Statistical manipulation of large radiometric data sets (big data) is increasingly applied to those grand challenges in archaeology that relate to past human‐behavioural dynamics and includes frequency analysis of radiocarbon ages (summed probability distributions [SPDs]). Australian SPD studies use the radiocarbon database “AustArch” to examine regional‐ and continental‐scale demographic change. We review Australian studies, focussing on sampling bias and taphonomic bias, finding that (i) time‐averaged radiometric data cannot simply be correlated across regions, and (ii) sedimentology imposes genuine constraints upon what can be known. Internationally, flaws in SPD use occur in all main research phases, and most importantly, at the initial phase of defining research questions, logic and general approach. Major problems stem from not planning to obtain a sound understanding of the variability of past sedimentary environments, potential occupation sites and site formation processes. Thus, cultural inferences are too often made from archaeological data without due consideration of the natural processes that may explain the data. Highlighting exemplar studies, we present practical approaches to improve SPD use for exploring changes in demography, aimed at reducing uncertainties and reconnecting archaeological, chronological, geological and sedimentary data. Most important is to increase understanding of physical processes and their control on the archaeological record.