# Quartiles and IQR

Quartiles cut sorted data into four equal groups. Q1 is the median of the lower half, and Q3 is the median of the upper half. The interquartile range (IQR) is Q3 minus Q1, the width of the middle half.

Statistics (university) · Part 01: Describing data · Card 7 of 9 · Last updated 2026-10-19

## Analogy

Split a queue into four equal blocks. The IQR is the length of the two middle blocks together.

## Example

**Finding the IQR**

Data: 1, 3, 5, 7, 9, 11, 13, 15
Lower half 1,3,5,7: Q1 = 4
Upper half 9,11,13,15: Q3 = 12
IQR = 12 - 4 = 8

## In practice

Boxplots draw a box from Q1 to Q3, so the box shows where the middle half of the data lies.

## Practice

### Flashcards

- **How do you compute the IQR?** Q3 minus Q1.
- **What is the upper fence for outliers?** Q3 plus 1.5 times the IQR.

## Questions people ask

### What does the interquartile range tell you?

It is the width of the middle 50 percent of the data, from Q1 to Q3. A small IQR means the central values are tightly packed. Unlike the range, it ignores extreme values at either end, so one outlier does not change it much.

### Why might different software give slightly different quartiles?

There are several accepted rules for placing quartiles, especially when the count does not split evenly. Some include the median in each half, some interpolate between values. Results differ slightly on small data sets. Always say which method you used, and be consistent within one analysis.

## Related concepts

- [Outliers](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-1/statistics-university-part-1-concept-8)
- [Standard deviation](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-1/statistics-university-part-1-concept-5)
- [Sample variance](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-1/statistics-university-part-1-concept-6)

Web page: https://studyvisually.com/learn/science/statistics-university/statistics-university-part-1/statistics-university-part-1-concept-7
Study this card in the app: https://studyvisually.com/app/learn?category=statistics-university&card=statistics-university-part-1-concept-7