[statistics] Various Averages

README.md

Calculate various averages.

• arithmetic mean
• weighted arithmetic mean
• percentile (including median and quartiles)
• mode
• mid-range
• geometric mean
• harmonic mean

averages.py

#python version 3.3.3
#assume that all parameters satisfy pre-conditions.
#programs do not deal with wrong parameters.

import math
import functools

#arithmetic mean
#l: data(list)
def arithmetic(l):
	return sum(l)/len(l)

#weighted arithmetic mean
#l: data(list), w: weight(list)
def weighted(l,w):
	return sum([l[i]*w[i] for i in range(len(l))])/sum(w)

#percentile/quantile
#l: data(list)
#q: percentage 0<=q<=1
def percentile(l,q):
	def helper(sl, i):
		hi, lo = int(math.ceil(i)), int(math.floor(i))
		return sl[int(i)] if i==int(i) else (hi-i)*sl[lo]+(i-lo)*sl[hi]
	return helper(sorted(l), (len(l)-1)*q)

#median
#l: data(list)
def median(l):
	return percentile(l,0.5)

#quartile
#l: data(list)
#returns: list of 5 q-quantiles (q=0,q=.25,q=.5,q=.75,q=1)
def quartile(l):
	return [percentile(l,0.25*x) for x in range(5)]

#frequency dictionary
#l: data(list), d: dict to store the frequencies
#returns: frecency dictionary(dict)
def freqDict(l,d):
	if not l:return d
	if l[0] in d.keys():
		d[l[0]] +=1
	else:
		d[l[0]] =1
	return freqDict(l[1:],d)

#mode
#l: data(list)
#returns: mode(list). note that if multiple modes, all in the resulting list.
def mode(l):
	d = freqDict(l,{})
	m = max(d.values())
	return [item[0] for item in d.items() if item[1]==m]

#mid-range
#l: data(list)
def midRange(l):
	return (max(l)+min(l))/2.0

#geometric mean
#l: data(list)
def geometric(l):
	return functools.reduce(lambda x,y:x*y,l)**(1/len(l))

#functools.reduce(lambda x,y:x*y,l) is 'product'
#here, the recursive expression
def product(l):
	return 1 if not l else l[0]*product(l[1:])

#harmonic mean
#l: data(list)
def harmonic(l):
	return len(l)/sum([1/l[i] for i in range(len(l))])