Standard deviation measures how spread out data is from the mean. A higher SD means more variability.

Relative frequency = frequency / total count. It expresses frequency as a proportion (0 to 1) or percentage.

Probability = number of favorable outcomes divided by total possible outcomes.

For mutually exclusive events: P(A or B) = P(A) + P(B). They can't happen at the same time.

A random variable is a variable whose value is determined by the outcome of a random process or experiment.

A box plot shows the 5-number summary: minimum, Q1 (25th percentile), median (Q2), Q3 (75th percentile), and maximum.

Z-score = (x - μ) / σ. It measures how many standard deviations a value x is from the mean μ.

P(A') is the complement of A — the probability A does not occur. P(A') = 1 - P(A).

Weighted average = Σ(value × weight) / Σ(weights). Used in GPA calculation, grade weighting, etc.

Discrete: countable values (e.g., number of students). Continuous: any value in a range (e.g., height, temperature).

A z-score of 2 means the value is 2 standard deviations above the mean.

Conditional relative frequency = joint frequency / row (or column) total. Used in two-way tables.

For independent events: P(A and B) = P(A) × P(B). Their probabilities multiply.

Parameter = numerical measure describing a population (e.g., μ). Statistic = numerical measure from a sample (e.g., x̄).

Range = Maximum value - Minimum value. It measures the spread of the data.

Mode is the most frequently occurring value. A data set can have no mode, one mode, or multiple modes.

r = 1 indicates a perfect positive linear relationship. r = -1 is perfect negative; r = 0 is no linear correlation.

Independent events: P(A|B) = P(A). The occurrence of B does not change the probability of A.

Permutations P(n,r) count ordered arrangements; Combinations C(n,r) count unordered groups. P(n,r) = C(n,r) × r!

In a uniform distribution, all outcomes are equally likely. Example: rolling a fair die — each face has probability 1/6.