Weighted Median

weighted_median.py

import numpy as np

def weighted_median(x, weights):
    
    #Sorting item and weights first
    sort    = np.argsort(x)
    x       = x[sort]
    weights = weights[sort]
    
    #Less than cumulative frequencies
    cumfreq = np.cumsum(weights)
    N       = np.sum(weights)
    assert N == cumfreq[-1]

    #Find minimum cumulative frequency >= N/2.
    #If equal, average of x corresponding to min and second min is return
    #otherwise x corresponding to min is reported
    idx = np.where(cumfreq>= N/2.)[0][0]
    if cumfreq[idx]==N/2.:
        Md = 0.5*(x[idx]  + x[idx+1])
    else:
        Md = x[idx]
    return Md 

if __name__=="__main__":
 
    x = np.array([19,28,27,32,37,41,42,24])
    freq = np.array([7,12,22,14,13,14,19,19])
    #x = np.array([19,28,27,32,37,41,42,24])
    #freq = np.array([7,12,25,14,13,14,19,19])
    #x    = np.array([155,160,165,170.,175,180])
    #freq = np.array([4,7,18,11,6,4.])  
    #freq = np.array([1]*8)
    print weighted_median( x, freq)
    print np.median(x)