return data[n // 2]
-def median_grouped(data, interval=1):
+def median_grouped(data, interval=1.0):
"""Estimates the median for numeric data binned around the midpoints
of consecutive, fixed-width intervals.
by exact multiples of *interval*. This is essential for getting a
correct result. The function does not check this precondition.
+ Inputs may be any numeric type that can be coerced to a float during
+ the interpolation step.
+
"""
data = sorted(data)
n = len(data)
- if n == 0:
+ if not n:
raise StatisticsError("no median for empty data")
- elif n == 1:
- return data[0]
# Find the value at the midpoint. Remember this corresponds to the
# midpoint of the class interval.
x = data[n // 2]
- # Generate a clear error message for non-numeric data
- for obj in (x, interval):
- if isinstance(obj, (str, bytes)):
- raise TypeError(f'expected a number but got {obj!r}')
-
# Using O(log n) bisection, find where all the x values occur in the data.
# All x will lie within data[i:j].
i = bisect_left(data, x)
j = bisect_right(data, x, lo=i)
+ # Coerce to floats, raising a TypeError if not possible
+ try:
+ interval = float(interval)
+ x = float(x)
+ except ValueError:
+ raise TypeError(f'Value cannot be converted to a float')
+
# Interpolate the median using the formula found at:
# https://www.cuemath.com/data/median-of-grouped-data/
- try:
- L = x - interval / 2 # The lower limit of the median interval.
- except TypeError:
- # Coerce mixed types to float.
- L = float(x) - float(interval) / 2
+ L = x - interval / 2.0 # Lower limit of the median interval
cf = i # Cumulative frequency of the preceding interval
f = j - i # Number of elements in the median internal
return L + interval * (n / 2 - cf) / f
data = [x]*count
self.assertEqual(self.func(data), float(x))
+ def test_single_value(self):
+ # Override method from AverageMixin.
+ # Average of a single value is the value as a float.
+ for x in (23, 42.5, 1.3e15, Fraction(15, 19), Decimal('0.28')):
+ self.assertEqual(self.func([x]), float(x))
+
def test_odd_fractions(self):
# Test median_grouped works with an odd number of Fractions.
F = Fraction