Representativeness Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumThe Representativeness Heuristic: A person is described as quiet, enjoys books, and is very detail-oriented. Most people guess 'librarian' over 'farmer.' Explain why this can be a probabilistic error using base rates.
Solution
- 1 Base rate: there are approximately 1 librarian per 10,000 people vs. many more farmers in the general population
- 2 The description matches stereotypes of a librarian, triggering representativeness heuristic
- 3 Bayesian thinking: even if 80% of librarians fit this description and only 20% of farmers do, if farmers vastly outnumber librarians, the person is probably a farmer
- 4 Math: depends on (base rate), which is very low
Answer
Ignoring base rates (low librarian frequency) makes the common guess 'librarian' statistically wrong.
The representativeness heuristic ignores prior probabilities (base rates). Bayesian reasoning requires combining both the description's match and the base rate probability. This cognitive bias leads to systematic errors in probability judgments.
About Representativeness
A sample is representative if its characteristics (distribution of key variables) closely match those of the population it is meant to represent.
Learn more about Representativeness →More Representativeness Examples
Example 1 easy
A city is 60% adults and 40% children. A survey samples 50 adults and 50 children. Is this sample re
Example 3 easyA sample of 10 people from a class of 30 is selected. List two methods to ensure the sample is repre
Example 4 hardA clinical trial recruits patients from a university hospital. Explain why results may not be repres