In a study of a town, the population is 30% age 40+, 50% age 25-39, and 20% age 24 and under. A sample of 50 includes 30 in 40+, 15 in 25-39, and 5 under 25. Is this sample representative?

• A. Yes, representative.
• B. No, overrepresents older than 40 and underrepresents younger than 25.
• C. No, underrepresents older than 40.
• D. No, biased toward younger than 25.

Answer: (B)

This question tests whether a sample reflects the population, i.e., its representativeness across age groups.

The town population is 30% age 40+, 50% age 25–39, and 20% under 25. The sample of 50 has 30 in 40+ (60%), 15 in 25–39 (30%), and 5 under 25 (10%). These proportions differ from the population: 60% vs 30% for 40+, 30% vs 50% for 25–39, and 10% vs 20% for under 25.

Because the sample does not match the population, it is not representative. The pattern shows an overrepresentation of older than 40 and an underrepresentation of younger than 25. It’s not biased toward younger than 25; it’s biased toward older than 40.