ACT Mathematics — statistics, counting and probability

Statistics and Probability is a Preparing for Higher Math subcategory on the enhanced ACT, and ACT describes it as center and spread of distributions, data collection methods, relationships in bivariate data, and probabilities with their sample spaces. This material covers each of those strands.

For center and spread, you find the median of an unsorted list with an even number of values, compare the standard deviations of four data sets that share a mean without using the formula, and decide how an extreme value changes the mean and the median. For probability, a survey of juniors and seniors is written out in the question as a two-way table in words; you use it once for a conditional probability, where the condition decides the denominator, and once for the addition rule for “A or B”, where the overlap must not be counted twice. Other questions cover the complement shortcut for “at least one”, two draws without replacement, and the difference between permutations (a podium of three medals) and combinations (a committee with equal roles).

The last group links probability and data to decisions: the expected net gain of a carnival game once the cost of playing is subtracted, the meaning of the slope of a line of best fit in the units of the problem, and the choice of a sampling method that avoids selection bias.

The material offers two formats. The quiz has twelve multiple-choice questions with four answer choices each, as on the enhanced ACT, and every explanation names the slip behind each wrong choice, so a miss tells you what to fix. The flashcards collect the rules and formulas worth knowing by heart.

The content is based on ACT's published description of the mathematics section (reporting categories and the topics listed for each). It is independent practice and is not produced or endorsed by ACT.

• Find and compare measures of center and spread, including the effect of an outlier
• Compute conditional and compound probabilities from a two-way table
• Use the complement and the multiplication rule for dependent events
• Count arrangements with permutations and combinations
• Compute an expected value, interpret the slope of a line of best fit and recognize an unbiased sampling method

Practice material written by Zestly, based on ACT's published description of the ACT mathematics section (act.org, Mathematics Test Description: Preparing for Higher Math — Statistics & Probability). Formulas beyond the basics are given in the questions, as ACT states that recall of complex formulas is not required.