"""Number formatting and numeric helpers""" import re def percent_of(part, whole): """What percent of ``whole`` is ``part``? >>> percent_of(5, 100) 5.0 >>> percent_of(13, 26) 50.0 """ # Use float to force true division. return float(part * 100) / whole def mean(r): """Return the mean of a sequence of numbers. The mean is the average of all the numbers. >>> mean([5, 10]) 7.5 """ try: return float(sum(r)) / len(r) except ZeroDivisionError: raise ValueError("can't calculate mean of empty collection") average = mean def median(r): """Return the median of an iterable of numbers. The median is the point at which half the numbers are lower than it and half the numbers are higher. This gives a better sense of the majority level than the mean (average) does, because the mean can be skewed by a few extreme numbers at either end. For instance, say you want to calculate the typical household income in a community and you've sampled four households: >>> incomes = [18000] # Fast food crew >>> incomes.append(24000) # Janitor >>> incomes.append(32000) # Journeyman >>> incomes.append(44000) # Experienced journeyman >>> incomes.append(67000) # Manager >>> incomes.append(9999999) # Bill Gates >>> median(incomes) 49500.0 >>> mean(incomes) 1697499.8333333333 The median here is somewhat close to the majority of incomes, while the mean is far from anybody's income. [20 000, 40 000, 60 000, 9 999 999] The median would be around 50 000, which is close to what the majority of respondents make. The average would be in the millions, which is far from what any of the respondents make. This implementation makes a temporary list of all numbers in memory. """ s = list(r) s_len = len(s) if s_len == 0: raise ValueError("can't calculate mean of empty collection") s.sort() center = s_len // 2 is_odd = s_len % 2 if is_odd: return s[center] # Return the center element. # Return the average of the two elements nearest the center. low = s[center-1] high = s[center+1] return mean([low, high]) def standard_deviation(r, sample=True): """Standard deviation, `from the Python Cookbook `_ Population mode contributed by Lorenzo Catucci. Standard deviation shows the variability within a sequence of numbers. A small standard deviation shows the numbers are close to the same. A large standard deviation shows they are widely different. In fact it shows how far the numbers tend to deviate from the average. This can be used to detect whether the average has been skewed by a few extremely high or extremely low values. By default the helper computes the unbiased estimate for the population standard deviation, by applying an unbiasing factor of sqrt(N/(N-1)). If you'd rather have the function compute the population standard deviation, pass ``sample=False``. The following examples are taken from Wikipedia. http://en.wikipedia.org/wiki/Standard_deviation >>> standard_deviation([0, 0, 14, 14]) # doctest: +ELLIPSIS 8.082903768654761... >>> standard_deviation([0, 6, 8, 14]) # doctest: +ELLIPSIS 5.773502691896258... >>> standard_deviation([6, 6, 8, 8]) 1.1547005383792515 >>> standard_deviation([0, 0, 14, 14], sample=False) 7.0 >>> standard_deviation([0, 6, 8, 14], sample=False) 5.0 >>> standard_deviation([6, 6, 8, 8], sample=False) 1.0 (The results reported in Wikipedia are those expected for whole population statistics and therefore are equal to the ones we get by setting ``sample=False`` in the later tests.) .. code-block:: pycon # Fictitious average monthly temperatures in Southern California. # Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec >>> standard_deviation([70, 70, 70, 75, 80, 85, 90, 95, 90, 80, 75, 70]) # doctest: +ELLIPSIS 9.003366373785... >>> standard_deviation([70, 70, 70, 75, 80, 85, 90, 95, 90, 80, 75, 70], sample=False) # doctest: +ELLIPSIS 8.620067027323... # Fictitious average monthly temperatures in Montana. # Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec >>> standard_deviation([-32, -10, 20, 30, 60, 90, 100, 80, 60, 30, 10, -32]) # doctest: +ELLIPSIS 45.1378360405574... >>> standard_deviation([-32, -10, 20, 30, 60, 90, 100, 80, 60, 30, 10, -32], sample=False) # doctest: +ELLIPSIS 43.2161878106906... Most natural and random phenomena follow the normal distribution (aka the bell curve), which says that most values are close to average but a few are extreme. E.g., most people are close to 5'9" tall but a few are very tall or very short. If the data does follow the bell curve, 68% of the values will be within 1 standard deviation (stdev) of the average, and 95% will be within 2 standard deviations. So a university professor grading exams on a curve might give a "C" (mediocre) grade to students within 1 stdev of the average score, "B" (better than average) to those within 2 stdevs above, and "A" (perfect) to the 0.25% higher than 2 stdevs. Those between 1 and 2 stdevs below get a "D" (poor), and those below 2 stdevs... we won't talk about them. """ avg = average(r) sdsq = sum([(i - avg) ** 2 for i in r]) if sample: normal_denom=len(r) - 1 or 1 else: normal_denom=len(r) return (sdsq / normal_denom) ** 0.5 class SimpleStats(object): """Calculate a few simple stats on data. This class calculates the minimum, maximum, and count of all the values given to it. The values are not saved in the object. Usage:: >>> stats = SimpleStats() >>> stats(2) # Add one data value. >>> stats.extend([6, 4]) # Add several data values at once. The statistics are available as instance attributes:: >>> stats.count 3 >>> stats.min 2 >>> stats.max 6 Non-numeric data is also allowed: >>> stats2 = SimpleStats() >>> stats2("foo") >>> stats2("bar") >>> stats2.count 2 >>> stats2.min 'bar' >>> stats2.max 'foo' If the ``numeric`` constructor arg is true, only ``int``, ``long``, and ``float`` values will be accepted. This flag is intended to enable additional numeric statistics, although none are currently implemented. ``.min`` and ``.max`` are ``None`` until the first data value is registered. Subclasses can override ``._init_stats`` and ``._update_stats`` to add additional statistics. """ __version__ = 1 def __init__(self, numeric=False): self.numeric = numeric self.count = 0 self.min = None self.max = None self._init_stats() def __nonzero__(self): """The instance is true if it has seen any data.""" return bool(self.count) def __call__(self, value): """Add a data value.""" if self.numeric: value + 0 # Raises TypeError if value is not numeric. if self.count == 0: self.min = self.max = value else: self.min = min(self.min, value) self.max = max(self.max, value) self.count += 1 self._update_stats(value) def extend(self, values): """Add several data values at once, akin to ``list.extend``.""" for value in values: self(value) ### Hooks for subclasses def _init_stats(self): """Initialize state data used by subclass statistics.""" pass def _update_stats(self, value): """Add a value to the subclass statistics.""" pass class Stats(SimpleStats): """A container for data and statistics. This class extends ``SimpleStats`` by calculating additional statistics, and by storing all data seen. All values must be numeric (``int``, ``long``, and/or ``float``), and you must call ``.finish()`` to generate the additional statistics. That's because the statistics here cannot be calculated incrementally, but only after all data is known. >>> stats = Stats() >>> stats.extend([5, 10, 10]) >>> stats.count 3 >>> stats.finish() >>> stats.mean # doctest: +ELLIPSIS 8.33333333333333... >>> stats.median 10 >>> stats.standard_deviation 2.8867513459481287 All data is stored in a list and a set for later use:: >>> stats.list [5, 10, 10] >> stats.set set([5, 10]) (The double prompt ">>" is used to hide the example from doctest.) The stat attributes are ``None`` until you call ``.finish()``. It's permissible -- though not recommended -- to add data after calling ``.finish()`` and then call ``.finish()`` again. This recalculates the stats over the entire data set. The ``SimpleStats`` hook methods are available for subclasses, and additionally the ``._finish_stats`` method. """ __version__ = 1 def __init__(self): SimpleStats.__init__(self, numeric=True) self.list = [] self.set = set() self.mean = None self.median = None self.standard_deviation = None self._init_stats() def __call__(self, value): if self.count == 0: self.min = self.max = value else: self.min = min(self.min, value) self.max = max(self.max, value) self.count += 1 self._update_stats(value) self.list.append(value) self.set.add(value) def finish(self): self.mean = mean(self.list) self.median = median(self.list) self.standard_deviation = standard_deviation(self.list) self._finish_stats() ### Hooks for subclasses. def _finish_stats(self): """Finish the subclass statistics now that all data are known.""" pass def format_number(n, thousands=",", decimal="."): """Format a number with a thousands separator and decimal delimeter. ``n`` may be an int, long, float, or numeric string. ``thousands`` is a separator to put after each thousand. ``decimal`` is the delimiter to put before the fractional portion if any. The default style has a thousands comma and decimal point per American usage: >>> format_number(1234567.89) '1,234,567.89' >>> format_number(123456) '123,456' >>> format_number(-123) '-123' Various European and international styles are also possible: >>> format_number(1234567.89, " ") '1 234 567.89' >>> format_number(1234567.89, " ", ",") '1 234 567,89' >>> format_number(1234567.89, ".", ",") '1.234.567,89' """ parts = str(n).split(".") parts[0] = re.sub( R"(\d)(?=(\d\d\d)+(?!\d))", R"\1%s" % thousands, parts[0]) return decimal.join(parts) if __name__ == "__main__": import doctest doctest.testmod()