What Are Percentiles?

Imagine you take a standardised test and score in the 85th percentile. Does that mean you got 85% of the questions right? Not at all! It means you scored higher than approximately 85% of all the people who took the test.

Percentile

The $k$ th percentile is the value at or below which approximately $k$ of the data falls. In other words, about $k$ of data points are less than or equal to that value.

Percentiles divide your data set into 100 equal parts. They help you understand where a particular data point sits relative to the rest of the data.

The 25th percentile means approximately 25% of data values are at or below this point
The 50th percentile means approximately 50% of data values are at or below this point (this is the median!)
The 75th percentile means approximately 75% of data values are at or below this point
The 90th percentile means approximately 90% of data values are at or below this point

Analogy

Think of percentiles like your position in a queue. If you're at the 90th percentile, you're near the front — about 90% of the people are behind you (at or below your position). If you're at the 10th percentile, you're near the back — only about 10% of people are behind you.

Warning

Being at the 85th percentile does not mean you scored 85% on the test. It means your score was at or above approximately 85% of all test-takers. You could score 85th percentile with a raw score of 60% if most other students scored even lower!

Quartiles — The Big Three Percentiles

Three percentiles are so important that they get their own special names: the quartiles. Quartiles divide your data into four equal groups.

Quartiles

Quartiles are the three values that divide an ordered data set into four equal parts. They are called the first quartile ( $Q_{1}$ ), the second quartile ( $Q_{2}$ ), and the third quartile ( $Q_{3}$ ).

Quartile	Percentile	Meaning
$Q_{1}$ (Lower quartile)	25th percentile	25% of data falls at or below this value
$Q_{2}$ (Median)	50th percentile	50% of data falls at or below this value
$Q_{3}$ (Upper quartile)	75th percentile	75% of data falls at or below this value

How to find quartiles:

Order your data from smallest to largest
Find the median ( $Q_{2}$ ) — the middle value of the entire data set
Find $Q_{1}$ — the median of the lower half of the data (the values below $Q_{2}$ )
Find $Q_{3}$ — the median of the upper half of the data (the values above $Q_{2}$ )

Warning

When finding $Q_{1}$ and $Q_{3}$ , do not include the median ( $Q_{2}$ ) in either the lower or upper half if the data set has an odd number of values.

Note

There are actually a few slightly different methods for calculating quartiles, and different calculators or software may give slightly different results. In these notes we use the exclusive method (excluding the median from both halves), which is the most common approach at MYP level. If your calculator gives a slightly different answer, don't panic — what matters most is that you understand what quartiles represent.

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