Populations, Samples, and Parameters
In statistics, we rarely study every individual or item in a group. Instead, we usually study a smaller part and use it to understand the whole. This lesson explains how that works.
To do this correctly, we must clearly understand three important ideas: population, sample, and parameter.
What Is a Population?
A population is the complete set of all individuals, items, or observations that we are interested in studying.
The population includes every possible case related to the question we are trying to answer.
Examples of populations:
- All students in a university
- All customers of a company
- All manufactured products in a factory
- All voters in a country
In many real-world situations, studying the entire population is difficult, expensive, or sometimes impossible.
What Is a Sample?
A sample is a smaller group selected from the population. The sample is used to represent the population.
Instead of collecting data from everyone, we collect data from a sample and analyze it.
Examples of samples:
- 200 students selected from a university
- 500 customers chosen from a customer database
- 50 products tested from a production batch
If a sample is chosen properly, it can provide very accurate information about the population.
Why Do We Use Samples?
Using samples is a practical necessity in statistics.
We use samples because:
- Studying the entire population may be too costly
- Collecting population data may take too much time
- Some populations are extremely large
- Testing every item may be destructive (for example, product testing)
Sampling allows us to make decisions efficiently while still maintaining accuracy.
Population vs Sample (Key Idea)
It is very important to understand the difference between population and sample:
- The population is the whole group
- The sample is a part of that group
Statistics uses sample data to make conclusions about the population.
What Is a Parameter?
A parameter is a numerical value that describes a characteristic of a population.
Parameters are fixed values, but they are usually unknown because we do not observe the entire population.
Examples of parameters:
- The average income of all citizens in a country
- The true proportion of defective products in a factory
- The exact average height of all students in a school
Because parameters describe the population, they are often difficult to measure directly.
Sample Statistics
When we calculate values using sample data, the results are called sample statistics.
Sample statistics are used to estimate population parameters.
Examples of sample statistics:
- Average height calculated from a group of students
- Percentage of satisfied customers from a survey
- Average test score from a class
The goal of statistics is to use sample statistics to learn about population parameters.
Why Sampling Must Be Done Carefully
If a sample does not properly represent the population, the conclusions will be incorrect.
Poor sampling can lead to:
- Biased results
- Incorrect predictions
- Wrong decisions
That is why sampling methods are extremely important and will be discussed in later lessons.
Real-World Example
Suppose a company wants to know whether customers are satisfied with a product.
Instead of asking every customer, the company surveys a group of customers.
- All customers → Population
- Surveyed customers → Sample
- True satisfaction rate → Parameter
- Survey result → Sample statistic
This is how statistics is applied in real-life decision-making.
What’s Next
In the next lesson, we will study Descriptive and Inferential Statistics. This will explain how statistics is used to summarize data and make conclusions about populations.