With common input readings and errors at most 0.05 mg/L, oxygen summaries bound the share below 5 mg/L at 5.10–13.18% in 244 US streams, summers 2010–2025

We tested what daily oxygen summaries show about the share of low readings. We reused 296,741 checked USGS days at 244 stream sites in June–August 2010–2025. Minimum, mean and maximum have a common input-series ID. Under a common-input support-and-mean model, with absolute errors at most 0.05 mg/L in each statistic, the weighted share below 5 mg/L is bounded by 5.10% and 13.18%. Days, summers and sites receive equal weights within their groups. The allowed range is 8.08 percentage points wide. It is not a confidence interval. Treating reports as exact gives 5.26–12.36%. The median site range width is 2.12 points; the maximum is 58.77 points. The elementary probability bounds are established mathematics. This contribution supplies a checked environmental application, proof, code and full source package. Independent scalar calculations check every day. Four hundred linear programs and 2,000 generated distributions check the formulas. Daily summaries do not establish reading counts, complete time coverage or instrument accuracy. The result bounds a reading share under stated assumptions. It does not measure continuous-day duration, biological damage, or a national stream rate.

dissolved oxygen · stream monitoring · probability bounds · daily summaries · reproducible research