A box plot (boxplot) is a graph of the five-number summary: the box spans Q1 to Q3 with a line at the median, whiskers extend to the most extreme non-outlier values, and outliers get their own symbols. On the AP Stats exam it's the go-to display for comparing distributions of a quantitative variable.
A box plot is the five-number summary turned into a picture. Per the CED (UNC-1.L.1 and UNC-1.L.2), the five-number summary is the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box stretches from Q1 to Q3, so it always contains the middle 50% of the data, with a line drawn at the median. The whiskers don't automatically run to the min and max. They extend from the quartiles out to the most extreme data point that is not an outlier, and any outliers beyond that get plotted as their own dots or asterisks.
Here's the trade-off to remember. A box plot shows you center (median), spread (range and IQR), skewness (which side of the box or whisker is stretched), and outliers, all in one compact display. What it hides is shape detail. You can't see gaps, clusters, or whether a distribution has two peaks. That's why box plots shine when you're comparing groups, and histograms or dotplots are better when you need the full shape of one distribution.
Box plots live in Unit 1 (Exploring One-Variable Data), specifically Topic 1.8 (Graphical Representations of Summary Statistics) and Topic 1.9 (Comparing Distributions of a Quantitative Variable). They directly support learning objectives 1.8.A (represent summary statistics graphically), 1.8.B (describe summary statistics shown graphically), and 1.9.A (compare graphical representations for multiple data sets). The payoff is bigger than Unit 1, though. Side-by-side box plots are the standard 'compare two groups' display the exam hands you, and the skills you build here (comparing center, variability, and outliers in context) come back when you analyze experiments and two-sample inference later in the course. If a distribution looks symmetric on the box plot, the mean and median sit close together; if it's skewed right, the mean usually gets pulled to the right of the median (UNC-1.M.2). That mean-vs-median reasoning is a classic exam move.
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Quartiles and the Median (Unit 1)
A box plot is literally built from these numbers. Q1, the median, and Q3 form the box itself, so if you can compute quartiles, you can draw and read any box plot. The IQR (Q3 minus Q1) is just the width of the box.
Outliers and the 1.5×IQR Fence (Unit 1)
Box plots are the one display that flags outliers automatically. Any point beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR gets plotted separately instead of being absorbed into a whisker, which is why MCQs love asking how a box plot identifies outliers.
Skewed to the Right (Unit 1)
You can read skew straight off a box plot. A longer right whisker or a median squished toward the left side of the box signals right skew, and right skew tells you the mean is probably bigger than the median.
Comparing Distributions in Experiments and Inference (Units 1, 3, and 7)
Side-by-side box plots are how the exam shows treatment vs. control or group A vs. group B. The 2023 FRQ on Alaskan streams compared water samples from colder and warmer streams exactly this way, and the same comparison habit feeds into two-sample inference later.
Multiple-choice questions ask you to read a box plot (find the median, IQR, or range), match a box plot to a histogram of the same data, or identify outliers using the fence rule. Free-response questions usually give you side-by-side box plots and ask you to compare distributions, like the 2023 FRQ comparing stream water samples colder and warmer than 8°C. When you compare, you need all three pieces or you lose points. Compare center (medians), compare variability (IQRs or ranges), mention outliers or skew if visible, and do it all in context with the actual variable names. Saying 'the cold-stream median is higher' beats 'one box is taller.' Use comparative language ('greater than,' 'more variable than'), not two separate descriptions. Also watch for questions where a box plot can't answer something, like 'how many values are above 10' or 'is the distribution bimodal.' A box plot doesn't show individual data points or shape details, and the exam tests whether you know that.
Both display one quantitative variable, but they show different things. A histogram shows the full shape of the distribution (peaks, gaps, clusters) by binning the data, while a box plot compresses everything into five summary numbers plus outliers. A box plot can never reveal bimodality, and a histogram doesn't mark the median or flag outliers for you. On the exam, 'compare several groups' usually means box plots; 'describe the shape in detail' usually means a histogram or dotplot.
A box plot graphs the five-number summary: minimum, Q1, median, Q3, and maximum, with the box covering the middle 50% of the data.
Whiskers extend to the most extreme values that are NOT outliers, and outliers are plotted separately using the 1.5×IQR fence rule.
The box always contains 50% of the data no matter how wide or narrow it looks; a wider box means more spread, not more data.
Read skew from a box plot by checking which whisker is longer and where the median sits inside the box; right skew usually pulls the mean to the right of the median.
When comparing side-by-side box plots on an FRQ, address center, variability, and outliers/skew using comparative language and the context of the variable.
Box plots cannot show gaps, clusters, or bimodality, so don't make shape claims a box plot can't support.
It's a graph of the five-number summary (minimum, Q1, median, Q3, maximum) where the box spans the quartiles, a line marks the median, whiskers reach the most extreme non-outlier points, and outliers are plotted separately. It comes from Topic 1.8 in Unit 1.
No. Whiskers extend only to the most extreme data values that are not outliers. Any point beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR is an outlier and gets its own symbol past the whisker.
A box plot summarizes the data with five numbers and flags outliers, while a histogram shows the full shape, including gaps and multiple peaks. A box plot can hide bimodality entirely, so use histograms for shape and box plots for comparing groups.
No. The box always contains the middle 50% of the data regardless of its size. A wider box means that middle 50% is more spread out (a larger IQR), not that it contains more values.
Compare center (medians), variability (IQRs or ranges), and any outliers or skew, using comparative language like 'greater than' and the real context of the variable. The 2023 FRQ did exactly this with side-by-side box plots of stream water samples colder and warmer than 8°C.