Practice Representativeness in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A sample is representative if its characteristics (distribution of key variables) closely match those of the population it is meant to represent.
A representative sample is a miniature version of the population — every relevant group is included in the right proportions so the sample mirrors the whole.
Example 1
easyA city is 60% adults and 40% children. A survey samples 50 adults and 50 children. Is this sample representative of the city's age distribution? Design a proportionally representative sample of 100 people.
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.
Example 3
easyA sample of 10 people from a class of 30 is selected. List two methods to ensure the sample is representative, and explain the limitation of randomly selecting 10 friends.
Example 4
hardA clinical trial recruits patients from a university hospital. Explain why results may not be representative of the general patient population, and identify at least two characteristics that may differ.