In AP Statistics, the minimum value is the smallest observation in a quantitative dataset. It is the first piece of the five-number summary (min, Q1, median, Q3, max) and marks the lower end of a distribution, though on a modified boxplot the whisker may stop short of it if the minimum is an outlier.
The minimum value is exactly what it sounds like, the smallest single data point in your dataset. Sort all the values from low to high, and the minimum is the one at the very bottom. Simple as that.
What makes it an AP term and not just common sense is its job in the five-number summary. Per the CED (UNC-1.L.1), the minimum, first quartile (Q1), median, third quartile (Q3), and maximum together summarize a quantitative distribution, and a boxplot is the graph of those five numbers (UNC-1.L.2). One catch to remember: on a modified boxplot, the lower whisker extends to the most extreme point that is not an outlier. So if the minimum falls below the lower fence (Q1 − 1.5×IQR), it gets plotted as its own dot beyond the whisker instead of being the whisker's endpoint. The minimum is also half of the range calculation (max − min), the simplest measure of spread.
The minimum lives in Topic 1.8 (Graphical Representations of Summary Statistics) in Unit 1: Exploring One-Variable Data. It directly supports learning objective 1.8.A (represent summary statistics graphically, which means building boxplots from the five-number summary) and 1.8.B (describe summary statistics shown in a graph and use them to justify claims in context). When you describe a distribution using SOCS (shape, outliers, center, spread), the minimum anchors your spread description. It also feeds the outlier check, since you compare the minimum to the lower fence to decide whether the smallest value is unusual. Because the minimum is a single extreme observation, it is sensitive to outliers, which is part of why AP Stats pushes you toward IQR-based summaries for skewed data.
Keep studying AP Statistics Unit 1
Box Plot (Unit 1)
A boxplot is literally the five-number summary drawn as a picture, and the minimum is its leftmost landmark. But on a modified boxplot, the whisker only reaches the smallest non-outlier value, so reading the whisker tip as the minimum is a classic MCQ trap.
Range (Unit 1)
Range = maximum − minimum. It's the quickest measure of spread you can compute, but since it depends entirely on the two most extreme points, one weird value can blow it up. That's why IQR is usually the better spread choice for skewed data.
Outlier (Unit 1)
The minimum is the first suspect in any low-end outlier check. Compute the lower fence, Q1 − 1.5×IQR, and if the minimum falls below it, the minimum is an outlier and gets its own symbol on the boxplot.
Maximum Value (Unit 1)
The minimum's mirror twin at the top of the data. Together they bookend the five-number summary and define the range, and both get the same outlier treatment using the 1.5×IQR fences.
On multiple choice, the minimum shows up inside five-number summary and boxplot problems. Typical stems hand you a five-number summary like Min = 12, Q1 = 18, Median = 23, Q3 = 30, Max = 52 and ask you to build the boxplot, compute the range, or decide whether the minimum is an outlier using the 1.5×IQR rule. Practice questions also flip it around and ask for the smallest value that would count as a low-end outlier, which tests whether you know the lower fence formula (Q1 − 1.5×IQR). On FRQs, comparing distributions is the big play. The 2017 FRQ on melon diameters and the 2023 FRQ on Alaskan stream samples both involved comparing distributions where summary values like the minimum help justify claims about spread and unusual values in context. The move the rubric rewards is using the minimum as evidence, not just stating it. Say what it tells you about the spread or the low end of the distribution in the context of the problem.
On a basic boxplot, the lower whisker ends at the minimum. On a modified boxplot, the kind AP Stats uses, the whisker ends at the smallest value that is NOT an outlier. The lower fence (Q1 − 1.5×IQR) is the cutoff for outliers, not an actual data value. So the minimum can sit below the whisker as a separate dot. If a question shows a boxplot with a dot past the whisker, that dot is the true minimum, not the whisker tip.
The minimum value is the single smallest observation in a dataset and the first number in the five-number summary (min, Q1, median, Q3, max).
Range equals maximum minus minimum, making the minimum half of the simplest spread calculation in AP Stats.
On a modified boxplot, the lower whisker extends to the smallest non-outlier value, so the minimum appears as its own symbol if it falls below Q1 − 1.5×IQR.
Check whether the minimum is an outlier by comparing it to the lower fence, which is Q1 − 1.5×IQR.
Because the minimum is an extreme value, it is sensitive to outliers, which is why IQR-based summaries are preferred over the range for skewed distributions.
When comparing distributions on an FRQ, use the minimum as evidence in context, not just a number you list.
It's the smallest data point in a quantitative dataset and the first number in the five-number summary (minimum, Q1, median, Q3, maximum), which is the basis for a boxplot under Topic 1.8.
No. On the modified boxplots AP Stats uses, the whisker extends only to the smallest value that isn't an outlier. If the minimum falls below Q1 − 1.5×IQR, it's plotted as a separate point beyond the whisker.
The minimum is an actual data point. The lower fence (Q1 − 1.5×IQR) is a calculated cutoff used to flag outliers, and it usually isn't a value in the dataset. You compare the minimum to the fence to see if it's an outlier.
Yes, and it often is. For example, with Q1 = 15 and Q3 = 35, the IQR is 20, so the lower fence is 15 − 1.5(20) = −15. A minimum of 5 would not be an outlier there, but any minimum below −15 would be.
The range depends entirely on the two most extreme values, so a single outlier can inflate it badly. The IQR covers the middle 50% of the data and is resistant to outliers, which makes it the better choice for skewed distributions.
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