Some reformatting (suggested by Black) and minor factoring. (GH-20865)

Lib/statistics.py

@@ -163,7 +163,7 @@ def _sum(data, start=0):
     T = _coerce(int, type(start))
     for typ, values in groupby(data, type):
         T = _coerce(T, typ)  # or raise TypeError
-        for n,d in map(_exact_ratio, values):
+        for n, d in map(_exact_ratio, values):
             count += 1
             partials[d] = partials_get(d, 0) + n
     if None in partials:
@@ -261,7 +261,7 @@ def _convert(value, T):
         return T(value)
     except TypeError:
         if issubclass(T, Decimal):
-            return T(value.numerator)/T(value.denominator)
+            return T(value.numerator) / T(value.denominator)
         else:
             raise
 
@@ -277,8 +277,8 @@ def _find_lteq(a, x):
 def _find_rteq(a, l, x):
     'Locate the rightmost value exactly equal to x'
     i = bisect_right(a, x, lo=l)
-    if i != (len(a)+1) and a[i-1] == x:
-        return i-1
+    if i != (len(a) + 1) and a[i - 1] == x:
+        return i - 1
     raise ValueError
 
 
@@ -315,7 +315,7 @@ def mean(data):
         raise StatisticsError('mean requires at least one data point')
     T, total, count = _sum(data)
     assert count == n
-    return _convert(total/n, T)
+    return _convert(total / n, T)
 
 
 def fmean(data):
@@ -403,11 +403,11 @@ def harmonic_mean(data):
         else:
             raise TypeError('unsupported type')
     try:
-        T, total, count = _sum(1/x for x in _fail_neg(data, errmsg))
+        T, total, count = _sum(1 / x for x in _fail_neg(data, errmsg))
     except ZeroDivisionError:
         return 0
     assert count == n
-    return _convert(n/total, T)
+    return _convert(n / total, T)
 
 
 # FIXME: investigate ways to calculate medians without sorting? Quickselect?
@@ -428,11 +428,11 @@ def median(data):
     n = len(data)
     if n == 0:
         raise StatisticsError("no median for empty data")
-    if n%2 == 1:
-        return data[n//2]
+    if n % 2 == 1:
+        return data[n // 2]
     else:
-        i = n//2
-        return (data[i - 1] + data[i])/2
+        i = n // 2
+        return (data[i - 1] + data[i]) / 2
 
 
 def median_low(data):
@@ -451,10 +451,10 @@ def median_low(data):
     n = len(data)
     if n == 0:
         raise StatisticsError("no median for empty data")
-    if n%2 == 1:
-        return data[n//2]
+    if n % 2 == 1:
+        return data[n // 2]
     else:
-        return data[n//2 - 1]
+        return data[n // 2 - 1]
 
 
 def median_high(data):
@@ -473,7 +473,7 @@ def median_high(data):
     n = len(data)
     if n == 0:
         raise StatisticsError("no median for empty data")
-    return data[n//2]
+    return data[n // 2]
 
 
 def median_grouped(data, interval=1):
@@ -510,15 +510,15 @@ class 3.5-4.5, and interpolation is used to estimate it.
         return data[0]
     # Find the value at the midpoint. Remember this corresponds to the
     # centre of the class interval.
-    x = data[n//2]
+    x = data[n // 2]
     for obj in (x, interval):
         if isinstance(obj, (str, bytes)):
             raise TypeError('expected number but got %r' % obj)
     try:
-        L = x - interval/2  # The lower limit of the median interval.
+        L = x - interval / 2  # The lower limit of the median interval.
     except TypeError:
         # Mixed type. For now we just coerce to float.
-        L = float(x) - float(interval)/2
+        L = float(x) - float(interval) / 2
 
     # Uses bisection search to search for x in data with log(n) time complexity
     # Find the position of leftmost occurrence of x in data
@@ -528,7 +528,7 @@ class 3.5-4.5, and interpolation is used to estimate it.
     l2 = _find_rteq(data, l1, x)
     cf = l1
     f = l2 - l1 + 1
-    return L + interval*(n/2 - cf)/f
+    return L + interval * (n / 2 - cf) / f
 
 
 def mode(data):
@@ -554,8 +554,7 @@ def mode(data):
     If *data* is empty, ``mode``, raises StatisticsError.
 
     """
-    data = iter(data)
-    pairs = Counter(data).most_common(1)
+    pairs = Counter(iter(data)).most_common(1)
     try:
         return pairs[0][0]
     except IndexError:
@@ -597,7 +596,7 @@ def multimode(data):
 # For sample data where there is a positive probability for values
 # beyond the range of the data, the R6 exclusive method is a
 # reasonable choice.  Consider a random sample of nine values from a
-# population with a uniform distribution from 0.0 to 100.0.  The
+# population with a uniform distribution from 0.0 to 1.0.  The
 # distribution of the third ranked sample point is described by
 # betavariate(alpha=3, beta=7) which has mode=0.250, median=0.286, and
 # mean=0.300.  Only the latter (which corresponds with R6) gives the
@@ -643,9 +642,8 @@ def quantiles(data, *, n=4, method='exclusive'):
         m = ld - 1
         result = []
         for i in range(1, n):
-            j = i * m // n
-            delta = i*m - j*n
-            interpolated = (data[j] * (n - delta) + data[j+1] * delta) / n
+            j, delta = divmod(i * m, n)
+            interpolated = (data[j] * (n - delta) + data[j + 1] * delta) / n
             result.append(interpolated)
         return result
     if method == 'exclusive':
@@ -655,7 +653,7 @@ def quantiles(data, *, n=4, method='exclusive'):
             j = i * m // n                               # rescale i to m/n
             j = 1 if j < 1 else ld-1 if j > ld-1 else j  # clamp to 1 .. ld-1
             delta = i*m - j*n                            # exact integer math
-            interpolated = (data[j-1] * (n - delta) + data[j] * delta) / n
+            interpolated = (data[j - 1] * (n - delta) + data[j] * delta) / n
             result.append(interpolated)
         return result
     raise ValueError(f'Unknown method: {method!r}')
@@ -689,9 +687,9 @@ def _ss(data, c=None):
     T, total, count = _sum((x-c)**2 for x in data)
     # The following sum should mathematically equal zero, but due to rounding
     # error may not.
-    U, total2, count2 = _sum((x-c) for x in data)
+    U, total2, count2 = _sum((x - c) for x in data)
     assert T == U and count == count2
-    total -=  total2**2/len(data)
+    total -= total2 ** 2 / len(data)
     assert not total < 0, 'negative sum of square deviations: %f' % total
     return (T, total)
 
@@ -740,7 +738,7 @@ def variance(data, xbar=None):
     if n < 2:
         raise StatisticsError('variance requires at least two data points')
     T, ss = _ss(data, xbar)
-    return _convert(ss/(n-1), T)
+    return _convert(ss / (n - 1), T)
 
 
 def pvariance(data, mu=None):
@@ -784,7 +782,7 @@ def pvariance(data, mu=None):
     if n < 1:
         raise StatisticsError('pvariance requires at least one data point')
     T, ss = _ss(data, mu)
-    return _convert(ss/n, T)
+    return _convert(ss / n, T)
 
 
 def stdev(data, xbar=None):
@@ -993,7 +991,7 @@ def overlap(self, other):
         if not isinstance(other, NormalDist):
             raise TypeError('Expected another NormalDist instance')
         X, Y = self, other
-        if (Y._sigma, Y._mu) < (X._sigma, X._mu):   # sort to assure commutativity
+        if (Y._sigma, Y._mu) < (X._sigma, X._mu):  # sort to assure commutativity
             X, Y = Y, X
         X_var, Y_var = X.variance, Y.variance
         if not X_var or not Y_var: