## 5 Conclusions  
A conservative approach was designed for data analysis when surveying for trace elements in fine-grained waste deposits, such as CRMs and heavy metals. Given that even-grained solid wastes are comminuted and milled before chemical and mineralogical analyses, it is evident that discrete distributions are inoperant for statistical data analysis in the screening of solid waste. The proposed model was designed to cover the gap in statistical data analysis as a fundamental theoretical approach, particularly in cases where the outcomes indicate a uniform distribution of the targeted elemental concentration values. The theoretical framework encompasses both ideal and practical measurement scenarios. In an ideal measurement case, the analytical process does not introduce uncertainty, while in practical situations, the analytical process distorts the results due to the unavoidable LOQ of the method and measurement uncertainty. A key finding of this study is the effect of weighing on the derivation of the concentration **pdf**. The weighing exactness allows a triangular **pdf** to be assigned to the aliquot mass variable \(\mathbf{X}\) with a very narrow **CV,** which effectively behaves as a Dirac distribution relative to the **pdf** of the analyte mass variable, \(\mathbf{X}\). The conservative approach was applied to a survey of iron ore tailings for CRMs, using incremental sampling followed by XRFS analyses. This application demonstrated the advantages of the conservative approach compared to classical and robust statistical analyses. It was found that classical and robust statistical analyses of concentration values close to the LOQ, for a suite of results that are uniformly distributed, yield higher values and smaller uncertainties. Consequently, classical statistical data analysis may present a false positive picture of a solid waste pile's contents, potentially leading to an erroneous decision to invest in trace element recovery. The relative uncertainty in measurement better reflects the precision of the entire analytical chain, including statistical data processing, as its value is smaller as the measurement process works better. Additionally, the relative uncertainties allow measurement procedures to be compared in cases where they are correctly assessed. The data provided in Table 3 highlight situations in which different statistical data processing approaches yield different relative uncertainty values. The proposed approach is deemed the most reliable in cases where the data are uniformly distributed. The approach we propose offers deeper insight into analyte distribution within a targeted batch (e.g., lot, pile, pond, dump) through the statistical modeling of the entire measurement chain, encompassing both sampling and analytical measurement. The model is versatile and can be applied to any fine-grained substance that is incrementally sampled when the distribution of the analyte in the lot is unknown. **Author Contributions**: Conceptualization, A.-L.T., I.P., A.P. and C.U. ; methodology, A.-L.T., I.P., A.P., Z.K. and D.F.M. ; software, A.P., R.-N.T. and G.I. ; validation, I.P., C.U., F.N. and A.C.M. ; formal analysis, Z.K., R.-N.T. and D.F.M. ; investigation, A.-L.T., I.P., C.U., F.N., G.I. and A.C.M. ; resources, A.-L.T., A.P., Z.K., G.I., D.F.M. and A.C.M. ; data curation, C.U., F.N., G.I. and A.C.M. ; writing--original draft preparation, I.P., C.U., R.-N.T. and G.I. ; writing--review and editing, I.P., A.P., R.-N.T. and G.I. ; visualization, I.P., Z.K., F.N., R.-N.T. and G.I. ; supervision, A.-L.T. and I.P. ; project administration, A.-L.T. and A.P. ; funding acquisition, A.-L.T., A.P., C.U., Z.K. and D.F.M. All authors have read and agreed to the published version of the manuscript. **Funding;** This research received no external funding. **Institutional Review Board Statement**: Not applicable. **Informed Consent Statement**: Not applicable. **Data Availability Statement**: The raw data supporting the conclusions of this article will be made available by the authors on request.