The study was conducted to (a) determine the development of children's understanding of seven properties of the arithmetic mean and (b) assess the effects of the material used in the testing (continuous, discontinuous) and the medium of presentation (story, concrete, and numerical). Twenty children were selected at each of the ages 8, 10, 12, and 14 years. Different developmental courses of the children's reasoning were found on some tasks measuring the properties of the average. No significant effects were found for the materials used or the medium of presentation. The findings are discussed in terms of their importance for developmental psychology and educational practice. The Lord must have loved the average man because he made more of them than the others.
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