Assume that the proportion or mean of a sample is equal to that of the population, and estimate the entire population.
📘 Example ① (Estimating a Proportion)
When 50 people were randomly selected from 500 people, 20 answered “in favor.” Estimate the number of people in favor in the entire population.
Answer:Sample proportion = 20/50 = 0.4 (40%). Estimated number = 500 × 0.4 = 200 people
When 50 people were randomly selected from 500 people, 20 answered “in favor.” Estimate the number of people in favor in the entire population.
Answer:Sample proportion = 20/50 = 0.4 (40%). Estimated number = 500 × 0.4 = 200 people
📘 Example ② (Fish in a Pond)
One hundred fish were caught from a pond, marked, and released. Later, 80 fish were caught, and 4 of them were marked. Estimate the total number of fish in the pond.
Answer:Proportion of marked fish = 4/80 = 1/20. Total number × (1/20) = 100, so total number = 2000 fish
One hundred fish were caught from a pond, marked, and released. Later, 80 fish were caught, and 4 of them were marked. Estimate the total number of fish in the pond.
Answer:Proportion of marked fish = 4/80 = 1/20. Total number × (1/20) = 100, so total number = 2000 fish
💡 Key Point
- Sample proportion = population proportion (assumed)
- Estimated value = population size × sample proportion
Practice Problem
- When 100 people were sampled from 1000 people, 30 answered “I use it.” Estimate the number of people who use it in the population.
Answer and Explanation
- Answer:300 people. Sample proportion=30/100=0.3. 1000×0.3=300.