Representing Number Sets: Encoding Statistical Properties


Previous research suggests that people often recall individual items when sets are smaller than four and aggregate set features for sets larger than four. One intriguing possibility is that the process of aggregating sets creates summary representations that maintain the statistical properties of the set itself. For sets of numbers, this process might implicitly create approximate means. We report the results of two experiments investigating memory for number sets and its relation to working memory and metacognitive monitoring. In both experiments, participants were shown a series of data sets that varied in size (4, 6, or 8 numbers) and variance (10% or 20% of the mean) and were then presented with an actual value from the set and the set mean. In Experiment 1, participants were asked to select the actual value, and in Experiment 2, participants were asked to select the set mean. Results indicated that the proportion of correct selections and metacognitive confidence decreased with set size. Working memory was related to performance only when the set size was 6. The findings suggest that participants often erroneously reported the set mean as being a member of the set and that this effect increased for sets larger than four. The findings suggest that the process of aggregating number sets results in approximate means.

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