--- title: "Q1 (First Quartile) — AP Stats Definition & Exam Guide" description: "Q1 is the first quartile, the 25th percentile that cuts off the lowest 25% of data. It powers the IQR, the 1.5×IQR outlier rule, and boxplots in AP Stats." canonical: "https://fiveable.me/ap-stats/key-terms/q1" type: "key-term" subject: "AP Statistics" unit: "Unit 1" --- # Q1 (First Quartile) — AP Stats Definition & Exam Guide ## Definition Q1, the first quartile, is the 25th percentile of a quantitative data set: the value that separates the lowest 25% of ordered data from the upper 75%. In AP Statistics, Q1 anchors the five-number summary, builds the IQR (Q3 − Q1), and sets the lower fence in the 1.5×IQR outlier rule. ## What It Is Q1 is the **[first quartile](/ap-stats/key-terms/first-quartile "fv-autolink")** of a quantitative data set. It marks the spot where 25% of the ordered data falls below and 75% falls above, which is why it's also called the 25th percentile. A quick way to find it: order the data, find the median, then take the median of the lower half. That's Q1. Q1 rarely shows up alone. It's one of the five numbers in the **[five-number summary](/ap-stats/unit-1/graphical-representations-summary-statistics/study-guide/szST2YgJZujXFuArUBjm "fv-autolink")** (Min, Q1, Median, Q3, Max), which is exactly what a boxplot draws. It's also half of the **interquartile range**, since IQR = Q3 − Q1, the spread of the middle 50% of the data. Because Q1 is a position-based measure (it only cares about where values sit in the ordered list, not how big they are), it is **[resistant](/ap-stats/unit-1/summary-statistics-for-quantitative-variable/study-guide/fDwLeu9W74iSnEcnKHOA "fv-autolink")** to outliers. A massive maximum value can't drag Q1 anywhere. ## Why It Matters Q1 lives in **Topic 1.7 (Summary Statistics for a [Quantitative Variable](/ap-stats/key-terms/quantitative-variable "fv-autolink"))** in [Unit 1](/ap-stats/unit-1 "fv-autolink"): Exploring One-Variable Data, and it supports three learning objectives at once. For **1.7.A** you calculate Q1 as a measure of position. For **1.7.B** you use it to build the IQR, one of the three core measures of variability. For **1.7.C** you use it in the outlier check (any value below Q1 − 1.5×IQR is an outlier) and you argue that quartile-based summaries are resistant while the mean and standard deviation are not. That resistance argument is one of the most commonly tested ideas in all of Unit 1, and Q1 is half the machinery behind it. ## Connections ### [Interquartile Range (IQR) (Unit 1)](/ap-stats/key-terms/interquartile-range-iqr) The IQR is literally Q3 minus Q1, so you can't compute it without Q1. The IQR measures the [spread](/ap-stats/key-terms/spread "fv-autolink") of the middle 50% of the data, and it inherits Q1's resistance to outliers. ### [Median (Unit 1)](/ap-stats/key-terms/median) The [median](/ap-stats/key-terms/median "fv-autolink") is Q2, the 50th percentile, so Q1 and the median are siblings in the same percentile family. On a skewed distribution, comparing the gap from Min to Q1 against the gap from Q3 to Max tells you which direction the tail stretches. ### Q3 and the outlier fences (Unit 1) Q1 and Q3 work as a pair to build the [1.5×IQR rule](/ap-stats/key-terms/1-5-iqr-rule "fv-autolink"). The lower fence is Q1 − 1.5×IQR and the upper fence is Q3 + 1.5×IQR, and anything outside those fences gets flagged as an outlier on a boxplot. ### Percentiles and the normal distribution (Units 1 & 5) Q1 is just the 25th percentile, and percentile thinking carries forward. In a normal distribution, Q1 sits about 0.67 standard deviations below the mean, so the quartile idea connects directly to z-scores and normal calculations later in the course. ## On the AP Exam Q1 is a workhorse on the exam, almost always inside a bigger task rather than as a standalone question. Multiple-choice questions hand you a five-number summary and ask you to spot skewness (a Median much closer to Q1 than Q3 signals a right skew), compute the IQR, or apply the 1.5×IQR rule. One classic stem gives Q1 = 20 and Q3 = 40 and asks for the largest value that avoids being an outlier (Q3 + 1.5×IQR = 70). On the free-response side, Question 1 routinely asks you to describe or compare distributions. The 2019, 2021, 2023, and 2024 FRQ Q1s all involved this kind of work with histograms and boxplots, where reading Q1 off a boxplot, checking outliers with the fences, or justifying the median/IQR over the mean/SD for skewed data earns the points. Always show the fence calculation when you claim something is an outlier; naming the rule without numbers won't get full credit. ## Q1 vs Median Both are percentiles, but they cut the data in different places. The median (Q2) is the 50th percentile and splits the data in half; Q1 is the 25th percentile and splits off just the bottom quarter. A quick check on a boxplot: the median is the line inside the box, while Q1 is the left (or bottom) edge of the box. Mixing them up will wreck an IQR or outlier calculation, since IQR uses Q1 and Q3, not the median. ## Key Takeaways - Q1 is the first quartile, the 25th percentile, meaning 25% of the ordered data falls below it and 75% falls above it. - To find Q1 by hand, order the data, split it at the median, and take the median of the lower half. - Q1 combines with Q3 to give the IQR (Q3 − Q1), which measures the spread of the middle 50% of the data. - The lower outlier fence is Q1 − 1.5×IQR, so any data value below that fence counts as an outlier under the 1.5×IQR rule. - Q1 is resistant to outliers because it depends on position in the ordered list, not on the size of extreme values, unlike the mean and standard deviation. - On a boxplot, Q1 is the lower edge of the box, and a long distance from Q3 to Max compared to Min to Q1 signals right skew. ## FAQs ### What is Q1 in AP Stats? Q1 is the first quartile, the value at the 25th percentile of a data set. It separates the lowest 25% of the ordered data from the upper 75% and appears in the five-number summary, the IQR, and the 1.5×IQR outlier rule. ### Is Q1 the same as the 25th percentile? Yes. Q1 is exactly the 25th percentile, just like the median is the 50th percentile (Q2) and Q3 is the 75th. "Quartile" and "percentile" are two names for the same positional idea. ### How is Q1 different from the median? The median splits the data in half at the 50th percentile, while Q1 splits off only the bottom quarter at the 25th percentile. On a boxplot, the median is the line inside the box and Q1 is the lower edge of the box. ### Does removing an outlier change Q1? Usually barely, if at all. Q1 is a resistant statistic because it depends on position in the ordered data, not on the size of extreme values. Exam questions exploit this: removing a few high outliers shifts the mean and range noticeably but leaves Q1 and the IQR nearly unchanged. ### How do you use Q1 to find outliers? Compute IQR = Q3 − Q1, then check whether any value falls below Q1 − 1.5×IQR (or above Q3 + 1.5×IQR). For example, if Q1 = 20 and Q3 = 40, the IQR is 20, so anything below 20 − 30 = −10 or above 40 + 30 = 70 is an outlier. ## Related Study Guides - [1.7 Summary Statistics for One Quantitative Variable](/ap-stats/unit-1/summary-statistics-for-quantitative-variable/study-guide/fDwLeu9W74iSnEcnKHOA) ## Structured Data ```json {"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/ap-stats/key-terms/q1#resource","name":"Q1 (First Quartile) — AP Stats Definition & Exam Guide","url":"https://fiveable.me/ap-stats/key-terms/q1","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/ap-stats/key-terms/q1#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-06-11T05:22:54.896Z","isPartOf":{"@type":"Collection","name":"AP Statistics Key Terms","url":"https://fiveable.me/ap-stats/key-terms"},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/ap-stats/key-terms/q1#term","name":"Q1","description":"Q1, the first quartile, is the 25th percentile of a quantitative data set: the value that separates the lowest 25% of ordered data from the upper 75%. In AP Statistics, Q1 anchors the five-number summary, builds the IQR (Q3 − Q1), and sets the lower fence in the 1.5×IQR outlier rule.","url":"https://fiveable.me/ap-stats/key-terms/q1","inDefinedTermSet":{"@type":"DefinedTermSet","name":"AP Statistics Key Terms","url":"https://fiveable.me/ap-stats/key-terms"}},{"@type":"FAQPage","mainEntity":[{"@type":"Question","name":"What is Q1 in AP Stats?","acceptedAnswer":{"@type":"Answer","text":"Q1 is the first quartile, the value at the 25th percentile of a data set. It separates the lowest 25% of the ordered data from the upper 75% and appears in the five-number summary, the IQR, and the 1.5×IQR outlier rule."}},{"@type":"Question","name":"Is Q1 the same as the 25th percentile?","acceptedAnswer":{"@type":"Answer","text":"Yes. Q1 is exactly the 25th percentile, just like the median is the 50th percentile (Q2) and Q3 is the 75th. \"Quartile\" and \"percentile\" are two names for the same positional idea."}},{"@type":"Question","name":"How is Q1 different from the median?","acceptedAnswer":{"@type":"Answer","text":"The median splits the data in half at the 50th percentile, while Q1 splits off only the bottom quarter at the 25th percentile. On a boxplot, the median is the line inside the box and Q1 is the lower edge of the box."}},{"@type":"Question","name":"Does removing an outlier change Q1?","acceptedAnswer":{"@type":"Answer","text":"Usually barely, if at all. Q1 is a resistant statistic because it depends on position in the ordered data, not on the size of extreme values. Exam questions exploit this: removing a few high outliers shifts the mean and range noticeably but leaves Q1 and the IQR nearly unchanged."}},{"@type":"Question","name":"How do you use Q1 to find outliers?","acceptedAnswer":{"@type":"Answer","text":"Compute IQR = Q3 − Q1, then check whether any value falls below Q1 − 1.5×IQR (or above Q3 + 1.5×IQR). For example, if Q1 = 20 and Q3 = 40, the IQR is 20, so anything below 20 − 30 = −10 or above 40 + 30 = 70 is an outlier."}}]},{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"AP Statistics","item":"https://fiveable.me/ap-stats"},{"@type":"ListItem","position":2,"name":"Key Terms","item":"https://fiveable.me/ap-stats/key-terms"},{"@type":"ListItem","position":3,"name":"Unit 1","item":"https://fiveable.me/ap-stats/unit-1"},{"@type":"ListItem","position":4,"name":"Q1"}]}]} ```