Ecological fallacy

The ecological fallacy, sometimes referred to as the ecological inference fallacy, describes a fallacious inference made about a particular individual from statistical data in reference to whatever group that individual is part of.[1] It's a fallacy very similar to the fallacy of composition/division or category mistake.

Cogito ergo sum
Logic and rhetoric
Key articles
General logic
Bad logic
v - t - e

Example
P1: Women on average tend to score higher on mathematical calculation when compared to men.
P2: Sarah is a woman, while Jack is a man.
C1: Therefore Sarah is better at mathematical calculation than Jack.

This is a fallacy because the inference about an individual doesn't necessarily follow from the group generalization. In statistics, the average, or arithmetic mean, is the sum of all the scores in a given set divided by the number of scores. More often than not, such statistical trends form a normal distribution (or Gaussian/bell curve) with individuals existing all over the distribution, though most will center in the middle. Sarah can be anywhere under the bell curve, she could be in the extreme low end, or even the extreme high end, we can't necessarily know without first testing her. Even if, hypothetically, women score higher on average in mathematical calculation there can still be great overlap between the bell curves for men and women. So it doesn't necessarily follow that Sarah will be better at math than Jack. This is, of course, assuming that such a distribution forms a bell curve; statistical distributions can take on other shapes. Regardless, you can't infer such a conclusion about an individual from a demographic generalization.

Reference
  1. Ecological Fallacy Logically Fallacious.
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