webhelpers.number¶

webhelpers.number.percent_of(part, whole)¶

What percent of whole is part?

>>> percent_of(5, 100)
5.0
>>> percent_of(13, 26)
50.0

webhelpers.number.mean(r)¶

Return the mean of a sequence of numbers.

The mean is the average of all the numbers.

>>> mean([5, 10])
7.5

webhelpers.number.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.

webhelpers.number.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.)

# 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.

class webhelpers.number.SimpleStats(numeric=False)¶

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.

extend(values)¶

Add several data values at once, akin to list.extend.

class webhelpers.number.Stats¶

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.

webhelpers.number.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'