Lines Matching refs:data
4 This module provides functions for calculating statistics of data, including
13 mean Arithmetic mean (average) of data.
15 geometric_mean Geometric mean of data.
16 harmonic_mean Harmonic mean of data.
17 median Median (middle value) of data.
18 median_low Low median of data.
19 median_high High median of data.
20 median_grouped Median, or 50th percentile, of grouped data.
21 mode Mode (most common value) of data.
22 multimode List of modes (most common values of data).
23 quantiles Divide data into intervals with equal probability.
26 Calculate the arithmetic mean ("the average") of data:
32 Calculate the standard median of discrete data:
38 Calculate the median, or 50th percentile, of data grouped into class intervals
39 centred on the data values provided. E.g. if your data points are rounded to
45 This should be interpreted in this way: you have two data points in the class
46 interval 1.5-2.5, three data points in the class interval 2.5-3.5, and one in
47 the class interval 3.5-4.5. The median of these data points is 2.8333...
56 pvariance Population variance of data.
57 variance Sample variance of data.
58 pstdev Population standard deviation of data.
59 stdev Sample standard deviation of data.
62 Calculate the standard deviation of sample data:
70 >>> data = [1, 2, 2, 4, 4, 4, 5, 6]
71 >>> mu = mean(data)
72 >>> pvariance(data, mu)
154 def _sum(data):
155 """_sum(data) -> (type, sum, count)
157 Return a high-precision sum of the given numeric data as a fraction,
179 >>> data = [D("0.1375"), D("0.2108"), D("0.3061"), D("0.0419")]
180 >>> _sum(data)
191 for typ, values in groupby(data, type):
208 def _ss(data, c=None):
209 """Return the exact mean and sum of square deviations of sequence data.
213 If given *c* is used the mean; otherwise, it is calculated from the data.
218 T, ssd, count = _sum((d := x - c) * d for x in data)
225 for typ, values in groupby(data, type):
414 def mean(data):
415 """Return the sample arithmetic mean of data.
428 If ``data`` is empty, StatisticsError will be raised.
430 T, total, n = _sum(data)
432 raise StatisticsError('mean requires at least one data point')
436 def fmean(data, weights=None):
437 """Convert data to floats and compute the arithmetic mean.
446 n = len(data)
454 data = count(data)
456 total = fsum(data)
458 raise StatisticsError('fmean requires at least one data point')
465 num = fsum(map(mul, data, weights))
467 raise StatisticsError('data and weights must be the same length')
474 def geometric_mean(data):
475 """Convert data to floats and compute the geometric mean.
487 return exp(fmean(map(log, data)))
493 def harmonic_mean(data, weights=None):
494 """Return the harmonic mean of data.
497 reciprocals of the data. It can be used for averaging ratios or
513 If ``data`` is empty, or any element is less than zero,
516 if iter(data) is data:
517 data = list(data)
519 n = len(data)
521 raise StatisticsError('harmonic_mean requires at least one data point')
523 x = data[0]
537 raise StatisticsError('Number of weights does not match data size')
540 data = _fail_neg(data, errmsg)
541 T, total, count = _sum(w / x if w else 0 for w, x in zip(weights, data))
549 def median(data):
550 """Return the median (middle value) of numeric data.
552 When the number of data points is odd, return the middle data point.
553 When the number of data points is even, the median is interpolated by
562 data = sorted(data)
563 n = len(data)
565 raise StatisticsError("no median for empty data")
567 return data[n // 2]
570 return (data[i - 1] + data[i]) / 2
573 def median_low(data):
574 """Return the low median of numeric data.
576 When the number of data points is odd, the middle value is returned.
585 data = sorted(data)
586 n = len(data)
588 raise StatisticsError("no median for empty data")
590 return data[n // 2]
592 return data[n // 2 - 1]
595 def median_high(data):
596 """Return the high median of data.
598 When the number of data points is odd, the middle value is returned.
607 data = sorted(data)
608 n = len(data)
610 raise StatisticsError("no median for empty data")
611 return data[n // 2]
614 def median_grouped(data, interval=1.0):
615 """Estimates the median for numeric data binned around the midpoints
618 The *data* can be any iterable of numeric data with each value being
643 >>> data = list(demographics.elements())
644 >>> median(data)
646 >>> round(median_grouped(data, interval=10), 1)
649 The caller is responsible for making sure the data points are separated
657 data = sorted(data)
658 n = len(data)
660 raise StatisticsError("no median for empty data")
664 x = data[n // 2]
666 # Using O(log n) bisection, find where all the x values occur in the data.
667 # All x will lie within data[i:j].
668 i = bisect_left(data, x)
669 j = bisect_right(data, x, lo=i)
679 # https://www.cuemath.com/data/median-of-grouped-data/
686 def mode(data):
687 """Return the most common data point from discrete or nominal data.
689 ``mode`` assumes discrete data, and returns a single value. This is the
695 This also works with nominal (non-numeric) data:
706 If *data* is empty, ``mode``, raises StatisticsError.
709 pairs = Counter(iter(data)).most_common(1)
713 raise StatisticsError('no mode for empty data') from None
716 def multimode(data):
720 or an empty list if *data* is empty.
729 counts = Counter(iter(data))
750 # For sample data where there is a positive probability for values
751 # beyond the range of the data, the R6 exclusive method is a
761 # For describing population data where the end points are known to
762 # be included in the data, the R7 inclusive method is a reasonable
773 def quantiles(data, *, n=4, method='exclusive'):
774 """Divide *data* into *n* continuous intervals with equal probability.
780 separate *data* in to 100 equal sized groups.
782 The *data* can be any iterable containing sample.
783 The cut points are linearly interpolated between data points.
785 If *method* is set to *inclusive*, *data* is treated as population
786 data. The minimum value is treated as the 0th percentile and the
791 data = sorted(data)
792 ld = len(data)
794 raise StatisticsError('must have at least two data points')
800 interpolated = (data[j] * (n - delta) + data[j + 1] * delta) / n
810 interpolated = (data[j - 1] * (n - delta) + data[j] * delta) / n
822 def variance(data, xbar=None):
823 """Return the sample variance of data.
825 data should be an iterable of Real-valued numbers, with at least two
827 the data. If it is missing or None, the mean is automatically calculated.
829 Use this function when your data is a sample from a population. To
834 >>> data = [2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]
835 >>> variance(data)
838 If you have already calculated the mean of your data, you can pass it as
841 >>> m = mean(data)
842 >>> variance(data, m)
846 ``data``. Giving arbitrary values for ``xbar`` may lead to invalid or
860 T, ss, c, n = _ss(data, xbar)
862 raise StatisticsError('variance requires at least two data points')
866 def pvariance(data, mu=None):
867 """Return the population variance of ``data``.
869 data should be a sequence or iterable of Real-valued numbers, with at least one
871 the data. If it is missing or None, the mean is automatically calculated.
879 >>> data = [0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25]
880 >>> pvariance(data)
883 If you have already calculated the mean of the data, you can pass it as
886 >>> mu = mean(data)
887 >>> pvariance(data, mu)
901 T, ss, c, n = _ss(data, mu)
903 raise StatisticsError('pvariance requires at least one data point')
907 def stdev(data, xbar=None):
916 T, ss, c, n = _ss(data, xbar)
918 raise StatisticsError('stdev requires at least two data points')
925 def pstdev(data, mu=None):
934 T, ss, c, n = _ss(data, mu)
936 raise StatisticsError('pstdev requires at least one data point')
943 def _mean_stdev(data):
945 T, ss, xbar, n = _ss(data)
947 raise StatisticsError('stdev requires at least two data points')
982 raise StatisticsError('covariance requires that both inputs have same number of data points')
984 raise StatisticsError('covariance requires at least two data points')
1010 raise StatisticsError('correlation requires that both inputs have same number of data points')
1012 raise StatisticsError('correlation requires at least two data points')
1038 estimated, and noise represents the variability of the data that was
1053 The data is fit to a line passing through the origin.
1067 raise StatisticsError('linear regression requires that both inputs have same number of data points')
1069 raise StatisticsError('linear regression requires at least two data points')
1188 def from_samples(cls, data):
1189 "Make a normal distribution instance from sample data."
1190 return cls(*_mean_stdev(data))