What is a percentile in statistics?
A percentile tells what percent of the values in a data set are at or below a given value. If your test score is at the 80th percentile, about 80% of the scores are at or below yours. The 25th, 50th and 75th percentiles are the first quartile, the median and the third quartile.
Percentile in a picture
Formal definition and notation
The kth percentile of a data set is a value such that about k% of the data are at or below it and about (100 − k)% are at or above it. One textbook method orders the n values and finds the position i = k100(n + 1); if i is not a whole number, average the values in the positions just below and above i. Software and calculators use several slightly different methods, so small data sets can give slightly different answers.
| Symbol | Read it as | Meaning |
|---|---|---|
| Pk | P sub k | the kth percentile, such as P90 |
| Q1,Q2,Q3 | Q one, Q two, Q three | the 25th, 50th and 75th percentiles |
Key facts
- A percentile is a rank, not a score: the 70th percentile does not mean 70% correct.
- Percentiles run from 0 to 100 and always need the data in order.
- The 50th percentile is the median; the 25th and 75th are the quartiles Q1 and Q3.
- The spread from the 25th to the 75th percentile is the interquartile range.
- In bell-shaped data, a z-score of 0 is the 50th percentile and z = 1 is about the 84th.
- Higher is not always better: for a race time or a cholesterol level, a low percentile can be the good one.
Percentile rank of a value
- x
- number of values below the value
- y
- number of values equal to it (including itself)
- n
- total number of values
Round to a whole number. To go the other way and find the value at the kth percentile, use the position i = k100(n + 1) in the ordered list.
Try it: quartiles are percentiles
The box covers the 25th to 75th percentiles and the line inside it is the 50th. Drag dots or add values and watch the percentiles move.
Percentile examples, step by step
Example 1: Read a percentile
Maya’s score is at the 72nd percentile among 400 students who took a test. About how many students scored at or below Maya?
- 72nd percentile means about 72% scored at or below her.
- 0.72 × 400 = 288.
Answer: About 288 students scored at or below Maya.
Example 2: Find the 30th percentile
Find the 30th percentile of 3, 5, 7, 8, 9, 11, 13, 15, 18, 20.
- The data are already in order and n = 10.
- Position: i = 30100(10 + 1) = 3.3.
- 3.3 is not a whole number, so use the 3rd and 4th values: 7 and 8.
- Average them: 7 + 82 = 7.5.
Answer: The 30th percentile is 7.5.
Example 3: Find a percentile rank
In a class of 25 students, 19 scored lower than Ana and nobody else tied her score of 88. What is the percentile rank of Ana’s score?
- Values below: x = 19. Values equal (just Ana): y = 1. Total: n = 25.
- 19 + 0.5 × 125 × 100 = 19.525 × 100.
- = 0.78 × 100 = 78.
Answer: Ana’s score is at about the 78th percentile.
Common mistakes
A percent is part of a whole; a percentile compares you with everyone else.
Percentiles are positions in the ordered data, like the median.
Percentile numbers are percents of the data, not data values.
Not to be confused with
A percent compares a part with a whole, like 45 of 50 correct = 90%. A percentile compares one value with all the others in a data set.
Quartiles are three special percentiles: Q1 is the 25th, Q2 the 50th and Q3 the 75th. Percentiles split the data into 100 parts, quartiles into 4.
Quick check: 3 questions
Your test score is at the 90th percentile. What does that mean?
Answer: B. A percentile ranks your score against everyone else: about 90% were at or below it. It says nothing direct about how many questions you got right or your number of points, and 10% is the share at or above you.Show answer and explanation
Which percentile is the same as the median?
Answer: D. Half the data lie at or below the median, so it is the 50th percentile. The 25th and 75th are the quartiles Q1 and Q3, and the 100th is the maximum.Show answer and explanation
In a race with 200 runners, Leo’s time is at the 35th percentile. About how many runners had times at or below his?
Answer: C. 0.35 × 200 = 70. 130 is the 65% at or above him, 35 forgets to multiply by 200, and 65 is the complement percent.Show answer and explanation
Percentile: frequently asked questions
Is a percentile the same as a percentage?
No. A percentage tells part of a whole, like getting 42 of 50 questions right, 84%. A percentile ranks a value against a group: at the 84th percentile, about 84% of the group scored at or below you. You can get 70% correct and still be at the 95th percentile on a hard test.
What does the 99th percentile mean?
About 99% of the values are at or below that value, so only about 1% are higher. On a test taken by 10,000 people, a 99th percentile score is better than or tied with roughly 9,900 of them. It does not mean the score was 99 or 99% correct.
Practice and tools
Sources
- OpenStax, Introductory Statistics 2e, 2.3 Measures of the Location of the Data
- Common Core State Standards, High School Statistics and Probability, Interpreting Categorical and Quantitative Data (HSS-ID.A.4)
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS HSS-ID.A.4
Cite this entry
Effortless Math Team. “Percentile.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/percentile/
Flashcard
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