A bimodal distribution has two modes (two peaks). It often indicates two distinct subgroups in the data.

Mean = Sum of all values ÷ Count. It is the arithmetic average of a data set.

A two-way table shows the relationship between two categorical variables, displaying joint and marginal frequencies.

General addition rule: P(A∪B) = P(A) + P(B) - P(A∩B). Subtract the overlap to avoid double-counting.

C(n,0) = n!/(0! × n!) = 1. There is exactly one way to choose 0 items from n — choose nothing.

In a right-skewed (positively skewed) distribution, the mean is pulled right by outliers, so mean > median.

For independent events: P(A and B) = P(A) × P(B). Multiply their individual probabilities.

Probability = number of favorable outcomes ÷ total possible outcomes.

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

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

Without replacement, events are dependent. The second probability changes: P = P(first) × P(second | first drawn).

Empirical Rule: ~68% of data falls within 1 SD, ~95% within 2 SD, ~99.7% within 3 SD of the mean in a normal distribution.

P(A|B) is conditional probability: the probability of A occurring given that B has already occurred.

Fundamental counting principle: multiply the number of choices for each step. If event A has m ways and B has n ways, together they have m × n ways.

Population = entire group of interest. Sample = subset of the population used to make inferences.

Geometric mean = √(a × b). Used for growth rates and ratios. The geometric mean of 4 and 9 = √36 = 6.

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

A histogram displays the frequency distribution of continuous data using adjacent bars. The x-axis shows intervals; y-axis shows frequency.

Expected value: E(X) = Σ(x × P(x)). Multiply each outcome by its probability and sum them all.

In a perfectly symmetric (normal) distribution, mean = median = mode. All three coincide at the center.