Question 1

How do I find a percentile?

Accepted Answer

Sort the numbers and find the position (n − 1) × p + 1, interpolating between neighbors. For 1 to 10, the 90th percentile is at position 9.1, so it is 9.1.

Question 2

Which method does it use?

Accepted Answer

The same one as Excel's PERCENTILE.INC and Google Sheets' PERCENTILE — linear interpolation between the closest ranks. Other methods can give slightly different answers on small lists. In R it is quantile type 7, the default there and the one NIST says Excel and R use; the nine types are catalogued in Hyndman and Fan (1996).

Question 3

Worked example: silicon wafer resistivity

Accepted Answer

The NIST/SEMATECH handbook (section 7.2.6.2) lists twelve resistivity readings, in ohm·cm: 95.0610, 95.0925, 95.1065, 95.1195, 95.1442, 95.1567, 95.1591, 95.1682, 95.1772, 95.1937, 95.1959, 95.1990 (sorted). For the 90th percentile this calculator takes position (12 − 1) × 0.9 + 1 = 10.9. That is 0.9 of the way from the 10th value, 95.1937, to the 11th, 95.1959: 95.1957. NIST’s own default rule multiplies p by N + 1 = 13, gets position 11.7 and interpolates between the 11th and 12th values to reach 95.1981. Both are reasonable; the handbook states that there is no universally accepted rule and that all of the methods it lists are used in practice. The median here is 95.1579.

Question 4

What is a percentile rank?

Accepted Answer

The percent of values below a given value, counting ties as half. In 1, 2, 3, 4, the value 3 has a percentile rank of 62.5%. In the wafer data, the value 95.1682 has 7 smaller readings out of 12, plus itself counted as half, so (7 + 0.5) ÷ 12 = 62.5%. Some tests count ties fully or not at all, so ranks on small data sets can differ by a few points between sources.

Question 5

Is the median a percentile?

Accepted Answer

Yes — the 50th percentile. The 25th and 75th percentiles are the first and third quartiles. NIST also names the deciles, which split the ordered data into tenths: the 10th, 20th, … 90th percentiles.

Question 6

Is a percentile the same as a percentage?

Accepted Answer

No. Scoring 80% on a test is a percentage of points; being in the 80th percentile means you scored higher than 80% of the people who took it.

Question 7

Common mistakes with percentiles

Accepted Answer

First, comparing results from different software without checking the method: Excel’s PERCENTILE.INC and R’s default agree, while the rule that multiplies by n + 1 (R type 6, used by Minitab and SPSS) gives somewhat different values on small lists. Second, expecting the percentile to be one of your data points; it often falls between two. Third, using the 99th percentile of a short list: with only 20 values, the top percentiles are decided by one or two numbers, so they say little. Fourth, mixing up the two questions: “what value is at the 90th percentile?” (the P field) and “what percentile is this value?” (the rank field). Fifth, reading a percentile rank as a grade; being at the 60th percentile says nothing about how far ahead the scores are.

Percentile calculator