AP Statistics — reading and comparing distributions

This material trains the data-description skills of Unit 1 of the AP Statistics course framework for 2026–27 (topics 1.3 to 1.9): representing one variable, computing summary statistics and comparing distributions. Unit 1 carries 20 to 30 percent of the multiple-choice section, and describing and comparing distributions in context runs through the free-response questions as well. The material is written at introductory college level; every display is given in words and numbers (ordered lists, frequency tables, cumulative relative frequency tables, a stem-and-leaf plot described leaf by leaf, five-number summaries), and some questions also show the box plot or histogram the exam would print.

The quiz asks you to find a five-number summary with the halves method, decide where a box-plot whisker ends when an outlier is present, draw a justified conclusion from two five-number summaries, describe a right-skewed income distribution and the position of its mean, locate the median of a grouped frequency table, read a proportion from a cumulative table, pick the complete comparison of two distributions (shape, center, variability and unusual features in context), see what adding a constant does to center and spread, apply the two-standard-deviation outlier rule, choose a display for a categorical variable, read a median from a stem-and-leaf plot, and explain why two histograms of the same data can look different. Each explanation gives the working and the reason every other answer fails.

The flashcards cover the four features of a description, quartiles and five-number summaries, both outlier rules, box-plot whiskers, the mean and median in skewed data, resistance, linear changes, percentiles and the choice of display by type of variable.

The written work is a printable sheet of eight free-response tasks: a full five-number summary with outliers and a box-plot description, a complete comparison of two drivers' delivery times, a grouped frequency table, adding a constant and changing units, a cumulative table of rents with percentiles, two outlier rules that disagree, relative frequencies and a display for a categorical variable, and the effect of bin width on a histogram. Handwritten answers are photographed and checked against model answers and key points.

The oral exam has an examiner describe data aloud and ask one question at a time, from summaries and outliers to a complete comparison in context, closing with short, precise feedback.

Choosing between mean and median for skewed data, standard deviation and z-scores are also practiced in another material of this category. All scenarios are invented and all questions are original practice items written by Zestly, not released exam questions. The material follows the published course framework but is independent practice and does not predict an exam score.

• Compute five-number summaries and identify outliers with the 1.5 times IQR rule and the two-standard-deviation rule
• Read box plots, frequency tables, cumulative relative frequency tables and stem-and-leaf plots given as numbers
• Describe a distribution's shape, center, variability and unusual features in context
• Write a complete, numerical comparison of two distributions
• Explain how adding a constant or changing units affects measures of center and spread
• Choose an appropriate display for categorical and quantitative variables and explain the effect of histogram bin width

Practice material written by Zestly, based on the College Board AP Statistics course framework effective fall 2026 (Unit 1, Exploring One-Variable Data and Collecting Data, topics 1.3–1.9). Original questions, not released exam items.