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**Mathilie****Member**- Registered: 2016-12-03
- Posts: 3

What do we mean by when we say percentile: percentile_of_score or score_at_percentile?

For [1, 3, 3, 4, 5, 6, 6, 7, 8, 8] written at https://www.mathsisfun.com/data/percentiles.html under "Quartiles" subtopic, the 25th, 50th, 75th percentile is written as 3, 5.5, 7, respectively.

But calculating it with python (numpy.percentile, i get the following output):

>>> from numpy import percentile

>>> data1 = [1, 3, 3, 4, 5, 6, 6, 7, 8, 8]

>>> for p in [25, 50, 75]: print(percentile(data1, p))

...

3.25

5.5

6.75

Why is there a difference? Which one is correct?

What is 25th percentile: 3 or 3.25?

What is 75th percentile: 7 or 6.75?

From mathisfun page, can I conclude the below information?

1 is the 0th percentile

3 is the 20th percentile

4 is the 30th percentile

5 is the 40th percentile

6 is the 60th percentile

7 is the 70th percentile

8 is the 90th percentile

Thanks

PS: the numpy link: https://docs.scipy.org/doc/numpy-dev/reference/generated/numpy.percentile.html & I don't know about the internal working of how it is calculated.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,689

Hi;

Mathematica says {3, 5.5, 7} and so does wolfram alpha. So I would say that MathsisFun is correct but there may be other ways to compute quartiles!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Mathilie****Member**- Registered: 2016-12-03
- Posts: 3

bobbym wrote:

Mathematica says {3, 5.5, 7} and so does wolfram alpha. So I would say that MathsisFun is correct but there may be other ways to compute quartiles!

Thanks for the reply.

I'm asking a definition type question: Is 100 percentile possible? I think theoretically no, but numpy.percentile for 100%ile doesn't give an error and gives the highest entry. Satirical: it solves the purpose what user may be seeking but is theoretically incorrect.

With your answer, my clouds of confusion over percentiles are reduced, & I wrote an answer here: http://www.mathisfunforum.com/viewtopic.php?pid=391172

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,689

In regards to your previous question.

There are at least 9 different definitions of empirical quantiles.

So both numpy and Mathematica etc are correct, depending on what definition the textbook is using.

Is 100 percentile possible? I think theoretically no

I would think that 100 percentile would mean the value that 100 percent of the data would be less than. But some definitions obviously include equal to also. I have seen many cases of 100 percentile computed and urge you to look at this answer:

http://math.stackexchange.com/questions … tile#33502

whuber, is an expert on statistics and he seems to indicate 100 percentile is allowed.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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