What You Will Learn
- What a statistical population means
- What a sample means
- How population and sample are related
- Why analysts often work with samples
- How sample size affects information available to us
- How to identify populations and samples in real situations
What Is a Population?
In statistics, a population is the complete group of people, objects, transactions, measurements, or observations that we want to study.
The word population does not necessarily mean people. A population can be customers, products, hospitals, transactions, machines, websites, students, or any other group relevant to a statistical question.
Example
A company wants to understand the satisfaction of all 50,000 customers who purchased a product during the year.
Population = all 50,000 customers
Think of the Population as the Full Group
Population
These symbols represent members of the complete population.
What Is a Sample?
A sample is a smaller group selected from the population for analysis.
Instead of collecting information from every member of a population, a researcher can collect information from a sample and use it to learn about the larger group.
Example
From the 50,000 customers, the company randomly selects 1,000 customers and asks them to rate their experience.
Sample = 1,000 selected customers
Population → Sample
Population
Sample
The sample is a subset of the population.
Why Don't We Always Study Everyone?
If the population is very large, collecting data from every individual can be expensive, slow, or difficult.
Cost
Collecting information from millions of observations can be expensive.
Time
Sampling can provide useful information much faster.
Scale
Some populations are so large that studying every member is impractical.
Important: A Sample Is Not Automatically Representative
Simply taking a small sample does not guarantee a reliable conclusion. How the sample is selected matters.
If a sample systematically excludes important parts of the population, the resulting estimate can be misleading. This is why sampling methods are an important part of inferential statistics.
We will study sampling methods in Lesson 3.
Example: Student Survey
Suppose a college has 10,000 students and wants to estimate the average amount of time students spend studying each week.
Population
10,000 students
Every student at the college.
Sample
500 students
The students selected for the study.
If the selected students are appropriately sampled, their data can provide evidence about the study habits of the larger student population.
Census vs Sample
There is an important distinction between studying the entire population and studying only a sample.
Interactive Practice
Test Your Understanding
CHECK YOUR UNDERSTANDING
A hospital has 25,000 patients in its database. Researchers select 800 patients for a study. What is the population?
CHECK YOUR UNDERSTANDING
In the same study, what are the 800 selected patients?
CHECK YOUR UNDERSTANDING
Which statement is correct?
CHECK YOUR UNDERSTANDING
Why might a company study a sample of customers instead of every customer?
CHECK YOUR UNDERSTANDING
Does a small sample automatically guarantee a reliable conclusion?
Fill in the Blanks
The complete group being studied is called the ______.
A smaller group selected from a population is called a ______.
Studying every member of a population is called a ______.
Data Analytics Scenario
Identify the Population and Sample
An online shopping platform has 2 million registered customers. The analytics team randomly selects 5,000 customers to study purchasing frequency.
CHECK YOUR UNDERSTANDING
What is the population?
CHECK YOUR UNDERSTANDING
What is the sample?
Key Takeaways
A population is the complete group of interest.
A sample is a subset selected from that population.
A population can contain people, transactions, products, measurements, or other observations.
A census attempts to study every member of the population.
Sampling can reduce the cost and time required for data collection.
A sample is not automatically representative; the sampling method matters.