Percentile — Definition, Formula & Examples

Percentile

The pth percentile of a set of data is the number such that p% of the data is less than that number. For example, a student whose SAT score is in the 78th percentile has scored higher than 78% of the students taking the test.

Note: The median is the 50th percentile.

See also

Quartiles, quintiles, deciles

Key Formula

L = \frac{p}{100} \times n

Where:

$L$ = Locator — the position in the ordered dataset that corresponds to the desired percentile
$p$ = The desired percentile (e.g., 25, 50, 90)
$n$ = The total number of data values in the set

Worked Example

Problem: Fifteen students scored the following on a quiz (already sorted): 52, 55, 58, 60, 63, 65, 68, 70, 72, 75, 78, 82, 85, 90, 95. Find the 40th percentile.

Step 1: Order the data (already done) and identify n = 15.

n = 15

Step 2: Compute the locator L using the formula.

L = \frac{40}{100} \times 15 = 6

Step 3: When L is a whole number, the pth percentile is the average of the value at position L and the value at position L + 1 in the ordered data. The 6th value is 65 and the 7th value is 68.

P_{40} = \frac{65 + 68}{2} = 66.5

Answer: The 40th percentile is 66.5. This means approximately 40% of the quiz scores fall below 66.5.

Another Example

Problem: Using the same 15 quiz scores (52, 55, 58, 60, 63, 65, 68, 70, 72, 75, 78, 82, 85, 90, 95), find the 75th percentile.

Step 1: Compute the locator L.

L = \frac{75}{100} \times 15 = 11.25

Step 2: When L is not a whole number, round it up to the next integer. Round 11.25 up to 12.

\lceil 11.25 \rceil = 12

Step 3: The 75th percentile is the value at position 12 in the ordered data.

P_{75} = 82

Answer: The 75th percentile is 82. About 75% of the scores are below 82.

Frequently Asked Questions

What is the difference between percentile and percentage?

A percentage represents a fraction out of 100 (like scoring 85 out of 100 points on a test, or 85%). A percentile is a ranking that tells you what proportion of values in a dataset fall below a particular value. Scoring in the 85th percentile does not mean you got 85% correct — it means you scored higher than 85% of everyone else.

Is the 50th percentile the same as the average?

Not necessarily. The 50th percentile is the median, which is the middle value when data is sorted. The average (mean) can differ significantly from the median, especially when the data is skewed. They are equal only when the data is perfectly symmetric.

Percentile vs. Percent (Percentage)

A percentile is a position in a ranked dataset — it tells you how a value compares to all other values. A percentage is simply a ratio expressed out of 100. Saying you scored 80% on a test means you earned 80 out of every 100 possible points. Saying you are in the 80th percentile means 80% of all test-takers scored lower than you. The two numbers can be very different for the same test.

Why It Matters

Percentiles are widely used in standardized testing (SAT, ACT, GRE) to show how you performed relative to other test-takers. Doctors use percentiles to track children's growth — for example, a child in the 60th percentile for height is taller than 60% of children the same age. Whenever you need to understand where a single value stands within a large group, percentiles are the standard tool.

Common Mistakes

Mistake: Confusing percentile with percentage score.

Correction: A percentile is a ranking among all values, not a score out of 100. Being in the 90th percentile does not mean you scored 90%; it means you scored higher than 90% of the group.

Mistake: Thinking the 100th percentile is achievable or meaningful.

Correction: By definition, no data point can be greater than 100% of all data (including itself). In most conventions, the maximum possible percentile is the 99th. Be cautious with boundary values.

Related Terms

Quartiles — Divide data at the 25th, 50th, 75th percentiles
Median — The 50th percentile of a dataset
Quintiles — Divide data into five equal groups by percentile
Deciles — Divide data into ten equal groups by percentile
Set — The collection of data values being ranked
Mean — Average value, often confused with the 50th percentile
Interquartile Range — Spread between the 25th and 75th percentiles