Your Brain Really Does Average Numbers, New Study Finds

Glance at a handful of numbers scattered across a screen and, within a fraction of a second, your mind seems to deliver a verdict about their average. For decades, psychologists have debated whether that verdict reflects genuine statistical computation or a clever shortcut. Now a new study published in the journal Attention, Perception, & Psychophysics provides some of the strongest evidence yet that the human mind can truly compute the mean of a set of symbolic numbers, and that heuristic strategies play only a supporting role. The research, conducted by Daniel Fitousi and Hadar Srulovich of Ariel University, used an elegant experimental design that pits the arithmetic mean against rival strategies in a direct contest, and the mean won decisively.

The question matters because ensemble perception, the ability to extract summary statistics from groups of objects, has been documented extensively for visual properties such as size, orientation, color, facial emotion, and rough numerosity. When people view a crowd of faces, they can rapidly judge the average emotional expression; when they see a field of textured lines, they can sense the mean orientation. These findings suggested that the visual system computes averages much as a statistician would. But when the items are symbolic numerals, such as the Arabic digits 2, 4, 7, and 9, the story becomes murkier. Observers might genuinely integrate the magnitudes of all four digits, or they might rely on shortcuts, such as attending only to the most extreme digit, or counting how many digits fall above versus below some reference value.

Distinguishing genuine averaging from heuristic shortcuts is notoriously difficult, because both strategies often produce similar patterns of behavior. If a set of numbers has a mean well above five, then typically most of its digits are also above five, and its largest digit is likely far above five as well. A participant who answers correctly could be doing full integration or could be exploiting any of these correlated cues. Fitousi and Srulovich solved this problem with a criterion-based design in which participants viewed a two-by-two array of four Arabic digits and had to decide, under time pressure, whether the arithmetic mean of the set was smaller or larger than five. The key insight is that a true mean-based mechanism makes a precise prediction: performance should depend on the distance between the set mean and the criterion of five. The closer the mean sits to five, the harder the judgment should be, producing slower responses and more errors. This is the classic distance effect known from single-number comparison research dating back to the landmark 1967 study by Moyer and Landauer, who showed that comparing numbers takes longer when the numbers are numerically close.

In their first experiment, with forty participants, the researchers found exactly that signature. Accuracy and response time showed a robust ensemble-distance effect: decisions were slowest and least accurate when the set mean was closest to five, and performance improved monotonically as the mean moved farther from the criterion. Crucially, the authors went beyond the aggregate pattern and conducted item-level model comparisons, asking which statistical property of each individual digit array best predicted the participant’s behavior on that trial. The mean distance outperformed prominent heuristic alternatives based on the most extreme digit in the array or on the majority of digits lying above versus below the criterion. In other words, what best explained the data was not any single salient element or a simple tally, but the computed average of the whole set.

The first experiment also uncovered a second, independent influence on performance: the dispersion of the digits within the set. When the four numbers were widely spread out, judgments were impaired even after accounting for the distance of the mean from the criterion. This dispersion effect is theoretically interesting because a perfect averaging mechanism that simply pools four magnitudes might be expected to be indifferent to how spread out those magnitudes are. The finding suggests that internal representations of numerical magnitude are noisy, and that this noise accumulates when items vary widely, degrading the precision of the pooled estimate. Similar effects of heterogeneity have been reported in ensemble perception for visual properties, and their appearance here with symbolic numbers hints at a common architecture for statistical summary computation across perceptual and symbolic domains.

Yet the strongest objections to ensemble averaging have always come from the possibility that correlated cues are doing the work. The second experiment was designed as a diagnostic test that would break those correlations. The researchers constructed stimulus regimes in which the heuristic cues became uninformative or actively misleading, while carefully matching the mean distance and the dispersion of the sets across regimes. In one regime, the majority cue was tied, meaning that an equal number of digits fell above and below the criterion, so counting digits could not help. In another regime, the extreme-item cue conflicted with the correct answer, meaning that the most extreme digit in the array pointed toward the wrong response. If participants were relying on heuristics, their performance should have collapsed or flipped in these critical regimes.

It did not. Across regimes, the model comparisons again favored mean distance as the best predictor of both accuracy and response time. The distance effect persisted when majority information carried no diagnostic value whatsoever, and it persisted when the most extreme digit favored the incorrect response. Participants continued to judge the sets according to their true averages, even when every available shortcut pointed elsewhere. This pattern is precisely what a genuine mean-based integration mechanism would produce, and it is difficult to reconcile with accounts in which averaging-like behavior is an illusion created by cue redundancy. The authors conclude that the results support real mean-based integration of symbolic magnitudes, while showing that heuristic strategies have only a secondary role, one that becomes apparent mainly under increased uncertainty.

The findings carry weight for several ongoing debates in cognitive science. First, they extend ensemble perception into the domain of abstract symbols, suggesting that the machinery for statistical summarization is not limited to low-level visual features but can operate on semantic, culturally learned magnitudes. This connects the ensemble literature to the numerical cognition literature, including the influential idea of a mental number line and the parietal circuits that represent numerical magnitude in a roughly continuous, analog format. If digits are converted to analog magnitudes and then pooled, ensemble averaging of numerals may share a perceptual-like population-coding mechanism with the averaging of dots, orientations, and faces, a possibility that previous theoretical work on approximate numerical averaging has explored.

Second, the study speaks to the long-running tension between heuristic and exhaustive processing in judgment and decision making. Since Tversky and Kahneman’s classic work on heuristics and biases, researchers have documented countless cases in which people substitute easy questions for hard ones. The new results show that this tendency is not absolute. When the task structure makes the summary statistic the only reliable guide, the mind appears capable of deploying genuine integration, at least for small sets of four items presented simultaneously. Heuristics, on this view, are not the default everywhere; they emerge as competitors chiefly when the diagnostic value of the true statistic is degraded or when uncertainty rises.

Finally, the work has practical resonance. Averaging lies at the heart of numerical literacy, from estimating a grocery bill to interpreting medical risk statistics, and prior research has linked competence with numerical integration to broader mathematics achievement. Understanding that adults can compute set means rapidly and automatically, and that their precision depends on the distance of the mean from a criterion and on the spread of the items, may inform models of how people extract statistical information from displays, dashboards, and data visualizations. The study also leaves open questions that future research can pursue: whether the same mechanisms hold for larger sets, for sequentially presented numbers, for fractions and decimals, and for children whose numerical representations are still developing. Data and stimuli from the study are publicly available, and the criterion-based paradigm it introduces offers a template for testing ensemble computation in any domain where summary statistics compete with salient single items for control of behavior.

Subject of Research: Ensemble averaging of symbolic numbers and the role of heuristic shortcuts in numerical summary judgments

Article Title: Ensemble averaging of symbolic numbers: Criterion mean judgments beat heuristics

Article References: Fitousi, D., & Srulovich, H. (2026). Ensemble averaging of symbolic numbers: Criterion mean judgments beat heuristics. Attention, Perception, & Psychophysics, 88(7), Article 204. https://doi.org/10.3758/s13414-026-03338-0

Image Credits: AI Generated

DOI: 10.3758/s13414-026-03338-0

Keywords: numerical cognition, ensemble perception, ensemble averaging, distance effect, heuristics, symbolic numbers, decision making, mental number line, summary statistics, psychophysics, criterion judgment, dispersion