Things are not so straightforward with composite scores, which are variables that summarize multiple test scores. Composite scores often behave in ways that violate our intuitions. 

The Seventh Assessment Service Bulletin (ASB) discusses in detail why composite scores are more extreme than the average of their parts. 

For example, if a person scores 70 on both visual processing tests of the Woodcock-Johnson® IV Tests of Cognitive Abilities, Visualization and Picture Recognition, we would expect that the composite, the Visual Processing cluster score, would also be 70. However, this is not the case, as the Visual Processing cluster score is around 65 (62 to 67, depending on the examinee’s age and pattern of scores).

This occurrence is coined the composite score extremity effect, which refers to the counterintuitive fact that a composite score consisting of imperfectly correlated scores is always more extreme—further from the population mean—than the average of its parts. Note that the more tests in the cluster, the larger the composite score extremity effect.    

The ASB notes that although it is unusual to have a particular deficit, it is even more unusual to have that deficit and several more. A composite score that summarizes all of these deficits would have to take this comparative rarity into account. It is for this reason that a composite score that consists of many low scores is lower than the average of those scores.