---
title: "Interquartile Range (IQR) — AP Stats Definition & Guide"
description: "The IQR is Q3 minus Q1, the spread of the middle 50% of data. Learn how AP Stats uses it for outlier checks (1.5 × IQR rule) and resistant summaries."
canonical: "https://fiveable.me/ap-stats/key-terms/interquartile-range"
type: "key-term"
subject: "AP Statistics"
unit: "Unit 1"
---

# Interquartile Range (IQR) — AP Stats Definition & Guide

## Definition

The interquartile range (IQR) is a measure of variability for quantitative data, calculated as Q3 − Q1, the difference between the third and first quartiles. It captures the spread of the middle 50% of the data and is resistant to outliers, which is why AP Stats pairs it with the median.

## What It Is

The interquartile range (IQR) is one of the three measures of variability you learn in [AP Stats](/ap-stats "fv-autolink"), alongside the [range](/ap-stats/key-terms/range "fv-autolink") and the standard deviation. The formula is simple. Find the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile), then subtract: IQR = Q3 − Q1. The answer tells you how wide the middle 50% of the data is. Think of it as the range with the extremes chopped off. The regular range (max minus min) gets dragged around by a single weird value, but the IQR ignores the top 25% and bottom 25% entirely, so one outlier can't touch it.

That's exactly why the CED calls the IQR (and the median) **resistant**, or robust. Outliers don't greatly affect their values, while the mean, standard deviation, and range are **nonresistant** because outliers pull them around. The IQR also powers the most-used outlier test in the course, the 1.5 × IQR rule. Any value above Q3 + 1.5 × IQR or below Q1 − 1.5 × IQR counts as an outlier. So the IQR isn't just a number you compute once and forget. It's a tool you use to flag unusual values and to decide which [summary statistics](/ap-stats/unit-1/graphical-representations-summary-statistics/study-guide/szST2YgJZujXFuArUBjm "fv-autolink") to trust.

## Why It Matters

The IQR 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. It directly supports learning objective 1.7.B, calculating measures of variability, and it's central to 1.7.C, explaining why you'd choose one measure of center and spread over another. That second skill is the one the exam actually rewards. When a distribution is skewed or has outliers, the right move is to report the median and IQR instead of the mean and standard deviation, because the resistant pair won't be distorted by extreme values. If you can compute an IQR, run the 1.5 × IQR outlier check, and justify why the median/IQR pair fits a skewed dataset, you've covered one of the most reliable point-earners in Unit 1.

## Connections

### Quartiles, Q1, and Q3 (Unit 1)

The IQR is literally built from Q1 and Q3, so you can't find it without first finding the [quartiles](/ap-stats/key-terms/quartile "fv-autolink"). Q1 is the median of the lower half of the ordered data and Q3 is the median of the upper half, which means the IQR is really two median calculations and a subtraction.

### [Median (Unit 1)](/ap-stats/key-terms/median)

The [median](/ap-stats/key-terms/median "fv-autolink") and IQR travel as a pair. Both are resistant to outliers, so when a distribution is skewed, you describe its center with the median and its spread with the IQR. Mixing pairs (say, mean with IQR) is a classic way to lose justification points.

### [Sensitivity to extreme values (Unit 1)](/ap-stats/key-terms/sensitivity-to-extreme-values)

The whole reason the IQR exists as a separate tool is resistance. The range uses the max and min, the two values most likely to BE [outliers](/ap-stats/key-terms/outliers "fv-autolink"), while the IQR only uses the middle 50%. Comparing the two on the same dataset is a quick way to see how much the extremes are inflating the spread.

### Boxplots and outliers (Unit 1)

The box in a boxplot stretches from Q1 to Q3, so its width IS the IQR. The fences at Q1 − 1.5 × IQR and Q3 + 1.5 × IQR decide which points get plotted as outlier dots, so reading or building a boxplot is an IQR exercise in disguise.

## On the AP Exam

On multiple choice, expect questions that hand you two distributions with the same mean and median but different spreads, then ask what must be true. Knowing that range and IQR measure spread differently (and that only one is resistant) is the key. You'll also compute IQR from a five-number summary or a boxplot, and run the 1.5 × IQR rule to check whether a value is an outlier. On the FRQ side, this shows up in 'describe the distribution' prompts. The 2019 FRQ Q1, for example, gave a histogram of room sizes and asked for a description of the distribution. For a skewed display like that, full credit comes from addressing shape, center, spread, and unusual features, and the IQR (or a quartile-based spread) is the appropriate measure of spread to cite when outliers are present. Practice prompts also lean on the IQR for justification, asking you to explain WHY median and IQR beat mean and standard deviation for a dataset like 2, 3, 5, 7, 7, 8, 10, 12, 15, 18, 50, where that 50 wrecks the nonresistant measures.

## interquartile range vs Range

Both measure spread by subtracting two values, but they use different values. The range is max minus min, so it depends entirely on the two most extreme points and gets inflated by a single outlier. The IQR is Q3 minus Q1, so it only describes the middle 50% and barely moves when an outlier appears. If a question says 'same IQR but very different ranges,' that's a signal one dataset has extreme values in its tails. On the exam, range is fine for quick comparisons of symmetric, outlier-free data, but the IQR is the defensible choice for skewed data.

## Key Takeaways

- The interquartile range equals Q3 minus Q1 and measures the spread of the middle 50% of a quantitative dataset.
- The IQR is resistant (robust) to outliers because it ignores the lowest and highest 25% of values, while the range and standard deviation are nonresistant.
- The 1.5 × IQR rule flags outliers: any value above Q3 + 1.5 × IQR or below Q1 − 1.5 × IQR is an outlier.
- When a distribution is skewed or has outliers, report the median and IQR together instead of the mean and standard deviation.
- On a boxplot, the width of the box from Q1 to Q3 is the IQR, and the fences that determine outlier dots are built from it.
- The IQR has the same units as the data, so a sentence like 'the middle 50% of room sizes span about 60 square feet' is a complete interpretation.

## FAQs

### What is the interquartile range in AP Stats?

The interquartile range (IQR) is Q3 − Q1, the difference between the third quartile (75th percentile) and the first quartile (25th percentile). It measures how spread out the middle 50% of a quantitative dataset is.

### Is the IQR affected by outliers?

No, and that's its whole selling point. The IQR only uses Q1 and Q3, so an extreme maximum or minimum barely changes it (often not at all). The CED calls the IQR and median resistant, while the mean, standard deviation, and range are nonresistant.

### How is the IQR different from the range?

The range is max minus min, so it depends on the two most extreme values and one outlier can balloon it. The IQR is Q3 minus Q1, so it describes only the middle 50% and stays stable when outliers show up. A dataset like 2, 3, 5, ..., 18, 50 has a huge range but a modest IQR because of that single 50.

### How do you find outliers using the IQR?

Use the 1.5 × IQR rule. Compute the IQR, then check whether any value is greater than Q3 + 1.5 × IQR or less than Q1 − 1.5 × IQR. Values past those fences are outliers, and on a boxplot they're drawn as individual dots.

### When should I use the IQR instead of standard deviation?

Use the IQR (with the median) when the distribution is skewed or has outliers, because standard deviation is pulled around by extreme values. For roughly symmetric data with no outliers, mean and standard deviation are the standard pair.

## Related Study Guides

- [1.7 Summary Statistics for One Quantitative Variable](/ap-stats/unit-1/summary-statistics-for-quantitative-variable/study-guide/fDwLeu9W74iSnEcnKHOA)

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