One-variable data: mean, median, mode and range, standard deviation as spread, the effect of outliers, and inference from sample statistics including margin of error and evaluating statistical claims.

What this skill is asking

One-variable data questions give a list, table, dot plot, histogram, or box plot and ask about its center and spread. The Digital SAT (Problem-Solving and Data Analysis domain) tests the mean, median, mode, and range, treats standard deviation as a conceptual measure of spread, asks how outliers shift these, and extends to inference: what a sample says about a population, margin of error, and judging statistical claims.

Center and spread

Each statistic captures a different feature of the data.

A worked center comparison

Comparing mean and median reveals skew.

Outliers, skew, and which measure to use

The relationship between mean and median signals the shape of the data. If the data is roughly symmetric, mean and median are close. If a few large values stretch the right tail (right skew), the mean exceeds the median; if a few small values stretch the left tail (left skew), the mean is below the median. Because the median is resistant to outliers and the mean is not, the median is the better summary of a typical value when outliers or strong skew are present (incomes are the classic example). The SAT often asks which measure a change affects: adding an extreme value shifts the mean noticeably and the range a lot, but may leave the median unchanged.

Sampling, margin of error, and statistical claims

The domain also tests inference. A sample is used to estimate a population parameter, and the estimate is only trustworthy if the sample is randomly selected and representative; a biased sampling method (volunteers, a convenient group) undermines any conclusion. The margin of error describes how far the true population value might be from the sample estimate; a larger and more random sample produces a smaller margin of error, so a result like "$52\%$ plus or minus $3\%$" means the population value plausibly lies between $49\%$ and $55\%$. When judging a statistical claim, ask two questions: was the sample random and representative (so results generalise to the stated population), and does the data actually support the conclusion drawn? Only a randomised experiment can support a cause-and-effect claim; an observational study can show association but not causation.