The interquartile range (IQR) is a measure of variability equal to Q3 − Q1, the spread of the middle 50% of a quantitative data set. Because it ignores the extreme 25% on each end, the IQR is resistant to outliers, and 1.5 × IQR beyond the quartiles is the AP Stats rule for flagging outliers.
The interquartile range (IQR) is the difference between the third quartile and the first quartile of a data set, written IQR = Q3 − Q1. Q1 is the value with 25% of the data below it, and Q3 has 75% below it, so the IQR tells you how wide the middle 50% of the data is. It's one of the three measures of variability named in the CED, alongside the range and the standard deviation.
The IQR's superpower is resistance. Because it only depends on the quartiles, a wild maximum or minimum can't budge it. That makes it the go-to spread measure for skewed distributions or data with outliers, where the standard deviation gets dragged around by extreme values. The IQR also powers the course's main outlier rule. Any value more than 1.5 × IQR below Q1 or above Q3 gets flagged as an outlier, which is exactly how box plots decide where to put their dots.
IQR lives in Unit 1 (Exploring One-Variable Data), specifically Topics 1.6 and 1.7. It directly supports learning objective 1.7.B (calculate measures of variability) and 1.7.C (explain which measure of center and variability fits a data set). That second one is the big deal. The CED explicitly labels the median and IQR as resistant (robust) and the mean, standard deviation, and range as nonresistant. So whenever a distribution is skewed or has outliers, the expected answer is to describe it with the median and IQR, and to justify that choice. The 1.5 × IQR outlier rule from 1.7.C also shows up constantly, both in calculations and in reading box plots. These describing-distributions skills get reused all year, anytime you summarize sample data before doing inference.
Keep studying AP Statistics Unit 1
Median (Unit 1)
Median and IQR are a matched pair. The median is the resistant measure of center, the IQR is the resistant measure of spread, and on the exam you report them together when data are skewed or have outliers.
Box Plot (Unit 1)
A box plot is basically the IQR drawn as a picture. The box itself spans Q1 to Q3, so the box's width IS the IQR, and the whiskers stop at the last values within 1.5 × IQR of the quartiles.
Skewness (Unit 1)
Skew is the signal that tells you to reach for the IQR. A long tail inflates the standard deviation and range, but the IQR only looks at the middle 50%, so it stays honest about typical spread.
Range (Unit 1)
The range is max minus min, so it depends entirely on the two most extreme values. The IQR is the same idea applied to the quartiles instead, which is why one outlier can wreck the range but barely touch the IQR.
IQR shows up in two main ways. First, calculation and application questions give you a five-number summary and ask you to compute the IQR or use the 1.5 × IQR rule to find outlier fences (for example, with Q1 = 20 and Q3 = 40, the IQR is 20 and the lower fence is 20 − 1.5 × 20 = −10). Second, and more often, you're asked to choose or justify a measure of spread. Multiple-choice stems love setups like a right-skewed income distribution or a new extreme value added to a data set, and the expected reasoning is that the IQR is resistant while the range and standard deviation are not. On FRQs, describing a distribution means addressing shape, center, variability, and unusual features, and for skewed data the strongest answers use the median and IQR with a one-line justification about resistance.
Both measure spread by subtracting two values, which is where the mix-up starts. The range is maximum minus minimum, so it uses the two most extreme points and is completely nonresistant. The IQR is Q3 minus Q1, so it measures only the middle 50% and barely flinches when an outlier appears. If a question adds an extreme value and asks which measure of spread changes most, the answer is the range (or standard deviation), not the IQR.
The interquartile range is Q3 minus Q1, and it measures the spread of the middle 50% of the data.
The IQR is resistant to outliers, while the range, mean, and standard deviation are not.
When a distribution is skewed or has outliers, describe it with the median and IQR instead of the mean and standard deviation.
The AP outlier rule flags any value more than 1.5 × IQR below Q1 or more than 1.5 × IQR above Q3.
On a box plot, the length of the box equals the IQR, and the whiskers extend to the last values inside the 1.5 × IQR fences.
Adding one extreme value to a data set changes the range a lot but the IQR very little, which is a favorite multiple-choice setup.
The IQR is Q3 − Q1, the distance covered by the middle 50% of a data set. It's one of the three CED measures of variability (along with range and standard deviation) and the resistant one of the bunch.
Use the 1.5 × IQR rule. Anything below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier. For example, if Q1 = 15 and Q3 = 31, the IQR is 16, so the upper fence is 31 + 24 = 55 and anything above that is an outlier.
No, or at least barely. The IQR depends only on the quartiles, so the extreme 25% on each end can't move it much. That's exactly why the CED calls it resistant (robust).
The range is max minus min, so one extreme value can blow it up. The IQR is Q3 minus Q1, which trims off the top and bottom 25% before measuring spread. With the summary Min = 15, Q1 = 22, Q3 = 35, Max = 62, the range is 47 but the IQR is only 13.
Use the IQR (paired with the median) when the distribution is skewed or has outliers, like a right-skewed distribution of household incomes. Standard deviation pairs with the mean and works best for roughly symmetric data without outliers.