# Innumeracies

*This article is at an early stage of development.*

An innumeracy is a mathematical error that we're biased towards committing, due to cognitive biases. *An* innumeracy is not the same thing as innumeracy, which is a general lack of numeracy. Given that cognitive biases are universal, even someone with good numeracy will still commit innumeracies.

The second form of representativeness bias - our bias towards concluding that the more representative something is of a particular category, the more likely it will be a member of that category - leads to errors in judgements of probability.

The framing effect - our cognitive bias towards forming judgements that are significantly affected by the framing of the information on which they’re based - leads to many different types of mathematical error. For example, in one study, subjects in one group were each asked to quickly estimate:

- 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

and subjects in another group were each given the same task, but with the numbers presented in the reverse order:

- 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

The average of the answers given by the first group was 2,250, but that given by the second was 512. The subjects' estimate was influenced by the initial sub-totals that they formed from the first numbers in the problem, with those sub-totals being significantly affected by framing of the problem.