ACT: Statistics and Probability

Mean, Median, Mode

Mean (Average)

$\bar{x} = \frac{\text{sum of values}}{\text{number of values}}$

Median

Middle value in ordered data.

Mode

Most frequent value.

Probability

$P(E) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$

Independent Events

$P(A \text{ and } B) = P(A) \times P(B)$

Complement

$P(\text{not } A) = 1 - P(A)$

Counting Principles

Permutations (order matters)

$P(n,r) = \frac{n!}{(n-r)!}$

Combinations (order does not matter)

$C(n,r) = \frac{n!}{r!(n-r)!}$

ACT Tip: Statistics problems are usually straightforward. Read carefully and look at the data provided.