The position method, step by step
Finding the P-th percentile of a dataset: step 1, sort the values. Step 2, compute the position L = 1 + (P/100) × (n − 1), counting from 1 at the smallest value. Step 3, if L is a whole number, that sorted value is the percentile. If L falls between positions, interpolate: take the lower value plus the fractional part of L times the gap to the next value. This is the linear-interpolation method spreadsheets call PERCENTILE.INC, and it is the method this site's calculators use.
Quiz scores sorted: 58, 65, 67, 69, 72, 72, 74, 76, 80, 91 (n = 10). The 90th percentile: L = 1 + 0.9 × 9 = 9.1, between the 9th value (80) and the 10th (91): 80 + 0.1 × 11 = 81.1. The 75th: L = 7.75, between 74 and 76: 74 + 0.75 × 2 = 75.5. The 50th: L = 5.5, between 72 and 72: 72, the median, as it must be.
Where percentiles run your life quietly
Child growth charts are percentile machines: a toddler at the 25th percentile for weight is heavier than 25% of the reference population of the same age, and paediatricians watch the percentile a child tracks along, not the kilograms. Test norms work the same way: scholarship cut-offs, "top 2%" societies and screening thresholds are percentile statements wearing formal clothes. In each case the percentile is doing the job this page teaches: locating one value inside a reference distribution.
Why textbooks disagree slightly
At least nine published percentile methods exist, differing in how the position is defined (some use (n + 1) instead of (n − 1), others round to the nearest rank). On large datasets they agree to a hair; on ten values they can differ by a point or two, which is why the same data give 81.1 here and 82 in a nearest-rank table. Neither is wrong: they are different conventions for locating a point inside a discrete set. What matters is using one method consistently and, in formal work, naming it.
Confusing "the 90th percentile" with "90 percent". A score at the 90th percentile beat 90% of the group; it need not be anywhere near 90% correct. On an easy test the 90th percentile might be 97% correct; on a brutal one, 55%.
Frequently asked questions
What is the formula for the position of a percentile?
L = 1 + (P/100)(n - 1) in the sorted data, with interpolation between neighbours when L is fractional. This is Excel's PERCENTILE.INC method.
Is the median a percentile?
Yes: the 50th percentile, also the second quartile and the fifth decile. All are the same cut read at different resolutions.
Why did my textbook give a different 90th percentile?
A different convention (nearest-rank, or the (n + 1) position rule). Methods differ by small amounts in small samples and converge as n grows.