Q3, the third quartile, is the value below which 75% of the data falls when the data are ordered. In AP Statistics it marks the 75th percentile, forms the upper edge of the box in a boxplot, and combines with Q1 to give the interquartile range (IQR = Q3 − Q1).
Q3 is the third quartile, the value that splits off the top 25% of an ordered data set. Put another way, it's the 75th percentile. If you line up every data value from smallest to largest, Q3 is the median of the upper half of the data. Together with the minimum, Q1, the median, and the maximum, it makes up the five-number summary, which is exactly what a boxplot draws.
Q3 does double duty in AP Stats. First, it's a measure of position that tells you where a value sits in the distribution (1.7.A). Second, it's half of the interquartile range, since IQR = Q3 − Q1, which is one of the three measures of variability the CED names alongside range and standard deviation (1.7.B). Because Q3 only depends on position in the ordered list, not on how extreme the largest values are, it's resistant to outliers. That resistance is why the median-and-IQR pairing gets recommended for skewed data.
Q3 lives in Topic 1.7 (Summary Statistics for a Quantitative Variable) in Unit 1 and supports three learning objectives at once. You calculate it as a measure of position (AP Stats 1.7.A), you use it to compute IQR as a measure of variability (AP Stats 1.7.B), and you plug it into the outlier rule when justifying which summary statistics to report (AP Stats 1.7.C). The CED's most-used outlier check is built directly on Q3. Any value greater than Q3 + 1.5 × IQR is an outlier. That single formula shows up constantly in multiple choice questions and in Question 1 of the free-response section, which is almost always an exploring-data question.
Keep studying AP® Statistics Unit 1
Interquartile Range (IQR) (Unit 1)
Q3 is half of the IQR formula, since IQR = Q3 − Q1. The IQR measures the spread of the middle 50% of the data, and it inherits Q3's resistance to outliers. If a question removes extreme high values, Q3 and the IQR barely move, which is exactly what one of our practice questions tests.
Q1 (Unit 1)
Q1 and Q3 are mirror images. Q1 cuts off the bottom 25%, Q3 cuts off the top 25%, and the box in a boxplot stretches from one to the other. Comparing the gap from Q1 to the median versus the median to Q3 is a quick visual skew check.
Percentile (Unit 1)
Q3 is just a percentile with a famous name. It's the 75th percentile, the same way Q1 is the 25th and the median is the 50th. If you can find a percentile, you can find Q3.
Sensitivity to extreme values (Unit 1)
Q3 is resistant (robust). A massive maximum value doesn't change Q3 at all because Q3 depends on the order of the data, not the size of the extremes. That's the whole argument for choosing median and IQR over mean and standard deviation when a distribution is skewed.
Q3 shows up in two main ways. In multiple choice, you'll get a five-number summary and have to read the story it tells. For example, a summary like (12, 15, 22, 35, 89) has a much bigger gap from Q3 to the max than from the min to Q1, which signals right skew or a high outlier. You'll also apply the 1.5×IQR rule directly. With Q1 = 20 and Q3 = 40, the IQR is 20, so the upper fence is 40 + 1.5(20) = 70, and anything above 70 is an outlier. On the free response, Q3 appears in the classic Question 1 exploring-data setup. The 2019 FRQ on dorm room sizes and the 2021 FRQ on hospital length of stay both required working with quartiles and identifying unusually large values. Be ready to calculate the fence, name the outliers, and explain why median and IQR are the better summaries when those outliers exist.
Q3 means 75% of the data falls AT OR BELOW it, not that the value itself equals 75% of anything. A common slip is reading Q3 = 35 and thinking it's 75% of the maximum, or thinking 75% of the data is above it. Only 25% of the data sits above Q3. Say it as a sentence on the exam: "75% of the rooms are 35 square feet or smaller."
Q3 is the third quartile, meaning 75% of the ordered data falls at or below it, leaving 25% above.
Q3 minus Q1 gives the interquartile range (IQR), which measures the spread of the middle half of the data.
The upper outlier fence is Q3 + 1.5 × IQR, and any value above that fence counts as an outlier under the CED's most common rule.
Q3 is resistant to outliers because it depends on position in the ordered list, so removing extreme high values usually changes the maximum and the mean but not Q3.
On a boxplot, Q3 is the right (or top) edge of the box, and a long whisker beyond Q3 suggests right skew.
Comparing the distance from the median to Q3 against the distance from Q1 to the median is a quick way to spot skew from a five-number summary alone.
Q3 is the third quartile, the value below which 75% of the data falls. It's the median of the upper half of an ordered data set and the upper edge of the box in a boxplot.
Compute IQR = Q3 − Q1, then the upper fence is Q3 + 1.5 × IQR. For example, if Q1 = 20 and Q3 = 40, the IQR is 20 and anything above 40 + 30 = 70 is an outlier.
Usually no, or only slightly. Q3 is a resistant statistic because it's based on position in the ordered data, so removing a few extreme high values changes the maximum, range, and mean far more than Q3.
Nothing, they're the same value. Q3 is just the standard name for the 75th percentile, the same way Q1 is the 25th percentile and the median is the 50th.
No. Q3 is a position in the data, not a fraction of the largest value. In the five-number summary (12, 15, 22, 35, 89), Q3 is 35 even though the max is 89, and that big gap between them actually signals a right-skewed distribution.
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