What it covers: Describing one-variable data (categorical and quantitative) and collecting trustworthy data through sampling and experiments.
Exam weight: About 20–30% of the AP Statistics exam — the largest unit.
The big question: How do we display and summarize a single variable, and how do we gather data so that our conclusions are valid?
Statistical practices: Formulate Questions (P1), Collect Data (P2), Analyze Data (P3), Interpret Results (P4).
Key topics at a glance
Two Kinds of Variables
Categorical variables sort individuals into groups; quantitative variables are numbers you can do arithmetic on. The variable type decides which display and statistics are appropriate.
Displaying Categorical Data
Frequency and relative-frequency tables, bar charts, and pie charts. Relative frequency = count ÷ total.
Displaying Quantitative Data
Dotplots, stemplots, and histograms show the distribution of a quantitative variable.
Describing a Distribution (SOCS)
Report Shape (symmetric / skewed / uniform / bimodal), Outliers, Center (mean or median), and Spread — in context.
Summary Statistics
Center: mean (not resistant) or median (resistant). Spread: range, IQR (resistant), standard deviation (not resistant). Skew pulls the mean toward the tail.
SRS is the benchmark; stratified, cluster, and systematic are other random methods. Beware undercoverage, nonresponse, response bias, and voluntary response.
Experiments vs. Observational Studies
An experiment imposes treatments and uses random assignment to allow cause-and-effect. An observational study only measures and can suffer confounding.
The key terms you must know
Categorical vs. quantitative — groups vs. meaningful numbers; determines the correct display.
Relative frequency — a category's count divided by the total, as a proportion or percent.
Distribution — the pattern of values a variable takes and how often each occurs.
SOCS — Shape, Outliers, Center, Spread — the checklist for describing a distribution.
Skewed left / right — the direction of the longer tail; the mean is pulled toward it.
Mean vs. median — average vs. middle value; median is resistant to outliers.
IQR — Q3 − Q1, the range of the middle 50% of the data; resistant to outliers.
Standard deviation — the typical distance of values from the mean; not resistant.
Five-number summary — min, Q1, median, Q3, max — the basis of a boxplot.
1.5 × IQR rule — flags a value as an outlier beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR.
Population vs. sample; parameter vs. statistic — the whole group vs. a subset; a fixed unknown vs. an estimate from data.
Bias — a systematic tendency to over- or under-estimate; caused by poor sampling or design.
Confounding — when two variables' effects on the response cannot be separated.
Key themes to remember
Variable type drives the analysis. Decide categorical vs. quantitative first — it determines every display and statistic you use.
Describe distributions with SOCS, in context. Shape, outliers, center, and spread — never a bare number.
Resistance matters. Use the median and IQR for skewed data or data with outliers; use the mean and standard deviation for roughly symmetric data.
How you collect data limits what you can conclude. Random sampling lets you generalize; random assignment lets you claim cause and effect.
Always answer in context. The AP exam rewards conclusions stated in terms of the actual variables and population.
Common exam traps
Skew direction is named for the tail, not the peak. A right-skewed distribution has its long tail on the right, with most data on the left.
Mean vs. median in skewed data. The mean is pulled toward the tail, so mean > median suggests right skew, mean < median suggests left skew.
Random sampling ≠ random assignment. Sampling is about who is studied (generalizing); assignment is about who gets which treatment (cause and effect).
Association is not causation. Only a well-designed experiment with random assignment supports a cause-and-effect claim.
A large sample does not fix bias. A biased method (like voluntary response) is biased no matter how many people respond.
Bar chart vs. histogram. Bar charts show categorical data with gaps; histograms show quantitative data in touching intervals.
Outliers are defined by the 1.5 × IQR rule, not by 'looking far away.' Show the calculation.