1. **Representation of Data Formulas:** - Mean (Arithmetic Mean): $$\bar{x} = \frac{\sum x_i}{n}$$ where $x_i$ are data points and $n$ is the number of points. - Median: The middle value when data is ordered. - Mode: The most frequently occurring value. - Range: $$\text{Range} = \text{Max} - \text{Min}$$ - Variance: $$\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$$ - Standard Deviation: $$\sigma = \sqrt{\sigma^2}$$ 2. **Central Tendencies:** - Mean: Average value. - Median: Middle value in ordered data. - Mode: Most frequent value. 3. **Probability Formulas:** - Probability of an event $E$: $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ - Complement Rule: $$P(E^c) = 1 - P(E)$$ - Addition Rule (for mutually exclusive events): $$P(A \cup B) = P(A) + P(B)$$ - Multiplication Rule (for independent events): $$P(A \cap B) = P(A) \times P(B)$$ 4. **Permutation Formulas:** - Number of permutations of $n$ distinct objects: $$n!$$ - Number of permutations of $n$ objects taken $r$ at a time: $$P(n,r) = \frac{n!}{(n-r)!}$$ These formulas cover basic data representation, central tendencies, probability, and permutations at the S1 level.