Identifying Populations and Samples

Populations and Samples

Population

  • In a statistical study, the population is the complete set of people or things being studied.
    • Examples:
      • All Americans
      • All books in a specific genre

Population Parameters

  • Specific numbers describing characteristics of a population.

    • Example 1: If the population is all Americans, a population parameter of interest might be the percentage of all Americans who will vote for a particular candidate in a national election.
    • Example 2: If the population is all books in a particular genre, a population parameter of interest might be the average page count of all books in that genre.

  • Often, it is impractical to examine every member of a population due to its size.

    • Too many books to look at every single one.
    • Too many Americans to survey each one.

Sample

  • A sample is a subset of the population from which data are obtained.
    • Example 1: Surveying a sample of 2,000 Americans instead of all Americans.
    • Example 2: Examining 1,000 books from a specific genre instead of every book in that genre.

Sample Statistics

  • Numbers describing particular characteristics of the sample, summarizing the raw data collected.
  • Sample statistics are used to estimate the value of a population parameter.
    • Example: Collecting data from a sample of 2,000 Americans to find the percentage in that sample who will vote for a particular candidate. This percentage from the sample is a statistic used to estimate the percentage of the entire population who will vote for that candidate.

Example 1

  • Study: Based on a study of 1,000 homeowners, it was estimated that 98% of all homeowners have internet access at home.
    • Sample: 1,000 homeowners
    • Population: All homeowners
    • Sample Statistic: 98% (used to estimate the percentage of all homeowners with internet access)

Example 2

  • Survey: In a survey of 2,500 college students, it was concluded that the average amount of time all college students spend studying per week was 2.25 hours per class.
    • Sample: 2,500 college students
    • Population: All college students
    • Sample Statistic: 2.25 hours (being used to estimate the average amount of time all college students spend studying per class each week)