A boxplot is a graph of the five-number summary (minimum, Q1, median, Q3, maximum) where the box spans the interquartile range, a line marks the median, whiskers extend to non-outlier values, and outliers are plotted as individual points.
A boxplot turns a quantitative dataset into a picture of its five-number summary. The box stretches from the first quartile (Q1) to the third quartile (Q3), so the box itself is the interquartile range (IQR), the middle 50% of the data. A line inside the box marks the median, and whiskers extend out to the most extreme values that aren't outliers. Any point beyond 1.5 × IQR from the box gets plotted separately as a potential outlier.
The real power of a boxplot is comparison. Stack two boxplots on the same scale and you can instantly compare centers, spreads, and skewness between groups. That's why boxplots show up twice in AP Stats. They're a Unit 1 tool for describing and comparing distributions, and they come back in Unit 7 as the go-to display for checking whether your data are normal enough to run a two-sample t-test for the difference of two population means (Topic 7.8).
Boxplots support learning objective AP Stats 7.8.C, which asks you to verify the conditions for a significance test for the difference of two population means. The essential knowledge is specific here. If either sample size is less than 30, you can't lean on the Central Limit Theorem, so you have to graph the sample data and check that there's no strong skewness or outliers. A boxplot is built for exactly that job because it makes skewness and outliers visually obvious. So when you see small samples (say n₁ = 12 and n₂ = 15), drawing parallel boxplots is how you justify, in writing, that the sampling distribution of x̄₁ - x̄₂ is approximately normal. Beyond inference, boxplots are one of the most common stimuli on the exam for 'compare the distributions' questions, where you're expected to discuss center, spread, shape, and outliers in context.
Keep studying AP Statistics Unit 7
Quartiles and the Interquartile Range (Unit 1)
A boxplot is literally quartiles drawn as a picture. Q1 and Q3 form the edges of the box, so the box width IS the IQR. If you can read a boxplot, you can report the five-number summary without doing any math.
Outliers and the 1.5 × IQR Rule (Unit 1)
Boxplots use the 1.5 × IQR rule automatically. Any value below Q1 - 1.5(IQR) or above Q3 + 1.5(IQR) gets its own dot beyond the whisker. This is why boxplots are the fastest way to spot outliers when checking inference conditions.
Conditions for a Two-Sample t-Test (Unit 7)
Topic 7.8 says that when n₁ or n₂ is under 30, you must check the sample data for strong skew or outliers before trusting the t-procedure. Parallel boxplots of both samples are the standard way to do that check and write a sentence defending normality.
The 10% Condition and Independence (Unit 7)
Boxplots handle the shape condition, but they say nothing about independence. You still need random sampling or random assignment plus the 10% condition (n ≤ 10% of N for each sample). A full condition check pairs the boxplot with these independence checks.
Boxplots show up in two main ways. First, as a stimulus you have to read. The 2021 FRQ Q6 gave boxplots summarizing 47 years of baseball attendance and asked for comparison and interpretation, and the 2023 FRQ Q1 had you compare distributions of stream measurements between two groups. When comparing, always address center, spread, shape, and outliers, and do it in context with actual values. Second, as the answer to a 'which display should you use' question. Multiple-choice questions regularly describe a planned two-sample t-test with small samples (like n₁ = 12 and n₂ = 15, or two groups of 15 plants) and ask which graphical display verifies the normality assumption. Boxplots (or dotplots) of each sample are the answer because they expose skewness and outliers. One caution for FRQs is that a boxplot cannot show gaps, clusters, or the number of peaks, so don't claim a distribution is 'unimodal' from a boxplot alone.
Both display one quantitative variable, but they show different things. A histogram shows the full shape of the distribution, including peaks, gaps, and clusters, while a boxplot compresses everything into five numbers plus outliers. A boxplot is better for flagging outliers and comparing several groups side by side; a histogram is better when shape details matter. You can never tell whether a distribution is unimodal or bimodal from a boxplot, because two very different histograms can produce the same boxplot.
A boxplot displays the five-number summary, with the box running from Q1 to Q3, a line at the median, whiskers to the most extreme non-outliers, and outliers shown as separate points.
The width of the box equals the IQR, and points beyond 1.5 × IQR from the box are flagged as potential outliers automatically.
In Topic 7.8, when either sample size is less than 30, boxplots of both samples are how you check for strong skew or outliers before running a two-sample t-test.
Boxplots are ideal for comparing distributions between groups, but when you compare them on an FRQ you must discuss center, spread, shape, and outliers in context.
A boxplot hides modality, so never claim a distribution is unimodal or bimodal based on a boxplot alone.
A boxplot is a graph of the five-number summary: minimum, Q1, median, Q3, and maximum. The box spans Q1 to Q3 (the IQR), a line marks the median, whiskers reach the most extreme non-outlier values, and outliers are plotted as separate points.
Partly. A boxplot reveals skewness (a longer whisker or larger half-box on one side) and outliers, but it cannot show gaps, clusters, or the number of peaks. So you can say 'skewed right' from a boxplot, but never 'unimodal' or 'bimodal.'
A histogram shows the full shape of the data including peaks and gaps, while a boxplot only shows the five-number summary and outliers. Use boxplots to compare groups or flag outliers; use histograms when modality matters.
When n₁ or n₂ is less than 30, the Central Limit Theorem doesn't guarantee a normal sampling distribution, so the CED requires you to check the sample data for strong skew or outliers. Boxplots make both of those visible at a glance, which is why they're the standard answer to 'which display verifies the normality assumption.'
It uses the 1.5 × IQR rule. Any value below Q1 - 1.5(IQR) or above Q3 + 1.5(IQR) falls outside the whiskers and is plotted as an individual point, flagging it as a potential outlier.