When I try to calculate the 75th percentile in MATLAB, I get a different value than I do in NumPy.
MATLAB:
>> x = [ 11.308 ; 7.2896; 7.548 ; 11.325 ; 5.7822; 9.6343;
7.7117; 7.3341; 10.398 ; 6.9675; 10.607 ; 13.125 ;
7.819 ; 8.649 ; 8.3106; 12.129 ; 12.406 ; 10.935 ;
12.544 ; 8.177 ]
>> prctile(x, 75)
ans =
11.3165
Python + NumPy:
>>> import numpy as np
>>> x = np.array([ 11.308 , 7.2896, 7.548 , 11.325 , 5.7822, 9.6343,
7.7117, 7.3341, 10.398 , 6.9675, 10.607 , 13.125 ,
7.819 , 8.649 , 8.3106, 12.129 , 12.406 , 10.935 ,
12.544 , 8.177 ])
>>> np.percentile(x, 75)
11.312249999999999
I've checked the answer with R too, and I'm getting NumPy's answer.
R:
> x <- c(11.308 , 7.2896, 7.548 , 11.325 , 5.7822, 9.6343,
+ 7.7117, 7.3341, 10.398 , 6.9675, 10.607 , 13.125 ,
+ 7.819 , 8.649 , 8.3106, 12.129 , 12.406 , 10.935 ,
+ 12.544 , 8.177)
> quantile(x, 0.75)
75%
11.31225
What is going on here? And is there any way to make Python & R's behavior mirror MATLAB's?
MATLAB apparently uses midpoint interpolation by default. NumPy and R use linear interpolation by default:
In [182]: np.percentile(x, 75, interpolation='linear')
Out[182]: 11.312249999999999
In [183]: np.percentile(x, 75, interpolation='midpoint')
Out[183]: 11.3165
The understand the difference between linear and midpoint, consider this simple example:
In [187]: np.percentile([0, 100], 75, interpolation='linear')
Out[187]: 75.0
In [188]: np.percentile([0, 100], 75, interpolation='midpoint')
Out[188]: 50.0
To compile the latest version of NumPy (using Ubuntu):
mkdir $HOME/src
git clone https://github.com/numpy/numpy.git
git remote add upstream https://github.com/numpy/numpy.git
# Read ~/src/numpy/INSTALL.txt
sudo apt-get install libatlas-base-dev libatlas3gf-base
python setup.py build --fcompiler=gnu95
python setup.py install
The advantage of using git instead of pip is that it is super easy to upgrade (or downgrade) to other versions of NumPy (and you get the source code too):
git fetch upstream
git checkout master # or checkout any other version of NumPy
cd ~/src/numpy
/bin/rm -rf build
cdsitepackages # assuming you are using virtualenv; otherwise cd to your local python sitepackages directory
/bin/rm -rf numpy numpy-*-py2.7.egg-info
cd ~/src/numpy
python setup.py build --fcompiler=gnu95
python setup.py install