Representativeness Math Example 3
Follow the full solution, then compare it with the other examples linked below.
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.
Solution
- 1 Method 1: Simple random sampling — assign numbers 1–30 to students, use random number generator to select 10
- 2 Method 2: Stratified sampling — if class has subgroups (gender, grade level), sample proportionally from each
- 3 Limitation of selecting friends: friendship groups tend to be similar in demographics, interests, attitudes — creates a biased, non-representative sample
Answer
Use simple random or stratified sampling. Friend selection creates biased, non-representative results.
Convenience samples (like selecting friends) almost always introduce bias because social groups are internally similar. Random selection is the only method that guarantees expected representativeness across all characteristics, including ones we haven't thought to control.
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 2 mediumThe Representativeness Heuristic: A person is described as quiet, enjoys books, and is very detail-o
Example 4 hardA clinical trial recruits patients from a university hospital. Explain why results may not be repres