Percentiles and Quartiles Explained

Your kid is in the 90th percentile for height. What does that actually mean? It means about 90 percent of children their age are the same height or shorter. That single idea, the percent of data at or below a value, is what a percentile is. Quartiles are just three famous percentiles that cut a sorted dataset into four equal parts. Together, percentiles and quartiles help you see where one value sits inside a whole group of numbers.

What a Percentile Is

A percentile tells you a value’s position inside a sorted dataset. It answers a simple question: what percent of the data sits at or below this number?

Say a test score lands at the 80th percentile. That means about 80 percent of the scores are equal to or lower than yours. It does not mean you got 80 percent of the questions right. Percentiles are about rank, not raw score.

This is why percentiles are so useful for comparison. A single number, like a height or a score, means little on its own. A percentile places it against everyone else in the group, so you instantly see whether it is low, middle, or high.

Percentiles show up everywhere. Growth charts for children, standardized test reports, and salary surveys all use them. In each case, the goal is the same: turn one raw value into a clear position within a larger group.

• Low percentile (like the 10th): most of the data is above this value.
• Middle percentile (the 50th): half the data is below, half above.
• High percentile (like the 95th): almost all the data is below this value.

What Quartiles Are

Quartiles are three specific percentiles that divide sorted data into four equal parts. Each part holds about a quarter, or 25 percent, of the values. The word quartile comes from quarter, which is a handy way to remember what they do.

There are exactly three quartiles, and each has a plain meaning:

• Q1, the first quartile, is the 25th percentile. About 25 percent of the data falls at or below it.
• Q2, the second quartile, is the 50th percentile. This is the median, the middle value of the data.
• Q3, the third quartile, is the 75th percentile. About 75 percent of the data falls at or below it.

So Q2 and the median are the same thing. If you want a deeper walkthrough of that middle value alone, see our guide on how to find the median. Quartiles simply add two more cut points, one on each side of the median.

How to Find Quartiles

Finding quartiles by hand is easier than it sounds. The key is to sort your data first, then find the median, then find the median of each half.

Let’s use a small sorted set of eight numbers: 2, 4, 5, 7, 8, 10, 12, 15. Here are the steps.

1. Sort the data. It is already in order from low to high.
2. Find Q2, the median. With 8 values, the middle sits between the 4th and 5th numbers, 7 and 8. So Q2 = (7 + 8) / 2 = 7.5.
3. Split into halves. The lower half is 2, 4, 5, 7. The upper half is 8, 10, 12, 15.
4. Find Q1. Q1 is the median of the lower half. The middle of 2, 4, 5, 7 sits between 4 and 5, so Q1 = (4 + 5) / 2 = 4.5.
5. Find Q3. Q3 is the median of the upper half. The middle of 8, 10, 12, 15 sits between 10 and 12, so Q3 = (10 + 12) / 2 = 11.

That gives Q1 = 4.5, Q2 = 7.5, and Q3 = 11. The number line below shows where each cut point lands.

The Interquartile Range (IQR) and Why It Matters

The interquartile range, or IQR, is a simple measure of spread. It is the distance between the first and third quartiles.

The formula is short: IQR = Q3 – Q1. Using our numbers, IQR = 11 – 4.5 = 6.5. That single value describes the width of the middle 50 percent of the data.

The IQR matters because it ignores the extreme low and high ends. A few very large or very small values, called outliers, barely move it. That makes the IQR a stable way to describe how tightly the bulk of your data is packed.

Compare that with the plain range, which is the highest value minus the lowest. The range is easily thrown off by one unusual number. The IQR stays steady because it only looks at the middle half, so it is often the better measure of spread for messy real-world data.

Analysts often use the IQR to flag possible outliers and to build box plots. The quartiles and the IQR are the heart of the five-number summary, which our sibling guide covers in full along with box plots.

A Note on Different Methods

Here is an honest catch: there is more than one accepted way to compute quartiles. Different textbooks and software can give slightly different values for Q1 and Q3.

The main split is between two approaches:

• Exclusive method: when the data has an odd count, the median is left out of both halves before finding Q1 and Q3.
• Inclusive method: the median is included in both halves. Some tools also use interpolation formulas that land between data points.

For our even set of 8 values, both simple methods agree, since no single value is the median. With other datasets, though, a calculator or spreadsheet may report Q1 or Q3 a bit differently. That is normal and expected.

The takeaway is to pick one method and stay consistent. When your homework or software gives a value that differs from a hand calculation, the method is usually the reason. Always follow the convention your course or tool uses.

Frequently Asked Questions About Percentiles and Quartiles

Sources

This article is for general education only, not professional statistical advice. Methods and notation can vary by field, course, or software, so follow your textbook or instructor for exact conventions. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 11, 2026.