What is Percentile: Definition and 19 Discussions

In statistics, a percentile (or a centile) is a score below which a given percentage of scores in its frequency distribution falls (exclusive definition) or a score at or below which a given percentage falls (inclusive definition). For example, the 50th percentile (the median) is the score below which (exclusive) or at or below which (inclusive) 50% of the scores in the distribution may be found.
The percentile (or percentile score) and the percentile rank are related terms. The percentile rank of a score is the percentage of scores in its distribution that are less than it, an exclusive definition, and one that can be expressed with a single, simple formula. In contrast, there are many formulas or algorithms for a percentile score. Hyndman and Fan identified nine and most statistical and spreadsheet software use one of the methods they describe. Algorithms either return the value of a score that exists in the set of scores (nearest-rank methods) or interpolate between existing scores and are either exclusive or inclusive.

The figure shows a 10-score distribution, illustrates the percentile scores that result from these different algorithms, and serves as an introduction to the examples given subsequently. The simplest are nearest-rank methods that return a score from the distribution, although compared to interpolation methods, results can be a bit crude. The Nearest-Rank Methods table shows the computational steps for exclusive and inclusive methods.

Interpolation methods, as the name implies, can return a score that is between scores in the distribution. Algorithms used by statistical programs typically use interpolation methods, for example, the percentile.exl and percentile.inc function in Microsoft Excel. The Interpolated Methods table shows the computational steps.
The term percentile and the related term percentile rank are often used in the reporting of scores from norm-referenced tests, but, as just noted, they are not the same. For percentile rank, a score is given and a percentage is computed. Percentile ranks are exclusive. If the percentile rank for a specified score is 90%, then 90% of the scores were lower. In contrast, for percentiles a percentage is given and a corresponding score is determined, which can be either exclusive or inclusive. The score for a specified percentage (e.g., 90th) indicates a score below which (exclusive definition) or at or below which (inclusive definition) other scores in the distribution fall.
The 25th percentile is also known as the first quartile (Q1), the 50th percentile as the median or second quartile (Q2), and the 75th percentile as the third quartile (Q3).

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  1. C

    B Milky Way is "in the top percentile of all the galaxies that exist"

    Our Galaxy is far bigger, brighter, and more massive than most others: Knowable Magazine Check out the amazing video, which shows all the many--more than 50!--satellite galaxies of the Milky Way burst into existence as they are discovered, year after year.
  2. RJLiberator

    For the cdf F(x) find the pmf f(x), 25th percentile, 60th percentile

    Homework Statement We have F(x) = ∑ (1/2)^j [Sum goes from j=1 to x] For the cdf F(x), find the pmf f(x), the 25th percentile, and the 60th percentile.Homework EquationsThe Attempt at a Solution I've been doing numerous of these for continuous distributions, however this one is tricking up...
  3. J

    B What Is the Probability of Scoring in the 88th Percentile for a Trait as a Male?

    I scored in the 88th percentile in a certain personality trait and am trying to figure out the probability of that given that I'm male. I'm trying the likelihood that I would land in the 88th percentile given that I'm male. Definitions: T = trait, M = males, F = female. Given: P(T|M) = 0.3...
  4. T

    Understanding Percentile Calculation: Confusion and Clarification

    Homework Statement I am confused between these 2 videos . In the first videos , it's same as what i learned in pre-university education course . When we are calculating kth percentile , the value that we get is whole number , then we need to the use (the value of the current number + value...
  5. T

    What is the correct method for finding the 60th percentile of grouped data?

    Homework Statement I am asked to find the 60th percentile of this question , so i found that 30 x 0.6 = 18 , So , the 60th percentile is the 18th term ? Or 19th term ? I am confused . I know whether it's 18th or 19th , it's still the same . I just want to get my concept correct Homework...
  6. Z

    75th percentile of the normal distribution

    Homework Statement The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentile of the distribution of X respectively. Find the value of the 75th percentile of the distribution of X. Homework Equations I found the above formula from internet. where...
  7. S

    B Understanding Percentile Ranks

    Hello! I am a bit confused about the percentile rank. Is the value of the percentile a lower or upper bound for your score. What I mean is, if you are let's say 95 percentile out of 100 people, does it means that there is a chance you scored the highest score with other 5 people, or there are 5...
  8. X

    I Percentiles and quartiles in the same graph

    I don't know where to put this question. So, I am trying in this forum. I have this dataset [1] that contains the duration of an execution with an input size from 1.5GB to 6GB. This dataset also contains the percentile 5%, 95%, and the 1st and 3rd quartile. I am thinking in creating a gnuplot...
  9. B

    Calculating mean from 5 number summary

    It seems like it should be possible to calculate the mean (usual average) from a 5-number summary of a set of numbers (min, first quartile or Q1, median, third quartile or Q3, and max). You should be able to calculate roughly what a percentile is, then by taking each discrete percentile and...
  10. T

    Z-score to Percentile Rank Formula?

    I was wondering, is there a formula that converts a given z-score to its respective percentile rank? I know I can look up the conversion in a table, but I have a lot of data, and would rather just program a formula into Excel. Obviously, there is some sort of way that whoever created the table...
  11. B

    Statistics: 90th percentile demand

    I'm a little confused on how you would do something like this: I have a cumulative probability distribution H(x): 0 0.31042 1 0.67825 2 0.89149 3 0.97196 4 0.9942 5 0.999 6 0.99985 7 0.99997 8 1 and I need to find the 90th percentile of demand.. I understand...
  12. N

    Another PGRE post: be happy with percentile or retake?

    Hello, I will only be applying to US Grad schools next year (circumstances...), but I took the GRE this year anyway cause there was no real reason not to and it would allow me to take it without too much pressure at the time. So I just got my scores: 980, in the 94-th percentile. From what I...
  13. veronica1999

    MHB AMC 8 2012 (contest score gender report with percentile)

    Hi, I recently took the AMC 8 and scored a 24 out of 25. While I was going through the statistics, I was surprised to see top scoring girls were seriously outnumbered by the boys. Out of 148,557 contestants there were 26 perfect scores for girls and 124 perfect score for boys. For score 24...
  14. pairofstrings

    What is the meaning of percentile in statistics?

    I want to know what is the meaning of percentile. what is the percentile : 23.79 means? Please give me explanation and also examples. Thanks!
  15. D

    Calculating percentile ranks of a Gaussian distribution

    I have been calibrating a sub-micron particle sizer with 1 um (1000 nm) standard. After testing the standard, the test results on my print-out: (X25 = 812.7 nm, X50 = 977.7 nm, X90 = 1389.0 nm) According to USP, the limits are +/- 6% of the reference standard values for X25, X50, and X90...
  16. U

    Understanding Percentiles: Solving MCQ Homework

    Homework Statement If a 30 percent of a reference group scored higher than you did on a test, your score would be: a)at the 30th percentile b)at the 70th percentile c)at the 71st percentile d)at the 29th percentile e)indeterminate from the available informationHomework Equations I think it is c...
  17. I

    What Is the Percentile Rank of a 20-Year-Old Machine?

    Homework Statement 60% of all machines inspected were 20 years or older. Give a percentile ranking for the age of 20 years in the distribution of all ages of inspected machines. Homework Equations Don't think there are any that apply to this question :/ I found this equation...
  18. N

    Solving Percentile Question: Find Canoe Carrying Capacity

    I am not exactly sure what I am supposed to do to solve this problem: The weight of people in a certain pacific island is normally distributed with a mean of 175 lb and a standard deviation of 33 lb. They want to design a one person canoe that will be able to serve 85% of the island's...
  19. J

    Sorting Objects into Percentile Groups

    Hello, Is there a well known method (algorithm, process, etc.) by which objects are sorted into percentile groups based on some aspect of the object such as weight or size?