Population, Sample, Parameter, and Statistic

These four terms are fundamental in statistics because they help us understand how data is collected and how conclusions are drawn.

1. Population

A population is the entire group of individuals, items, or observations that we want to study.

Key Points

• It is the complete set.
• Can be large or small.
• Can be finite or infinite.

Examples

• All students in a school
• All voters in a country
• All manufactured bulbs in a factory

2. Sample

A sample is a small part of the population selected for study. Because studying the entire population is often costly or impossible, we study a sample instead.

Key Points

• It represents the population.
• Should be chosen carefully to avoid bias.

Examples

• 100 students selected from a school
• 1,000 voters selected from a country
• 50 bulbs tested from a factory

3. Parameter

A parameter is a numerical value that describes a characteristic of the population.

Key Points

• It is based on the entire population.
• Usually unknown because studying an entire population is difficult.
• Represented by Greek letters (e.g., μ for population mean, σ for population standard deviation).

Examples

• The average height of all students in a school
• The percentage of all citizens who support a political party
• The true lifespan of all bulbs produced

4. Statistic

A statistic is a numerical value calculated from the sample.

Key Points

• It estimates the population parameter.
• Represented by English letters (e.g., x̄ for sample mean, s for sample standard deviation).
• Used in inferential statistics to make predictions.

Examples

• The average height of the 100 selected students
• The proportion of 1,000 sampled voters supporting a party
• The average lifespan of 50 tested bulbs

Summary Table

Simple Way to Remember

• Population = Whole group
• Sample = Small group
• Parameter = Information about population
• Statistic = Information about sample