statistics vs Manual mean: Stdlib Lab

Intro — what this post promises

How expensive is statistics.mean / median / stdev versus a hand sum/len, statistics.fmean, or a sorted mid? This lab times numpy-free reductions on float lists on Linux localhost.

Related links:

• 01shoppercove.comnlargest vs sorted slice localhost lab
• 02shoppercove.combisect vs linear lookup localhost lab
• 03shoppercove.comperf_counter vs time localhost lab
• 04shoppercove.comarray vs list ints localhost lab
• 05shoppercove.comCounter vs dict tally localhost lab
• 06shoppercove.comitertools chain vs flatten localhost lab
• 07shoppercove.comattrgetter vs getattr localhost lab
• 08shoppercove.comfrozenset vs set membership localhost lab

Lab honesty (1 Oct 2026 IST): Python 3.13.5. No NumPy. Correctness checks vs manual helpers: {'mean_close': True, 'fmean_close': True, 'median_close': True, 'pstdev_close': True}. Affiliates: 0. statistics.mean favors numeric care over micro-speed; fmean is the float fast path.

Verdict up front (N=10 000): sum/len ~209M elem/s vs statistics.mean ~3.4M (~62×); fmean ~24× statistics.mean. Median: manual ≈ statistics (~1.00×). Manual pstdev ~6.3× statistics.pstdev.

Arms

Lab topology

N in {100, 1000, 10000, 100000}; multiple trials/size
ops = full reductions/s; also elem/s = N * trials / p50

Script: lab-evidence/69-statistics-vs-manual-mean/results/run_lab.py.

Lead table — mean N=10 000 (p50)

Median & spread N=10 000

Scale — sum/len ÷ statistics.mean

fmean closes much of the gap (~24× vs statistics.mean at N=10 k) while staying in the statistics module.

Reading it

• Hot float means — prefer statistics.fmean or sum/len; treat statistics.mean as the careful/general API.
• Median — sorting dominates; stdlib ≈ manual here.
• stdev/pstdev — manual two-pass beat stdlib by ~6× at N=10 k; Welford is competitive when you want one pass.
• Correctness first — for mixed int/Fraction inputs, statistics.mean’s care may matter more than ns.

Why statistics.mean looks “slow”

On floats, statistics.mean takes a more general numeric path than fmean / a bare sum. That shows up as tens of × in a microbench — fine for reports and mixed types, noisy for a per-request float gauge. If the hot path is “average of floats I already trust,” call fmean (or sum/len) and reserve mean for clarity at API boundaries. Median’s cost is the sort either way; do not expect a helper rename to erase O(n log n).

Pitfalls

1. Calling statistics.mean in a tight float telemetry loop — use fmean.
2. Re-sorting for median every time on a static array — sort once.
3. Sample vs population stdev — stdev vs pstdev (n−1 vs n).
4. Assuming NumPy is required — stdlib covers a lot; NumPy wins on huge arrays/vectorization (out of scope).

When to pick what

Reproduce

python3 lab-evidence/69-statistics-vs-manual-mean/results/run_lab.py

Evidence: /workspace/lab-evidence/69-statistics-vs-manual-mean/results/.

Closing

Use fmean for float speed; mean for generality. On this box N=10 k sum/len beat statistics.mean by ~62×, fmean by ~24×, while median stayed a wash and manual pstdev led by ~6×. Match the helper to whether you are optimizing a hot float path or writing clear stats code.