PSAT Data — reading distributions: frequency tables, histograms, box plots, range and standard deviation

College Board's description of Problem-Solving and Data Analysis for the PSAT/NMSQT asks students to analyze and interpret distributions of data, to calculate, compare and interpret mean, median and range, and to compare distributions with the same and different standard deviation. This material works through exactly that, with the data written into every question and, where the test would show a chart, a drawn bar chart, histogram or box plot as well.

The twelve quiz questions each take a different step. The first reads a median from counts, where the tempting wrong answer is the middle of the listed values rather than the middle employee. The second finds which histogram interval holds the median by keeping a running total. A box plot of home prices asks for the range and the interquartile range, and two stores' box plot summaries are compared for center and spread, including one option about the mean, which a box plot cannot show. The mean of 25 star ratings has to be weighted by the number of reviews.

The rest is about spread and its behavior. What happens to the mean and the standard deviation when a constant is added to every value, and when every value is doubled. A combined mean of two groups of different size, and a missing score recovered from a target mean. Two filling machines with the same mean and different standard deviations, a right-skewed salary distribution, and two data sets with the same mean and the same range but clearly different standard deviations, which is the comparison students most often get wrong. No question asks you to compute a standard deviation by formula; the test asks you to compare and interpret, and so does this material.

The flashcards cover the vocabulary: mean, median, mode, range, quartiles, interquartile range, the five-number summary and the parts of a box plot, standard deviation, skew, outliers, and the two transformation rules.

The printable written work has eight open problems with no options: a mean and median from a frequency table, a five-number summary read in full, two stores compared in writing, two thermostats with the same mean and very different spread, shifting and stretching a data set, a combined mean that is not the average of the two means, a missing value followed by a median, and the right statistic to report for skewed home prices.

The oral exam asks one question at a time and wants the reason as well as the number.

All data sets are invented for practice, and nothing is taken from any published test.

• Find the median and the mean of data given as a frequency table or bar chart
• Locate the interval containing the median in a histogram with a running total
• Read range and interquartile range from a five-number summary or box plot
• Compare two distributions by center and by spread, knowing a box plot shows no mean
• Compare standard deviations without computing them, including sets with equal means and equal ranges
• Predict the effect of adding a constant or multiplying by a constant on mean and standard deviation
• Compute a combined mean of groups of different sizes and recover a missing value from a mean
• Explain why right skew puts the mean above the median and which center to report

Practice material written by Zestly, based on the PSAT/NMSQT Math skill "One-variable data: distributions and measures of center and spread" as described in College Board's Fall 2026 PSAT/NMSQT Student Guide and the Assessment Framework for the Digital SAT Suite (version 3.01, August 2024). All data sets are invented. Zestly is not affiliated with College Board.