[statistics] Frequency Distribution Table

README.md

Create Frequency Distribution Table

• frequency distribution
• comulaive frequency
• relative frequency
• comulative relative frequency
• sturges' formula

In order to deal with large data, tail recursive optimisation is needed.
I just used a decorator class, written by George Sakkis here.
-> rec.py

freq.py

#rec.py is a decorator class written by George Sakkis. See(http://code.activestate.com/recipes/496691/)
import math,functools
from rec import tail_recursive

def _count(l, test):
	@tail_recursive
	def helper(l, test, count):
		if not l: return count
		if test(l[0]): count += 1
		return helper(l[1:],test, count)
	return helper(l, test, 0)

def freq(l, binWidth, lim=0):
	#the number of classes and test condition of the last class change if a limit is given.
	if lim == 0:
		num_of_classes = math.ceil(max(l)/binWidth)
		last_test = lambda x: True if binWidth*(num_of_classes-1) <= x <= binWidth*num_of_classes else False
	else:
		num_of_classes = lim//binWidth + 1
		last_test = lambda x: True if binWidth*(lim//binWidth) <= x else False
	
	#bottom:inclusive, top:exclusive.
	test = lambda bottom, top, x: True if bottom <= x < top else False
	
	result = [_count(l, functools.partial(test, binWidth*i, binWidth*(i+1))) for i in range(num_of_classes-1)]
	result.append(_count(l, last_test))
	return result

#freqList: a list generated by freq.
def comulativeFreq(freqList):
	return [sum(freqList[:i]) for i in range(1, len(freqList)+1)]

#freqList: a list generated by freq.
def relativeFreq(freqList):
	total = sum(freqList)
	return [freqList[i]/total for i in range(len(freqList))]

#freqList: a list generated by freq.
def comulativeRelativeFreq(freqList):
	rel = relativeFreq(freqList)
	return [sum(rel[:i]) for i in range(1, len(rel)+1)]

#n: the number of samples. When the data is a list l, n = len(l)
def sturges(n):
	return 1 + math.log(n,2)

sampledata.csv

8
7
17
23
21
28
24
27
25
28
38
34
37
40
35
39
38
33
34
32
50
44
43
44
42
46
46
47
46
45
44
46
43
47
46
51
53
53
57
56
56
55
55
53
53
54
51
52
58
55
54
60
53
54
53
57
57
59
66
63
65
65
67
68
65
64
69
64
65
63
69
65
67
68
62
64
61
80
75
77
73
79
72
79
78
76
79
72
72
72
75
84
90
82
82
83
84
97
93
100