + 5 = 10$$