F5: Truncation bias in the mean

F5 — Truncation bias in the mean. Cutting the low tail biases the mean upward by at least 1% for every cut tested. 100 of 100 verified.
IDClaimValueVerified
F5-001Cutting the bottom 5% at sigma=0.30 biases the mean +2.5%2.52holds
F5-002Cutting the bottom 6% at sigma=0.32 biases the mean +3.1%3.14holds
F5-003Cutting the bottom 7% at sigma=0.34 biases the mean +3.8%3.78holds
F5-004Cutting the bottom 8% at sigma=0.36 biases the mean +4.5%4.48holds
F5-005Cutting the bottom 9% at sigma=0.38 biases the mean +5.2%5.21holds
F5-006Cutting the bottom 10% at sigma=0.40 biases the mean +6.0%6.0holds
F5-007Cutting the bottom 11% at sigma=0.42 biases the mean +6.8%6.76holds
F5-008Cutting the bottom 12% at sigma=0.44 biases the mean +7.6%7.6holds
F5-009Cutting the bottom 13% at sigma=0.46 biases the mean +8.5%8.48holds
F5-010Cutting the bottom 14% at sigma=0.48 biases the mean +9.4%9.43holds
F5-011Cutting the bottom 15% at sigma=0.50 biases the mean +10.3%10.26holds
F5-012Cutting the bottom 16% at sigma=0.52 biases the mean +11.3%11.28holds
F5-013Cutting the bottom 17% at sigma=0.54 biases the mean +12.4%12.39holds
F5-014Cutting the bottom 18% at sigma=0.56 biases the mean +13.4%13.36holds
F5-015Cutting the bottom 19% at sigma=0.58 biases the mean +14.6%14.58holds
F5-016Cutting the bottom 20% at sigma=0.60 biases the mean +15.7%15.68holds
F5-017Cutting the bottom 21% at sigma=0.62 biases the mean +16.8%16.82holds
F5-018Cutting the bottom 22% at sigma=0.64 biases the mean +18.1%18.08holds
F5-019Cutting the bottom 23% at sigma=0.66 biases the mean +19.3%19.3holds
F5-020Cutting the bottom 24% at sigma=0.68 biases the mean +20.8%20.8holds
F5-021Cutting the bottom 5% at sigma=0.70 biases the mean +4.3%4.27holds
F5-022Cutting the bottom 6% at sigma=0.72 biases the mean +5.2%5.18holds
F5-023Cutting the bottom 7% at sigma=0.74 biases the mean +6.1%6.1holds
F5-024Cutting the bottom 8% at sigma=0.76 biases the mean +7.0%7.03holds
F5-025Cutting the bottom 9% at sigma=0.78 biases the mean +8.0%8.03holds
F5-026Cutting the bottom 10% at sigma=0.80 biases the mean +9.1%9.05holds
F5-027Cutting the bottom 11% at sigma=0.82 biases the mean +10.1%10.08holds
F5-028Cutting the bottom 12% at sigma=0.84 biases the mean +11.1%11.15holds
F5-029Cutting the bottom 13% at sigma=0.86 biases the mean +12.2%12.19holds
F5-030Cutting the bottom 14% at sigma=0.88 biases the mean +13.4%13.39holds
F5-031Cutting the bottom 15% at sigma=0.90 biases the mean +14.5%14.53holds
F5-032Cutting the bottom 16% at sigma=0.92 biases the mean +15.8%15.78holds
F5-033Cutting the bottom 17% at sigma=0.94 biases the mean +17.0%17.02holds
F5-034Cutting the bottom 18% at sigma=0.96 biases the mean +18.3%18.25holds
F5-035Cutting the bottom 19% at sigma=0.98 biases the mean +19.6%19.58holds
F5-036Cutting the bottom 20% at sigma=1.00 biases the mean +20.9%20.9holds
F5-037Cutting the bottom 21% at sigma=1.02 biases the mean +22.3%22.34holds
F5-038Cutting the bottom 22% at sigma=1.04 biases the mean +23.7%23.71holds
F5-039Cutting the bottom 23% at sigma=1.06 biases the mean +25.3%25.26holds
F5-040Cutting the bottom 24% at sigma=1.08 biases the mean +26.7%26.73holds
F5-041Cutting the bottom 5% at sigma=1.10 biases the mean +4.9%4.94holds
F5-042Cutting the bottom 6% at sigma=1.12 biases the mean +6.0%5.98holds
F5-043Cutting the bottom 7% at sigma=1.14 biases the mean +7.1%7.06holds
F5-044Cutting the bottom 8% at sigma=1.16 biases the mean +8.1%8.14holds
F5-045Cutting the bottom 9% at sigma=1.18 biases the mean +9.2%9.24holds
F5-046Cutting the bottom 10% at sigma=1.20 biases the mean +10.4%10.4holds
F5-047Cutting the bottom 11% at sigma=1.22 biases the mean +11.5%11.55holds
F5-048Cutting the bottom 12% at sigma=1.24 biases the mean +12.7%12.74holds
F5-049Cutting the bottom 13% at sigma=1.26 biases the mean +14.0%13.96holds
F5-050Cutting the bottom 14% at sigma=1.28 biases the mean +15.2%15.22holds
F5-051Cutting the bottom 15% at sigma=1.30 biases the mean +16.5%16.47holds
F5-052Cutting the bottom 16% at sigma=1.32 biases the mean +17.8%17.84holds
F5-053Cutting the bottom 17% at sigma=1.34 biases the mean +19.1%19.12holds
F5-054Cutting the bottom 18% at sigma=1.36 biases the mean +20.5%20.51holds
F5-055Cutting the bottom 19% at sigma=1.38 biases the mean +22.0%21.97holds
F5-056Cutting the bottom 20% at sigma=1.40 biases the mean +23.4%23.37holds
F5-057Cutting the bottom 21% at sigma=1.42 biases the mean +24.9%24.93holds
F5-058Cutting the bottom 22% at sigma=1.44 biases the mean +26.5%26.51holds
F5-059Cutting the bottom 23% at sigma=1.46 biases the mean +28.0%28.01holds
F5-060Cutting the bottom 24% at sigma=1.48 biases the mean +29.6%29.6holds
F5-061Cutting the bottom 5% at sigma=1.50 biases the mean +5.2%5.18holds
F5-062Cutting the bottom 6% at sigma=1.52 biases the mean +6.3%6.27holds
F5-063Cutting the bottom 7% at sigma=1.54 biases the mean +7.4%7.39holds
F5-064Cutting the bottom 8% at sigma=1.56 biases the mean +8.5%8.53holds
F5-065Cutting the bottom 9% at sigma=1.58 biases the mean +9.7%9.69holds
F5-066Cutting the bottom 10% at sigma=1.60 biases the mean +10.9%10.88holds
F5-067Cutting the bottom 11% at sigma=1.62 biases the mean +12.1%12.12holds
F5-068Cutting the bottom 12% at sigma=1.64 biases the mean +13.4%13.37holds
F5-069Cutting the bottom 13% at sigma=1.66 biases the mean +14.6%14.63holds
F5-070Cutting the bottom 14% at sigma=1.68 biases the mean +15.9%15.94holds
F5-071Cutting the bottom 15% at sigma=1.70 biases the mean +17.3%17.27holds
F5-072Cutting the bottom 16% at sigma=1.72 biases the mean +18.6%18.65holds
F5-073Cutting the bottom 17% at sigma=1.74 biases the mean +20.0%20.03holds
F5-074Cutting the bottom 18% at sigma=1.76 biases the mean +21.5%21.51holds
F5-075Cutting the bottom 19% at sigma=1.78 biases the mean +23.0%22.96holds
F5-076Cutting the bottom 20% at sigma=1.80 biases the mean +24.5%24.47holds
F5-077Cutting the bottom 21% at sigma=1.82 biases the mean +26.0%26.02holds
F5-078Cutting the bottom 22% at sigma=1.84 biases the mean +27.6%27.64holds
F5-079Cutting the bottom 23% at sigma=1.86 biases the mean +29.2%29.25holds
F5-080Cutting the bottom 24% at sigma=1.88 biases the mean +31.0%30.99holds
F5-081Cutting the bottom 5% at sigma=1.90 biases the mean +5.2%5.24holds
F5-082Cutting the bottom 6% at sigma=1.92 biases the mean +6.4%6.36holds
F5-083Cutting the bottom 7% at sigma=1.94 biases the mean +7.5%7.5holds
F5-084Cutting the bottom 8% at sigma=1.96 biases the mean +8.7%8.65holds
F5-085Cutting the bottom 9% at sigma=1.98 biases the mean +9.8%9.85holds
F5-086Cutting the bottom 10% at sigma=2.00 biases the mean +11.1%11.05holds
F5-087Cutting the bottom 11% at sigma=2.02 biases the mean +12.3%12.29holds
F5-088Cutting the bottom 12% at sigma=2.04 biases the mean +13.6%13.56holds
F5-089Cutting the bottom 13% at sigma=2.06 biases the mean +14.9%14.85holds
F5-090Cutting the bottom 14% at sigma=2.08 biases the mean +16.2%16.19holds
F5-091Cutting the bottom 15% at sigma=2.10 biases the mean +17.5%17.54holds
F5-092Cutting the bottom 16% at sigma=2.12 biases the mean +18.9%18.94holds
F5-093Cutting the bottom 17% at sigma=2.14 biases the mean +20.4%20.37holds
F5-094Cutting the bottom 18% at sigma=2.16 biases the mean +21.8%21.83holds
F5-095Cutting the bottom 19% at sigma=2.18 biases the mean +23.3%23.33holds
F5-096Cutting the bottom 20% at sigma=2.20 biases the mean +24.9%24.85holds
F5-097Cutting the bottom 21% at sigma=2.22 biases the mean +26.4%26.43holds
F5-098Cutting the bottom 22% at sigma=2.24 biases the mean +28.1%28.05holds
F5-099Cutting the bottom 23% at sigma=2.26 biases the mean +29.7%29.68holds
F5-100Cutting the bottom 24% at sigma=2.28 biases the mean +31.4%31.4holds

What the failures mean

A failing entry is not a defect in the code — it is a case where the stated inequality does not hold over the full range, which bounds the claim's domain of validity. Those cases are kept.


Incoprea Research · study 10, 1,000 verified claims · 3 November 2026. Computation only.