[statistics] Various Measures of Dispersion

README.md

Calculate various measures of dispersion.

• Naive range of data
• Quartile deviation
• Mean deviation
• Variance
• Standard deviation
• Weighted variance
• Weighted standard deviation
• Coefficient of variation

Needs averages.py

dispersion.py

#needs averages.py (https://gist.github.com/shotahorii/8206127)

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

import averages as avg
import math

#calculates raw range of data.
#l: list of numbers
def naiveRange(l):
	return max(l)-min(l)

#calculates quartile deviation.
#l: list of numbers
def quartileDev(l):
	return (avg.percentile(l,.75)-avg.percentile(l,.25))/2.0

#calculates mean deviation.
#l: list of numbers
def meanDev(l):
	m = avg.arithmetic(l)
	return sum([math.fabs(l[i]-m) for i in range(len(l))])/len(l)

#calculates variance.
#l: list of numbers
def variance(l):
	m = avg.arithmetic(l)
	return sum([(l[i]-m)**2 for i in range(len(l))])/len(l)

#calculates standard deviation.
#l: list of numbers
def stdDev(l):
	return variance(l)**0.5

#calculates weighted variance.
#l: list of numbers(data), w: list of numbers(weight)
def weightedVariance(l,w):
	m = avg.weighted(l,w)
	return sum([w[i]*((l[i]-m)**2) for i in range(len(l))])/sum(w)

#calculates weighted standard deviation.
#l: list of numbers(data), w: list of numbers(weight)
def weightedStdDev(l,w):
	return weightedVariance(l,w)**0.5

#calculates coefficient of variation
#l: list of numbers
def coef(l):
	return stdDev(l)/avg.arithmetic(l)