Function _ss

Lib/statistics.py:1511–1555

Return the exact mean and sum of square deviations of sequence data. Calculations are done in a single pass, allowing the input to be an iterator. If given *c* is used the mean; otherwise, it is calculated from the data. Use the *c* argument with care, as it can lead to garbage results

(data, c=None)

def _ss(data, c=None):
    """Return the exact mean and sum of square deviations of sequence data.

    Calculations are done in a single pass, allowing the input to be an iterator.

    If given *c* is used the mean; otherwise, it is calculated from the data.
    Use the *c* argument with care, as it can lead to garbage results.

    """
    if c is not None:
        T, ssd, count = _sum((d := x - c) * d for x in data)
        return (T, ssd, c, count)

    count = 0
    types = set()
    types_add = types.add
    sx_partials = defaultdict(int)
    sxx_partials = defaultdict(int)

    for typ, values in groupby(data, type):
        types_add(typ)
        for n, d in map(_exact_ratio, values):
            count += 1
            sx_partials[d] += n
            sxx_partials[d] += n * n

    if not count:
        ssd = c = Fraction(0)

    elif None in sx_partials:
        # The sum will be a NAN or INF. We can ignore all the finite
        # partials, and just look at this special one.
        ssd = c = sx_partials[None]
        assert not _isfinite(ssd)

    else:
        sx = sum(Fraction(n, d) for d, n in sx_partials.items())
        sxx = sum(Fraction(n, d*d) for d, n in sxx_partials.items())
        # This formula has poor numeric properties for floats,
        # but with fractions it is exact.
        ssd = (count * sxx - sx * sx) / count
        c = sx / count

    T = reduce(_coerce, types, int)  # or raise TypeError
    return (T, ssd, c, count)


def _isfinite(x):