From b73a4554394c133567a580228189412b0b387921 Mon Sep 17 00:00:00 2001
From: Raymond Hettinger <raymond.hettinger@gmail.com>
Date: Mon, 13 Apr 2026 09:57:24 -0500
Subject: [PATCH] Normalize the input first

---
 Lib/statistics.py | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/Lib/statistics.py b/Lib/statistics.py
index 26cf925529ea60..e635b99f958e44 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -145,6 +145,7 @@
 from collections import Counter, namedtuple, defaultdict
 
 _SQRT2 = sqrt(2.0)
+_SQRT2PI = sqrt(tau)
 _random = random
 
 ## Exceptions ##############################################################
@@ -1257,11 +1258,11 @@ def samples(self, n, *, seed=None):
 
     def pdf(self, x):
         "Probability density function.  P(x <= X < x+dx) / dx"
-        variance = self._sigma * self._sigma
-        if not variance:
+        sigma = self._sigma
+        if not sigma:
             raise StatisticsError('pdf() not defined when sigma is zero')
-        diff = x - self._mu
-        return exp(diff * diff / (-2.0 * variance)) / sqrt(tau * variance)
+        z = (x - self._mu) / sigma
+        return exp(-0.5 * z * z) / (_SQRT2PI * sigma)
 
     def cdf(self, x):
         "Cumulative distribution function.  P(X <= x)"