---
title: "Quartiles"
url: https://www.learningloftinstitute.com/glossary/quartile
source: Learning Loft Institute
language: en
updated: 2026-08-21
section: "Glossary › Quartiles"
---
# Quartiles
> **Answer.** A quartile is one of three values that cut an ordered data set into four equal parts. Q1, the lower quartile, has a quarter of the data below it. Q2 is the median, with half below. Q3, the upper quartile, has three quarters of the data below it.
## Key facts
| | |
| --- | --- |
| Definition | A quartile is one of the three values that split an ordered data set into four equally sized parts. |
| Where students meet it | Grade 8 on short ordered lists, and again at GCSE and IGCSE in cumulative frequency and box plot questions. |
| Also known as | Lower quartile (Q1), Upper quartile (Q3) |
## Three cuts, four parts
The prefix means quarter, and there are three of them because it takes three cuts to divide something into four pieces — the same reason two cuts give three pieces of cake. Q2 is not a separate idea; it is the median under another name, and being reminded of that saves a lot of confusion when a question mixes the two words.
A quartile is a value, not a group. Students often say "she is in the first quartile" meaning the bottom quarter of the class, which is fine in conversation but wrong on a maths paper, where Q1 is a single number on the scale. If a question asks you to find the lower quartile, the answer is one number with units.
## Finding the positions
Order the data first — every quartile method assumes it, and an unordered list is the single most common reason a correct method produces a wrong answer. Then use the positions below, remembering that these give you the place in the list, not the answer itself. Position 3 means "the third value", which here is 18, not 3.
When (n + 1)/4 does not land on a whole number, the quartile falls between two values and is taken as the midpoint of them. With n = 8, position (8 + 1)/4 = 2.25 is usually resolved by taking the value a quarter of the way from the second to the third, though many school courses simply average the second and third.
- Lower quartile Q1: position (n + 1)/4
- Median Q2: position (n + 1)/2
- Upper quartile Q3: position 3(n + 1)/4
- With n = 11 these give positions 3, 6 and 9
## Why two textbooks can disagree
There is more than one accepted rule. The other common school method splits the ordered list at the median, discards the median itself, and takes the median of each half. On the eleven values above that gives the median of 12, 15, 18, 21, 24 for Q1, which is 18, and the median of 29, 31, 35, 38, 47 for Q3, which is 35 — the same answers.
The methods agree whenever n + 1 divides by 4, and can differ by a small amount otherwise, which is also why spreadsheet functions sometimes return a quartile your textbook does not. For an exam, use the method your course teaches and show the position you used; for a box plot read from a cumulative frequency curve, the reading is approximate anyway and the difference disappears.
## Questions
### Is Q2 the same as the median?
Yes, exactly the same value. Half the data lies below it and half above, which is precisely what the median means. The Q2 label exists only so that the three quartiles can be numbered in order; a question will almost always just say median instead.
### How do I read quartiles from a cumulative frequency graph?
Go up the vertical axis to a quarter, a half and three quarters of the total frequency, read across to the curve, and drop down to the horizontal axis. With 80 pieces of data that means reading at 20, 40 and 60. Note that graph work uses n/4 rather than (n + 1)/4, because the curve is treating the data as continuous.
### What do quartiles show that the mean does not?
Shape and spread. The mean gives one number for the centre; the quartiles show where the middle half of the data sits and how far the ends stretch beyond it. Two classes can share a mean of 60 while one has quartiles at 55 and 65 and the other at 35 and 85, which are very different classes to teach.
### Do I include the median when splitting the list into halves?
No, when n is odd. Take it out and work with the values either side of it, so an eleven-value list splits into two halves of five. When n is even there is no single middle value to remove and the list splits cleanly down the middle. Mixing these up shifts both quartiles by one position.
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