Percentiles:
what the number tells you and how to find it

A percentile is a position in the line, not a mark

Imagine a class of 20 students standing in a queue, ordered from lowest marks to highest. A percentile describes where someone stands in that queue. A student at the 80th percentile has done at least as well as about 80 out of every 100 people in the group. Nothing is said about the actual marks.

That is why two very different results can share a percentile. In an easy paper a mark of 92 might be the 80th percentile; in a hard one, 61 might be. The percentile stays the same because the position in the queue is the same.

The 50th percentile deserves special mention: half the values sit below it and half above, which makes it the median. When a report quotes the P25 and P75 as well, you are looking at the quartiles that frame the middle half of the data.

A percentile finder simply sorts your numbers and returns the value sitting at the requested position. You can do the same by hand for short lists, which is how the example below works.

The nearest-rank rule for picking the value

Several definitions of percentile exist. The nearest-rank method is the easiest to apply by hand, and it always returns a number that really appears in your data.

1. 1Sort the values from smallest to largest and count them to get N.
2. 2Multiply P ÷ 100 by N.
3. 3Round the result up to the next whole number. That is the rank.
4. 4Count along the sorted list to that rank and read the value.

Worked example: 20 test marks

A teacher has already sorted 20 marks out of 100: 42, 48, 51, 55, 58, 60, 62, 64, 67, 69, 71, 73, 75, 78, 80, 83, 86, 90, 93, 97. She wants the 90th percentile to describe how strong the top group is.

The same steps give the other common cut points. For the median the rank is ⌈0.50 × 20⌉ = 10, so the value is 69.

Why another tool may give a different 50th percentile

In the table above the median came out as 69. A spreadsheet function or a statistics package might return 70 for the same data. Neither is wrong; they follow different conventions.

With 20 values the middle falls between the 10th (69) and the 11th (71). The nearest-rank method rounds up to a real data point and reports the 10th. Interpolation methods take the average of the two neighbours, which gives (69 + 71) ÷ 2 = 70.

The gap shrinks as the data set grows. For exam boards, wage surveys and growth charts the convention is usually stated in the documentation, so use the same one when you compare against published figures.

Percentile rank versus percentage score

People often mix up three ideas that sound alike. The table separates them.

Percentile rank is the reverse question: start from a score and ask how much of the group it beats. Divide the count of values below it by N and multiply by 100. For a mark of 80 that is 14 ÷ 20 × 100 = 70. Some definitions add half the values equal to the score, so tied scores can shift the answer slightly.

Where you meet percentiles in daily life

Percentiles turn up wherever a single number has to be placed against a crowd. Entrance-exam results are reported as percentile scores so that candidates from different sittings, with papers of different difficulty, can be compared. A child's height or weight on a growth chart is plotted against percentile curves for the same age, and a clinician reads the position on the curve, not just the raw measurement.

Pay and salary surveys quote the median and the 75th or 90th percentile of an occupation, which tells you what a typical role earns and what well-paid ones earn without being pulled upward by a handful of very high salaries. Website speed reports do something similar: the 95th percentile of page load time shows what the slowest one-in-twenty visits experience, which an average would hide.

In each case the benefit is the same. A percentile is resistant to extreme values, so one enormous outlier does not drag it the way it drags the mean. That is also why analysts prefer it for skewed data such as incomes, response times and house prices.

• Use the median when you want the typical value of skewed data.
• Use the 90th or 95th percentile when you care about the worse-off end, such as latency.
• Use percentile rank when you start from one person's score and want to know where it stands.

Reading percentiles without fooling yourself

• A percentile compares you with a specific group. The 90th percentile of a small coaching batch means something quite different from the 90th percentile of lakhs of national candidates.
• Percentiles are unevenly spaced in marks. Jumping from the 50th to the 60th percentile might take two marks in a crowded middle, while the top five percentiles can take twenty.
• A single value near an extreme is fragile. With only 20 values the 90th percentile rests on the 18th mark alone.
• Percentiles say nothing on their own about whether a result is good. Pair them with the actual scores or the scale used.