Statistics & Probability

What you'll learn

• Calculate mean, median, mode, and range for data sets
• Solve weighted average problems
• Calculate basic probability: P(event) = favorable outcomes / total outcomes
• 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 = favorable outcomes / total outcomes, and is always between 0 and 1. 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%.'