Permutations: nPr = n! / (n-r)!. Order DOES matter in permutations.

Two dice: 6 × 6 = 36 total outcomes. Use the multiplication principle for independent events.

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

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

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

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

An outlier is a data point significantly different from the rest. It can heavily affect the mean but not the median.

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

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

A scatter plot shows the relationship (correlation) between two quantitative variables, with one on each axis.

Probability = number of favorable outcomes ÷ total possible outcomes.

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.

A census collects data from every member of the population. A survey uses a sample instead.

Law of Large Numbers: as the number of trials increases, the experimental probability approaches the theoretical probability.

The number of arrangements of n distinct items = n! (n factorial). Example: 4 items = 4! = 24 ways.

When mean > median, the distribution is right-skewed (positively skewed). High outliers pull the mean rightward.

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

Experimental probability = (number of times event occurred) / (total number of trials). Based on actual results, not theory.

A frequency distribution shows how often each value or range of values occurs in a data set.

C(n,n) = 1. There is exactly one way to choose all n items from n — choose everything.