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$ ./python -m test -W -R3:3 test_statistics
[1/1] test_statistics
[...]
======================================================================
FAIL: assertApproxEqual (test.test_statistics.NumericTestCase)
Doctest: test.test_statistics.NumericTestCase.assertApproxEqual
----------------------------------------------------------------------
Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 2193, in runTest
 raise self.failureException(self.format_failure(new.getvalue()))
AssertionError: Failed doctest test for test.test_statistics.NumericTestCase.assertApproxEqual
 File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 153, in assertApproxEqual
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 165, in test.test_statistics.NumericTestCase.assertApproxEqual
Failed example:
 class MyTest(NumericTestCase):
 def test_number(self):
 x = 1.0/6
 y = sum([x]*6)
 self.assertApproxEqual(y, 1.0, tol=1e-15)
 def test_sequence(self):
 a = [1.001, 1.001e-10, 1.001e10]
 b = [1.0, 1e-10, 1e10]
 self.assertApproxEqual(a, b, rel=1e-3)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics.NumericTestCase.assertApproxEqual[0]>", line 1, in <module>
 class MyTest(NumericTestCase):
 NameError: name 'NumericTestCase' is not defined
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 177, in test.test_statistics.NumericTestCase.assertApproxEqual
Failed example:
 suite = unittest.TestLoader().loadTestsFromTestCase(MyTest)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics.NumericTestCase.assertApproxEqual[3]>", line 1, in <module>
 suite = unittest.TestLoader().loadTestsFromTestCase(MyTest)
 NameError: name 'MyTest' is not defined
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 178, in test.test_statistics.NumericTestCase.assertApproxEqual
Failed example:
 unittest.TextTestRunner(stream=StringIO()).run(suite)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics.NumericTestCase.assertApproxEqual[4]>", line 1, in <module>
 unittest.TextTestRunner(stream=StringIO()).run(suite)
 NameError: name 'suite' is not defined
======================================================================
FAIL: _DoNothing (test.test_statistics)
Doctest: test.test_statistics._DoNothing
----------------------------------------------------------------------
Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 2193, in runTest
 raise self.failureException(self.format_failure(new.getvalue()))
AssertionError: Failed doctest test for test.test_statistics._DoNothing
 File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 99, in _DoNothing
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 112, in test.test_statistics._DoNothing
Failed example:
 approx_equal(12.345, 12.346, tol=1e-3)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics._DoNothing[0]>", line 1, in <module>
 approx_equal(12.345, 12.346, tol=1e-3)
 NameError: name 'approx_equal' is not defined
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 114, in test.test_statistics._DoNothing
Failed example:
 approx_equal(12.345e6, 12.346e6, tol=1e-3) # tol is too small.
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics._DoNothing[1]>", line 1, in <module>
 approx_equal(12.345e6, 12.346e6, tol=1e-3) # tol is too small.
 NameError: name 'approx_equal' is not defined
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 120, in test.test_statistics._DoNothing
Failed example:
 approx_equal(12.345, 12.346, rel=1e-4)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics._DoNothing[2]>", line 1, in <module>
 approx_equal(12.345, 12.346, rel=1e-4)
 NameError: name 'approx_equal' is not defined
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 122, in test.test_statistics._DoNothing
Failed example:
 approx_equal(12.345e6, 12.346e6, rel=1e-4)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics._DoNothing[3]>", line 1, in <module>
 approx_equal(12.345e6, 12.346e6, rel=1e-4)
 NameError: name 'approx_equal' is not defined
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 131, in test.test_statistics._DoNothing
Failed example:
 approx_equal(12.345e6, 12.346e6, tol=1e-3, rel=1e-4)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics._DoNothing[4]>", line 1, in <module>
 approx_equal(12.345e6, 12.346e6, tol=1e-3, rel=1e-4)
 NameError: name 'approx_equal' is not defined
======================================================================
FAIL: _calc_errors (test.test_statistics)
Doctest: test.test_statistics._calc_errors
----------------------------------------------------------------------
Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 2193, in runTest
 raise self.failureException(self.format_failure(new.getvalue()))
AssertionError: Failed doctest test for test.test_statistics._calc_errors
 File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 25, in _calc_errors
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 28, in test.test_statistics._calc_errors
Failed example:
 _calc_errors(100, 75)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics._calc_errors[0]>", line 1, in <module>
 _calc_errors(100, 75)
 NameError: name '_calc_errors' is not defined
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 30, in test.test_statistics._calc_errors
Failed example:
 _calc_errors(100, 100)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics._calc_errors[1]>", line 1, in <module>
 _calc_errors(100, 100)
 NameError: name '_calc_errors' is not defined
======================================================================
FAIL: approx_equal (test.test_statistics)
Doctest: test.test_statistics.approx_equal
----------------------------------------------------------------------
Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 2193, in runTest
 raise self.failureException(self.format_failure(new.getvalue()))
AssertionError: Failed doctest test for test.test_statistics.approx_equal
 File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 41, in approx_equal
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 54, in test.test_statistics.approx_equal
Failed example:
 approx_equal(1.2589, 1.2587, tol=0.0003, rel=0)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics.approx_equal[0]>", line 1, in <module>
 approx_equal(1.2589, 1.2587, tol=0.0003, rel=0)
 NameError: name 'approx_equal' is not defined
----------------------------------------------------------------------
File "/home/antoine/cpython/default/Lib/test/test_statistics.py", line 56, in test.test_statistics.approx_equal
Failed example:
 approx_equal(1.2589, 1.2587, tol=0.0001, rel=0)
Exception raised:
 Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/doctest.py", line 1324, in __run
 compileflags, 1), test.globs)
 File "<doctest test.test_statistics.approx_equal[1]>", line 1, in <module>
 approx_equal(1.2589, 1.2587, tol=0.0001, rel=0)
 NameError: name 'approx_equal' is not defined

I don't know how to interpret this. Where can I find out more about refleak mode? Thanks.

The best way to learn about the different testing modes is to run
"./python -m test -h".
Basically "-R" executes the given tests several times in a row. This failure shows that test_statistics doesn't like being executed several times, which is a bug.
(the same problem arises with "-F" instead of "-R")

(ah, actually "-F" seems to work fine with test_statistics :-))

#20746 seems to have a patch for this.

This issue can be closed.
After changeset 7bc53cf8b2df by Zachary Ware in issue 22104:
./python -m test -R3:3 test_statistics
is ok now.

Thanks, Xavier!