Key takeaway: A percentile tells the percent of values in a data set that fall below a given value, so a score at the 84th percentile beats 84 percent of the observations.
Grade 12 – AP StatisticsAP Statistics Unit 1Statistics and Data
Definition of Percentile
A percentile describes position in a distribution rather than the size of a score. If a value is at the 84th percentile, about 84 percent of the data lie below it and 16 percent lie above it.
This rank lets results from different tests or groups be compared on one scale. The median sits at the 50th, and the quartiles at the 25th and 75th. A rank is not a score: a student can rank high while earning a modest percent correct.
Formula and notation
The rank of a value is the share of the data below it:
\[ \text{rank}=\frac{\text{number of values below}}{\text{total number of values}}\times 100. \]
Some texts count values at or below it. State which convention you use. The result is a number from 0 to 100.
Key facts
- A rank of 50 means the value is at the median, with half the data below it.
- The 25th and 75th ranks mark the first and third quartiles.
- Equal gaps in rank can hide very different gaps in score, especially in the tails.
- In a normal distribution, a z-score of 1 sits near the 84th rank.
Percentile example
On a quiz given to 25 students, Maya scored 82. Exactly 21 of the 25 scores were lower than hers. Find her rank as a percentile.
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Count the scores below hers: 21.
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Divide by the class size: \(\frac{21}{25}=0.84\).
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Convert to a percent: \(0.84\times 100=84\).
Maya’s score is at the 84th percentile: she did better than 84 percent of the class.
Common mistake
Watch out
Hearing that her quiz score was 82, a student concludes that she must be at the 82nd percentile.
Why it is wrong
A score and a rank are different quantities. The 82 is points earned, and the rank depends on how the others did. With 21 of 25 scores below hers, the rank is 84. If most classmates had scored higher, an 82 could sit near the 30th.
Related terms and lessons
Browse the glossary: A–Z list · AP Statistics vocabulary · Statistics and Data