The entire group being studied is called the population, and a portion taken from it is called a sample.
・Population mean μ, population variance σ²
・Sample mean X̄, sample variance s²
Example ① Estimate the mean height μ of all high school students in the country using the sample mean X̄ of a random sample of 100 students. What are the population and sample?
Solution:Population = all high school students in the country; sample = the 100 selected students.
Solution:Population = all high school students in the country; sample = the 100 selected students.
Key Point
- Population parameters (μ, σ²) are usually unknown and are estimated from a sample
- Random sampling is fundamental
Practice Problems
- In “the approval rating of voters in a town was investigated through an opinion poll of 1000 people,” identify the population and sample.
Solutions and Explanations
- Solution:Population = all voters in the town; sample = the 1000 people surveyed.