Python统计模块statistics用法精要

      有些统计学术语把握不是特别准确，担心有翻译错的，所以在不确定的地方保留了英文原文，如果有翻译错的也请路过的同行指出，多谢！
1、mean()

计算平均值

>>> import statistics 

 

  >>> statistics.mean([1, 2, 3, 4, 5, 6, 7, 8, 9]) 

 

  5.0 

 

  >>> statistics.mean(range(1,10)) 

 

  5.0 

 

  >>> import fractions 

 

  >>> x = [(3, 7), (1, 21), (5, 3), (1, 3)] 

 

  >>> y = [fractions.Fraction(*item) for item in x] 

 

  >>> y 

 

  [Fraction(3, 7), Fraction(1, 21), Fraction(5, 3), Fraction(1, 3)] 

 

  >>> statistics.mean(y) 

 

  Fraction(13, 21) 

 

  >>> import decimal 

 

  >>> x = ('0.5', '0.75', '0.625', '0.375') 

 

  >>> y = map(decimal.Decimal, x) 

 

  >>> y 

 

  <map object at 0x00000000033465C0> 

 

  >>> list(y) 

 

  [Decimal('0.5'), Decimal('0.75'), Decimal('0.625'), Decimal('0.375')] 

 

  >>> statistics.mean(y) 

 

  Traceback (most recent call last): 

 

    File "<pyshell#411>", line 1, in <module> 

 

      statistics.mean(y) 

 

    File "C:\Python 3.5\lib\statistics.py", line 292, in mean 

 

      raise StatisticsError('mean requires at least one data point') 

 

  statistics.StatisticsError: mean requires at least one data point 

 

  >>> list(y) 

 

  [] 

 

  >>> y = map(decimal.Decimal, x) 

 

  >>> statistics.mean(y) 

 

  Decimal('0.5625') 

 
2、median()、median_low()、median_high()、median_grouped()
 

  各种中位数 

 

  >>> statistics.median([1, 3, 5, 7]) 

 

  4.0 

 

  >>> statistics.median_low([1, 3, 5, 7]) 

 

  3 

 

  >>> statistics.median_high([1, 3, 5, 7]) 

 

  5 

 

  >>> statistics.median([1, 3, 7]) 

 

  3 

 

  >>> statistics.median([5, 3, 7]) 

 

  5 

 

  >>> statistics.median(range(1,10)) 

 

  5 

 

  >>> statistics.median_low([5, 3, 7]) 

 

  5 

 

  >>> statistics.median_high([5, 3, 7]) 

 

  5 

 

  >>> statistics.median_grouped([5, 3, 7]) 

 

  5.0 

 

  >>> statistics.median_grouped([5, 3, 7, 1]) 

 

  4.5 

 

  >>> statistics.median_grouped([52, 52, 53, 54]) 

 

  52.5 

 

  >>> statistics.median_low([52, 52, 53, 54]) 

 

  52 

 

  >>> statistics.median_high([52, 52, 53, 54]) 

 

  53 

 

  >>> statistics.median_high([1, 3, 3, 5, 7]) 

 

  3 

 

  >>> statistics.median_low([1, 3, 3, 5, 7]) 

 

  3 

 

  >>> statistics.median_grouped([1, 3, 3, 5, 7]) 

 

  3.25 

 

  >>> statistics.median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5]) 

 

  3.7 

 

  >>> statistics.median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5], interval=2) 

 

  3.4 

 
3、mode()

返回最常见数据或出现次数最多的数据（most common data）

>>> statistics.mode([1, 3, 5, 7]) 

 

  Traceback (most recent call last): 

 

    File "<pyshell#435>", line 1, in <module> 

 

      statistics.mode([1, 3, 5, 7]) 

 

    File "C:\Python 3.5\lib\statistics.py", line 434, in mode 

 

      'no unique mode; found %d equally common values' % len(table) 

 

  statistics.StatisticsError: no unique mode; found 4 equally common values 

 

  >>> statistics.mode([1, 3, 5, 7, 3]) 

 

  3 

 

  >>> statistics.mode([1, 3, 5, 7, 3, 5]) 

 

  Traceback (most recent call last): 

 

    File "<pyshell#437>", line 1, in <module> 

 

      statistics.mode([1, 3, 5, 7, 3, 5]) 

 

    File "C:\Python 3.5\lib\statistics.py", line 434, in mode 

 

      'no unique mode; found %d equally common values' % len(table) 

 

  statistics.StatisticsError: no unique mode; found 2 equally common values 

 

  >>> statistics.mode([1, 3, 5, 7, 3, 5, 5]) 

 

  5 

 

  >>> statistics.mode(["red", "blue", "blue", "red", "green", "red", "red"]) 

 

  'red' 

 

  >>> statistics.mode(list(range(5)) + [3]) 

 

  3 

 
4、pstdev()
 

  返回总体标准差（population standard deviation ，the square root of the population variance)。 

 

  >>> statistics.pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75]) 

 

  0.986893273527251 

 

  >>> statistics.pstdev(range(20)) 

 

  5.766281297335398 

 

  >>> statistics.pstdev([1, 2, 3, 4, 5, 10, 9, 8, 7, 6]) 

 

  2.8722813232690143 

 
5、pvariance()
 

  返回总体方差（population variance）或二次矩（second moment）。 

 

  >>> statistics.pvariance([1.5, 2.5, 2.5, 2.75, 3.25, 4.75]) 

 

  0.9739583333333334 

 

  >>> statistics.pvariance([1, 2, 3, 4, 5, 10, 9, 8, 7, 6]) 

 

  8.25 

 

  >>> x = [1, 2, 3, 4, 5, 10, 9, 8, 7, 6] 

 

  >>> mu = statistics.mean(x) 

 

  >>> mu 

 

  5.5 

 

  >>> statistics.pvariance([1, 2, 3, 4, 5, 10, 9, 8, 7, 6], mu) 

 

  8.25 

 

  >>> statistics.pvariance(range(20)) 

 

  33.25 

 

  >>> statistics.pvariance((random.randint(1,10000) for i in range(30))) 

 

  10903549.933333334 

 
6、variance()、stdev()
 
sample variance 
 ）和样本标准差（ 
 sample standard deviation， 
 the square root of the sample variance， 
 也叫均方差）。
 

  >>> statistics.variance((random.randint(1,10000) for i in range(30))) 

 

  10229013.655172413 

 

  >>> statistics.stdev((random.randint(1,10000) for i in range(30))) 

 

  3106.2902337180203 

 

  >>> _ * _ #注意，上面的两个样本数据并不一样，因为都是随机数 

 

  9649039.016091954 

 

  >>> statistics.variance(range(20)) 

 

  35.0 

 

  >>> statistics.stdev(range(20)) 

 

  5.916079783099616 

 

  >>> _ * _ 

 

  35.0 

 

  >>> statistics.variance([1, 2, 3, 4, 5, 10, 9, 8, 7, 6]) 

 

  9.166666666666666 

 

  >>> statistics.stdev([1, 2, 3, 4, 5, 10, 9, 8, 7, 6]) 

 

  3.0276503540974917 

 

  >>> statistics.variance([1.5, 2.5, 2.5, 2.75, 3.25, 4.75]) 

 

  1.16875 

 

  >>> statistics.stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75]) 

 

  1.0810874155219827 

 

  >>> _ * _ 

 

  1.1687500000000002 

 

  >>> statistics.variance([3, 3, 3, 3, 3, 3]) 

 

  0.0 

 

  >>> statistics.stdev([3, 3, 3, 3, 3, 3]) 

 
 0.0