# WebHelpers / webhelpers / number.py

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328``` ```"""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): """Standard deviation, from the Python Cookbook http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/442412 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. The following examples are taken from Wikipedia. http://en.wikipedia.org/wiki/Standard_deviation >>> standard_deviation([0, 0, 14, 14]) 8.0829037686547611 >>> standard_deviation([0, 6, 8, 14]) 5.7735026918962582 >>> standard_deviation([6, 6, 8, 8]) 1.1547005383792515 (Wikipedia reports 7, 5, and 1 respectively. Some of the difference is due to rounding, but the rest may be a bug?) # 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]) 9.0033663737851999 # Fictitious average mothly 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]) 45.137836040557403 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. a large standard i.e., how far they deviate from the average. If all numbers are the same, the standard deviation is zero. If the numbers are widely different from average, no matter whether above or below, the standard deviation will be high. Most natural distributions follow the bell curve and have a standard deviation of 1. """ avg = average(r) sdsq = sum([(i - avg) ** 2 for i in r]) return (sdsq / (len(r) - 1 or 1)) ** 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 8.3333333333333339 >>> 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() ```