fix(stat_summary): compute mean_se from the sample variance

[dylanpulver]

mean_se builds the standard error from np.var(series), whose default ddof=0 is the population variance. The standard error of the mean uses the sample variance, so the interval is too narrow by sqrt((n-1)/n) — 29% at n=2, 5% at n=10.

ggplot2's reference implementation (R/stat-summary.R):

se <- mult * sqrt(stats::var(x) / length(x))

R's stats::var is the sample variance.

The two sibling summary functions in this module already use sample estimators — mean_sdl via Series.std() and mean_cl_normal via scipy.stats.sem, both ddof=1. mean_se was the only one on ddof=0.

Measured half-width for [2,4,4,4,5,5,7,9] (n=8):

	half-width
before	0.7071067812
s/sqrt(n) = scipy.stats.sem = ggplot2	0.7559289460

ratio 0.9354143467 = sqrt(7/8) exactly.

The fix keeps ggplot2's sqrt(var/n) shape. series.std()/sqrt(n) also passes the suite, but is worse: ndarray.std() defaults to ddof=0, so it would keep the bug for array input and raise on a list.

mean_se is the default fun_data for stat_summary_bin, so mean_se.png is regenerated (via tools/update_baseline_images.py, then oxipng -o 4 --strip safe).

Tests: 850 passed, 5 skipped, 1 xpassed, 0 failed. An earlier version of this description reported 6 test_geom_smooth failures; those were missing dependencies in my checkout. The added test fails on the unpatched function.

Found and drafted with Claude Opus 5 (claude-opus-5); I reviewed and verified the change.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 88.20%. Comparing base (8aa2879) to head (de31647).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1119   +/-   ##
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  Coverage   88.20%   88.20%           
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  Files         222      222           
  Lines       16253    16253           
  Branches     2080     2080           
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  Hits        14336    14336           
  Misses       1315     1315           
  Partials      602      602           

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[has2k1]

Thanks for catching that. For now I prefer no AI attribution in the commit message.

[has2k1]

We can remove this test. The comment in the function and the visual test are sufficient.

[has2k1]

@dylanpulver, thank you.