One-variable data: Distributions and measures of center and spread
A SAT overview of how one-variable data distributions are described by center and spread.
核心知识
Every data set has a shape, a center, and a spread. The SAT tests whether you can read that information from tables, dot plots, histograms, and box plots — and whether you know how adding, removing, or changing values shifts the center and spread.
深入理解
Most SAT data-analysis questions boil down to three things:
- Where is the middle? That's the center — mean or median.
- How spread out are the values? That's range, IQR, or standard deviation.
- What happens when the data changes? Add an outlier, remove a value, or shift every point — how do center and spread respond?
You won't need to crunch massive calculations by hand. The test gives you a graph or small table and asks you to read it accurately, pick the right measure, or predict how a change affects the statistics.
The most common mistakes: confusing mean and median when outliers are present, misreading which quartile is which on a box plot, and forgetting that standard deviation measures distance from the mean — not from the median.
This topic shows up in 2–4 questions per test. Master the core definitions, know when each measure is appropriate, and practice reading every graph type quickly.
知识点教程
7Read and interpret frequency tables and dot plots.
Reading exact values, totals, and medians from frequency tables and dot plots.
Read and interpret histograms and box plots (including median, quartiles, IQR).
Reading histogram shapes and box plots, including quartiles, median, and IQR.
Compute and interpret mean, median, range, and interquartile range (IQR).
How to compute the mean, median, range, and IQR from a small data set.
Identify outliers and describe their impact on center/spread.
How outliers affect the mean, median, range, standard deviation, and IQR.
Compare multiple distributions using measures of center and spread.
Compare two data sets by their center and spread to tell which group is typically higher or more con
Understand standard deviation as a measure of spread; compare spreads qualitatively without calculating.
Using standard deviation to compare how tightly or loosely data values cluster around the mean.
Determine mean/median from a frequency table and analyze how changes affect center/spread.
Find the mean or median from a frequency table and update the statistics when one value changes.