Introduction to Sample and Population in Statistics

This lecture explains the concepts of sample and population in statistics, supported by examples.

Definitions

• Population: Refers to the entire group of individuals or observations of interest in a study. Example: All individuals worldwide with a disease (e.g., Disease X).
• Sample: A subset of the population selected for the study, usually because it is impractical or impossible to study the entire population.
  • Example: 50 people with Disease X selected randomly for a study.

Importance of Sampling

• Recruiting an entire population is often impractical due to:
  • Declination of participation.
  • Geographical dispersion.
• A sample helps in making general conclusions about the population.

Statistical Measures

• Statistic: A measure obtained from a sample.

  • Example: Average life expectancy in the sample is 51 years.
  • Denoted by symbol: ( \bar{x} ) (x-bar).

• Parameter: A measure obtained from the entire population.

  • Example: Average life expectancy in the population is 56 years.
  • Denoted by symbol: ( \mu ) (mu).

Differences Between Sample Statistics and Population Parameters

• Variations occur due to:
  • Sampling Error: Random differences between the sample and the population due to not sampling the entire population.
    • Example: Sample may have more individuals with unhealthy habits than the general population, affecting results.
  • Selection Bias: Occurs when the sample is not randomly selected.
    • Example: Advertising study through Facebook may exclude non-Facebook users.

Conclusion

• Population: Contains all observations.
• Sample: A subset used to infer conclusions about the population.
• Statistics from samples differ from population parameters due to sampling error and selection bias.

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