SAT Math — histograms, dot plots, box plots and frequency tables

College Board's description of the SAT Math skill on one-variable data asks students to analyze and interpret numerical data shown in frequency tables, histograms, dot plots and box plots, to calculate and compare mean, median and range, to compare distributions with different standard deviations, and to describe the effect of outliers on the mean and the median. On the test, most of these questions start from a picture rather than a list of numbers. This material is built the same way: nine of its twelve questions come with a drawn display, and every value you need is also given in words for anyone reading without the picture.

Histograms come first. One question asks which interval holds the median commute distance of 35 employees, which means finding the 18th value by adding bars from the left; another asks what percent of 40 phones lasted at least 10 hours, where the trap is to read a single bar instead of all the bars that qualify.

Dot plots follow. You compute a mean by weighting each value by the number of dots above it, decide what happens to the mean and the median when a 31-day delivery is removed from otherwise quick orders, and compare two dot plots with the same mean of 5 days, where only the spread differs. A plot of work absences with a long right tail asks you to compare the mean and the median and to see why the tail pulls one and not the other.

Box plots take three questions: the interquartile range as the width of the box, the fact that about a quarter of the data lie above the third quartile (so about 20 of 80 home sales), and a comparison of two stores whose medians, interquartile ranges, ranges and maximums you read and test one by one. Frequency tables written in words close the set: a mean from counts of books read, a median from household sizes with an even number of households, and the five-number summary of a short list with quartiles taken as the medians of the two halves.

The explanations show every step and name the slip behind each wrong answer, for example dividing by the number of categories instead of the number of people, or reading the median of a box plot as its interquartile range. The flashcards summarize how to read each display, the five-number summary, the interquartile range, the share of data in each part of a box plot, skew, outliers and standard deviation.

The material offers a quiz and flashcards. It is independent practice with invented data; no question is taken from any published test.

• Find the interval of a histogram that contains the median, and the share of data in a range of intervals
• Compute a mean and a median from a dot plot or a frequency table
• Read the five-number summary and interquartile range from a box plot, and the share of data in each part
• Compare two box plots by center, spread and extremes
• Compare standard deviations of distributions with the same mean
• Describe the effect of an outlier and of skew on the mean and the median

Practice material written by Zestly, based on the SAT Math skill "One-variable data: distributions and measures of center and spread" in the Problem-Solving and Data Analysis domain, as described in College Board's Assessment Framework for the Digital SAT Suite (version 3.01, August 2024, Appendix B). All data sets and situations are invented. Zestly is not affiliated with College Board.