Statistics & Probability

What you'll learn

• Calculate mean, median, mode, and range for data sets
• Solve weighted average problems
• Calculate basic probability when outcomes are equally likely: P(event) = favorable outcomes / total outcomes
• Apply the complement rule P(not A) = 1 - P(A) and the multiplication rule for independent events P(A and B) = P(A) x P(B)
• Read a probability off a two-way frequency table (the row/column count divided by the relevant total)
• Apply counting principles (fundamental counting principle, permutations, combinations)
• Interpret data from tables, charts, and graphs in math contexts

Key concepts

The mean (average) is the sum divided by the count. The median is the middle value when data is ordered; for an even count, average the two middle values. The mode is the most frequent value. Probability is always between 0 and 1. The formula probability = favorable outcomes / total outcomes applies only when every outcome is equally likely; when it is not (for example a weighted bag or a frequency table), you count actual frequencies instead. Two rules the ACT tests often: the complement rule, P(not A) = 1 - P(A), which is the fast way to handle 'at least one' questions, and the multiplication rule for independent events, P(A and B) = P(A) x P(B). The ACT also asks you to read a probability directly off a two-way frequency table: divide the count in the relevant cell (or row/column) by the appropriate total. The fundamental counting principle states that if event A has m outcomes and event B has n outcomes, together they have m × n outcomes. Combinations (order doesn't matter) use C(n,r) = n! / (r!(n−r)!); permutations (order matters) use P(n,r) = n! / (n−r)!. Statistics and probability account for about 8-12% of ACT Math questions.

Pro tips

• For median, always arrange the numbers in order first. A common ACT trap is providing unsorted data.
• If a question says 'at least one,' it's often easier to calculate 1 minus the probability of 'none.'
• Weighted averages appear in problems like 'your quiz average is 80% of your grade and the final is 20%.'