Representativeness Math Example 1
Follow the full solution, then compare it with the other examples linked below.
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.
Solution
- 1 Current sample: 50 adults (50%), 50 children (50%) — does NOT match 60%/40% city distribution
- 2 For representativeness: sample should reflect 60% adults, 40% children
- 3 Proportionally representative sample of 100: adults; children
- 4 Method: stratified random sampling — randomly select from each group (stratum) proportional to its size
Answer
Current sample is not representative. A representative sample of 100 needs 60 adults and 40 children.
A representative sample mirrors the population's characteristics. Stratified sampling ensures each subgroup is represented in proportion to its population share, eliminating systematic under/over-representation of any group.
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
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