What You Will Learn
- What inferential statistics means
- The difference between a population and a sample
- The difference between a parameter and a statistic
- How samples can be used to learn about populations
- Why uncertainty is important in statistical inference
- How inferential statistics is used in data analytics
What Is Inferential Statistics?
Inferential statistics is the branch of statistics that helps us use information from a sample to make estimates, comparisons, or decisions about a larger population.
Imagine that a company has 100,000 customers. It may be expensive or impossible to ask every customer a question. Instead, the company can select a smaller group of customers, collect their responses, and use the sample data to learn about the larger customer population.
The basic idea
Population
Sample
Inference
Descriptive vs Inferential Statistics
A useful way to understand inferential statistics is to compare it with descriptive statistics.
Population and Sample
Population
A population is the complete group that we are interested in studying.
For example, if we want to understand the average monthly spending of all customers of a company, all of those customers form the population.
Sample
A sample is a smaller group selected from the population for analysis.
A university has 20,000 students. Researchers select 500 students and ask them about their daily study time.
Population
20,000 university students
Sample
500 selected students
Parameter and Statistic
Two important words in inferential statistics are parameter and statistic.
Parameter
A parameter describes a characteristic of the entire population.
Example: Population mean
Statistic
A statistic describes a characteristic calculated from a sample.
Example: Sample mean
Population → Parameter
Sample → Statistic
Why Do We Use Samples?
In many real-world situations, studying every member of a population is impractical.
Cost
Studying an entire population may require significant resources.
Time
Collecting information from everyone can take too long.
Practicality
Sometimes measuring the whole population is simply not possible.
The Statistical Inference Process
Define the population
Identify the group you want to understand.
Collect a sample
Select observations from that population.
Calculate statistics
Calculate values such as the sample mean or proportion.
Quantify uncertainty
Recognize that a sample does not perfectly represent the population.
Make an inference
Use the evidence to estimate or evaluate something about the population.
Real-World Data Analytics Example
Suppose an e-commerce company has 500,000 customers and wants to estimate the average amount customers spend per month.
Instead of calculating the spending of all 500,000 customers, the company selects a sample of 1,000 customers and calculates their average monthly spending.
Population
500,000 customers
Sample
1,000 customers
Goal
Estimate population spending
This is the core idea of inferential statistics: use information from a sample to learn about a population while accounting for uncertainty.
Interactive Practice
Check Your Understanding
Answer the questions before moving to the next lesson.
CHECK YOUR UNDERSTANDING
A company has 100,000 customers and researchers select 2,000 customers for a survey. What are the 2,000 customers?
CHECK YOUR UNDERSTANDING
Which branch of statistics uses sample information to learn about a population?
CHECK YOUR UNDERSTANDING
A value calculated from a sample is called a:
CHECK YOUR UNDERSTANDING
Which statement best describes a parameter?
CHECK YOUR UNDERSTANDING
Why might a researcher use a sample instead of studying the entire population?
Fill in the Blanks
A smaller group selected from a population is called a ______.
A numerical measure calculated from a sample is called a ______.
A numerical characteristic describing an entire population is called a ______.
The branch of statistics that uses samples to learn about populations is called ______ statistics.
Scenario Challenge
Think Like a Data Analyst
A food delivery company has 200,000 customers. The analytics team randomly selects 1,500 customers and finds that their average monthly spending is ₹2,800.
CHECK YOUR UNDERSTANDING
What is the population in this example?
CHECK YOUR UNDERSTANDING
What does ₹2,800 represent in this example?
Key Takeaways
Inferential statistics uses sample data to learn about a population.
A population is the complete group being studied.
A sample is a subset selected from the population.
A parameter describes a population.
A statistic describes a sample.
Inference always involves uncertainty because a sample may not perfectly represent the population.