"""Descriptive statistical analysis tool. """ __author__ = "Chad J. Schroeder" __revision__ = "$Id$" __version__ = "0.1" __all__ = [ "StatisticsException", "Statistics" ] class StatisticsException(Exception): """Statistics Exception class.""" pass class Statistics(object): """Class for descriptive statistical analysis. Behavior: Computes numerical statistics for a given data set. Available public methods: None Available instance attributes: N: total number of elements in the data set sum: sum of all values (n) in the data set min: smallest value of the data set max: largest value of the data set mode: value(s) that appear(s) most often in the data set mean: arithmetic average of the data set range: difference between the largest and smallest value in the data set median: value which is in the exact middle of the data set variance: measure of the spread of the data set about the mean stddev: standard deviation - measure of the dispersion of the data set based on variance identification: Instance ID Raised Exceptions: StatisticsException Bases Classes: object (builtin) Example Usage: x = [ -1, 0, 1 ] try: stats = Statistics(x) except StatisticsException, mesg: print "N: %s" % stats.N print "SUM: %s" % stats.sum print "MIN: %s" % stats.min print "MAX: %s" % stats.max print "MODE: %s" % stats.mode print "MEAN: %0.2f" % stats.mean print "RANGE: %s" % stats.range print "MEDIAN: %0.2f" % stats.median print "VARIANCE: %0.5f" % stats.variance print "STDDEV: %0.5f" % stats.stddev print "DATA LIST: %s" % stats.sample """ def __init__(self, sample=[], population=False): """Statistics class initializer method.""" # Raise an exception if the data set is empty. if (not sample): raise StatisticsException, "Empty data set!: %s" % sample # The data set (a list). self.sample = sample # Sample/Population variance determination flag. self.population = population self.N = len(self.sample) self.sum = float(sum(self.sample)) self.min = min(self.sample) self.max = max(self.sample) self.range = self.max - self.min self.mean = self.sum/self.N # Inplace sort (list is now in ascending order). self.sample.sort() self.__getMode() self.__getMedian() self.__getVariance() self.__getStandardDeviation() # Instance identification attribute. self.identification = id(self) def __getMode(self): """Determine the most repeated value(s) in the data set.""" # Initialize a dictionary to store frequency data. frequency = {} # Build dictionary: key - data set values; item - data frequency. for x in self.sample: if (x in frequency): frequency[x] += 1 else: frequency[x] = 1 # Create a new list containing the values of the frequency dict. Convert # the list, which may have duplicate elements, into a set. This will # remove duplicate elements. Convert the set back into a sorted list # (in descending order). The first element of the new list now contains # the frequency of the most repeated values(s) in the data set. # mode = sorted(list(set(frequency.values())), reverse=True)[0] # Or use the builtin - max(), which returns the largest item of a # non-empty sequence. mode = max(frequency.values()) # If the value of mode is 1, there is no mode for the given data set. if (mode == 1): self.mode = [] return # Step through the frequency dictionary, looking for values equaling # the current value of mode. If found, append the value and its # associated key to the self.mode list. self.mode = [(x, mode) for x in frequency if (mode == frequency[x])] def __getMedian(self): """Determine the value which is in the exact middle of the data set.""" if (self.N%2): # Number of elements in data set is odd. self.median = float(self.sample[self.N/2]) else: midpt = self.N/2 # Number of elements in data set is even. self.median = (self.sample[midpt-1] + self.sample[midpt])/2.0 def __getVariance(self): """Determine the measure of the spread of the data set about the mean. Sample variance is determined by default; population variance can be determined by setting population attribute to True. """ x = 0 # Summation variable. # Subtract the mean from each data item and square the difference. # Sum all the squared deviations. for item in self.sample: x += (item - self.mean)**2.0 try: if (not self.population): # Divide sum of squares by N-1 (sample variance). self.variance = x/(self.N-1) else: # Divide sum of squares by N (population variance). self.variance = x/self.N except: self.variance = 0 def __getStandardDeviation(self): """Determine the measure of the dispersion of the data set based on the variance. """ from math import sqrt # Mathematical functions. # Take the square root of the variance. self.stddev = sqrt(self.variance) if __name__ == "__main__": import os # Miscellaneous OS interfaces. import sys # System-specific parameters and functions. # Self-test a = [ -1, 0, 1 ] b = [ -1.0, 0.0, 1.1 ] c = [] d = [ 12.23 ] e = [ 12.23, 99.543, 66.08 ] f = [ -1, 0, 2, -2, 1, 3, 0, -3, 2 ] g = [ 0, 9, 1, 8, 2, 7, 3, 6, 4, 5 ] h = [ -1, -1 ] for x in a, b, c, d, e, f, g, h: try: stats = Statistics(x) except StatisticsException, mesg: print; print "Exception caught: %s" % mesg; print continue print print "N: %s" % stats.N print "SUM: %s" % stats.sum print "MIN: %s" % stats.min print "MAX: %s" % stats.max print "MODE: %s" % stats.mode print "MEAN: %0.2f" % stats.mean print "RANGE: %s" % stats.range print "MEDIAN: %0.2f" % stats.median print "VARIANCE: %0.5f" % stats.variance print "STDDEV: %0.5f" % stats.stddev print "DATA LIST: %s\n" % stats.sample print sys.exit(0)