# Math Is Fun Forum

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## #1 Re: Coder's Corner » Comparing percentile by python or numpy with the definition » 2016-12-03 06:48:58

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!

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

## #2 Re: Help Me ! » definition of percentile? » 2016-12-03 06:35:38

Understanding percentile by an example of the data of marks of students in a class.
Percentile of Score:
To calculate percentile of a student having unique marks in the class:
Percentage of "Students having marks lower than him" over "Total students in class"

To calculate percentile of a student not having unique marks in the class:
Percentage of "sum of students having lower marks than him, and half of all students getting same marks as him" over "Total students in class"

Above we calculated the percentile of a 'student' or better, student's marks.
What if someone asks what is 50% percentile for the class i.e. Score at percentile?
Multiply the percentile number (as a percentage) with the students in the class. Say, there are 40 students in the class, you take 50% of 40 i.e. 20.
If after multiplication the product is a whole number:
then take average of the whole number & the item next to it(data should be arranged in ascending order).
i.e. average of 20th and 21st student's marks.
If after multiplication the product is not a whole number:
then roundup the product, and this item will be the required scoreatpercentile
say, if there were 45 students in the class, then score at 50th percentile will be 23rd item's marks(i.e roundup of 22.5 = 50% of 45)

## #3 Coder's Corner » Comparing percentile by python or numpy with the definition » 2016-12-03 01:28:29

Mathilie
Replies: 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.