ACT Math Statistics & Probability: Data, Graphs & Chance

Statistics and Probability accounts for roughly 5–8 of the 45 ACT Math questions. Question types include: computing mean (average), median (middle value), and mode (most frequent value); understanding what happens to the mean when a value is added or removed; interpreting data from tables, bar charts, and scatterplots; basic probability (P = favorable outcomes / total outcomes); and occasionally expected value or two-way table analysis.

These questions often look easier than they are because they involve reading and interpreting presented data rather than algebraic manipulation. The traps are in misreading the chart or misidentifying which statistic the question is asking for.

For mean problems, remember: mean = sum / count. If the mean changes when a value is added, the new mean = (old sum + new value) / (old count + 1). To find a missing value given a mean: total sum = mean × count, then subtract the known values.

For median problems with an even number of values, the median is the average of the two middle values. Sort the data first — the ACT sometimes gives values out of order.

For probability, always identify: (1) the favorable outcomes, and (2) the total possible outcomes. For compound probability, "and" means multiply; "or" (when events are mutually exclusive) means add. For dependent events, the second probability changes based on the first outcome.

Confusing mean and median — these are different statistics, and the ACT deliberately uses both in the same problem. Re-read the question to confirm which one is being asked for.

For data-table questions, misidentifying the total. Two-way tables have row totals, column totals, and a grand total — make sure you're dividing by the right denominator for the conditional probability the question asks about.

Ignoring the "at least" language in probability. "At least one success in 3 trials" is easier to compute as 1 − P(zero successes) than by adding up each success case individually.

Practice reading two-way tables specifically — the ACT uses them frequently and students who haven't seen them before waste significant time figuring out the layout on test day.

For mean/median/mode questions under time pressure, list the values in order before doing any computation. This one-step prevents sorting errors and makes both the median and mode immediately visible.