Humans and animals are capable of estimating and discriminating nonsymbolic numerosities via mental representation of magnitudes—the approximate number system (ANS). There are two models of the ANS system, which are similar in their prediction in numerosity discrimination tasks. The log-Gaussian model, which assumes numerosities are represented on a compressed logarithmic scale, and the scalar variability model, which assumes numerosities are represented on a linear scale. In the first experiment of this paper, we contrasted these models using averaging of numerosities. We examined whether participants generate a compressed mean (i.e., geometric mean) or a linear mean when averaging two numerosities. Our results demonstrated that half of the participants are linear and half are compressed; however, in general, the compression is milder than a logarithmic compression. In Experiments 2 and 3, we examined averaging of numerosities in sequences larger than two. We found that averaging precision increases with sequence length. These results are in line with previous findings, suggesting a mechanism in which the estimate is generated by population averaging of the responses each stimulus generates on the numerosity representation.

人类和动物能够通过数量的心理表征——近似数系统（ANS）来估计和区分非符号数字。ANS系统有两种模型，它们在数量识别任务中的预测相似。假设数值以压缩对数尺度表示的对数高斯模型，以及假设数值以线性尺度表示的标量可变性模型。在本文的第一个实验中，我们使用数值的平均值来对比这些模型。我们检查了参与者在平均两个数值时是否生成压缩平均值（即几何平均值）或线性平均值。我们的结果表明，一半的参与者是线性的，一半是压缩的；然而，一般来说，压缩比对数压缩更温和。在实验 2 和 3 中，我们检查了大于 2 的序列中数量的平均值。我们发现平均精度随着序列长度的增加而增加。这些结果与先前的研究结果一致，表明估计值是通过对每个刺激在数量表示上产生的响应进行总体平均来生成的。