statistics.quantiles vs Manual Percentile: Localhost Lab

Intro — what this post promises

Compute quartiles / percentiles on a float list via statistics.quantiles vs a sorted-index manual method. This lab reports ops/s on Linux localhost.

It is not statistics-vs-manual-mean (lab 69) — that was means; this is quantiles/percentiles.

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Lab honesty (1 Oct 2026 IST): Python 3.13.5. Affiliates: 0. Uniform random floats.

Verdict up front (n=10 000): quantiles exclusive ~903.9 ops/s; manual sort+index ~904.3; quantiles on already-sorted input ~11596.9; index-only on pre-sorted ~876423.3. Sorting dominates; prefer stdlib for method semantics.

Arms

Lab topology

n in {1000, 10000, 100000} · 7 rounds · p50
metric: ops/s = 1 / p50_s (one quartile/percentile pass)

Script: lab-evidence/116-statistics-quantiles-vs-manual/results/run_lab.py.

Lead table — n=10 000 (p50 ops/s)

Scale sketch (exclusive quantiles vs manual sort)

Throughput collapses with n log n sort cost — expected.

Reading it

• Unsorted data → statistics.quantiles (clear methods, maintained).
• Already sorted stream → index math can win big (~876423.3 ops/s here) but document the rule.
• Do not confuse with mean benches (lab 69).
• Inclusive vs exclusive change cut points — pick one and stick to it in dashboards.

Method names matter

exclusive vs inclusive exist because “quartile” is not one universal formula. Shipping a blog-post index recipe into finance/report pipelines without naming the method causes silent dashboard drift. Prefer documenting statistics.quantiles(..., method=...) in the runbook.

Sort once

If you need p50, p90, p99, sort (or maintain a sorted structure) once, then index. Repeated full sorts per percentile were not the happy path on this box at n=100k (~48.9 ops/s exclusive).

Streaming / online note

These arms assume an in-memory list. True online percentiles (t-digest, P², HDR histograms) are a different design space — do not paste quantiles(list(all_samples)) into a hot telemetry path that retains every float forever. Batch windows of fixed size, then call stdlib once per window.

Comparison to mean lab

Lab 69’s mean/fsum story is O(n) without a full sort. Quartiles pay for ordering. If a dashboard only needs central tendency, do not upgrade it to quantiles “for free” — you buy n log n unless the array is already sorted for another reason.

Pitfalls

• DIY percentiles that disagree with Excel/pandas/quantiles method.
• Assuming pre-sorted input skips work inside statistics.quantiles (it still sorts).
• Computing many one-off percentiles each with a full sort — sort once.
• Floating ties and tiny samples (unstable cuts).

Reproduce

python3 lab-evidence/116-statistics-quantiles-vs-manual/results/run_lab.py

Evidence: summary.json, summary.txt.

Limits

One Linux box. Uniform floats only. Manual arms are illustrative — not bit-identical to every method=. Not numpy/pandas.

Takeaway

At 10 k floats, quantiles ~903.9 ops/s ≈ manual sort+index ~904.3. Prefer stdlib quantiles for semantics; reuse a sorted buffer if you need many cuts.