Welcome to a brand-new chapter! So far we have mastered Permutations, Combinations and the basics of Probability. Now we step into the world of Statistics — the subject that helps us make sense of data and uncertainty in everyday life.
In simple words, Statistics is the science of collecting, organising, analysing, interpreting and presenting data so that we can take better decisions.
Statistics is the study of data — how to gather it, how to understand it, and how to use it to answer questions about the real world.
This is an introductory chapter. Here is the roadmap we will follow:
We will start slowly and build everything step by step.
When we are not sure about the outcome of an experiment, such experiments are called random experiments. The numerical quantity that takes different values depending on the outcome of a random experiment is called a Random Variable.
A Random Variable is a variable whose value is determined by the outcome of a random experiment.
We mainly classify random variables into two types:
Definition: A discrete random variable takes countable values such as 0, 1, 2, 3, …
Examples:
Definition: A continuous random variable can take any value within a continuous range (including decimal values).
Examples:
| Discrete Random Variable | Continuous Random Variable |
|---|---|
| Takes countable values | Takes any value within a range |
| Usually counted | Usually measured |
| Example: Number of books | Example: Weight of a book |
| Probability is assigned to exact points | Probability is assigned to intervals |
Discrete = Count | Continuous = Measure
Here is a clean, beginner-friendly classification of Random Variables that you can memorise:
Quick memory tip: Discrete → Count (PMF) | Continuous → Measure (PDF)
This is just an overview, so don’t worry if some of these terms went over your head! We’ll break everything down step by step and cover it all in detail in the upcoming lessons. No panic, just probability! 😎📚
In the next lesson we will start with Discrete Random Variables and learn how to write the Probability Mass Function (PMF) with simple examples.
