Statistics is the science of collecting, organizing, analyzing and interpreting data, so that a decision can rest on evidence instead of a guess.
1 Our example for this lesson
Imagine a maths class of 12 students. After the first semester, their marks are:
82, 85, 77, 70, 74, 66, 79, 80, 91, 94, 95, 96
This small class is the example we will use for the whole lesson.
2 What is data?
Data are facts or pieces of information recorded about something. For our class, we could record:
- each student’s marks (numbers),
- each student’s age (numbers),
- each student’s favourite subject (categories),
- each student’s blood group (categories).
So data can be numbers or categories. This difference matters, because it decides which methods we can use later.
3 Two kinds of questions
Let’s ask two questions about our class.
3.1 Question 1: “What is the average mark in this class?”
We already have all 12 marks, so nothing is missing. Add them up (989) and divide by 12:
\[ \text{Average} = \frac{989}{12} \approx 82.4 \]
Organizing and summarizing the data you already have is called descriptive statistics. It uses tables, charts, and numbers such as the average.
3.2 Question 2: “Are the marks in this class similar to the marks of all maths classes in the college?”
Now we are asking about students whose marks we never collected. We only have one class, so we must infer the answer from it, and accept that we cannot be completely sure. This is inferential statistics: using a small group to draw conclusions about a larger group, and saying how uncertain those conclusions are.
| Descriptive statistics | Inferential statistics | |
|---|---|---|
| Question | “What is in my data?” | “What does my data say about everyone else?” |
| Our example | The average mark of these 12 students | Whether this class is like all maths classes |
| Based on | Only the data you have | A small group standing in for a larger one |
| Certainty | Exact for these 12 students | Comes with some uncertainty |
You will learn both in this series.
4 Why do we need statistics?
A school, a hospital or a government can have more data than anyone could read line by line. Statistics turns that pile of numbers into an answer people can act on, and tells them how sure that answer is.
5 The learning path
The course has 10 parts, which fall into three stages.
| Stage | Parts | What you learn |
|---|---|---|
| Describe the data | 1–4 | Types of data, tables and charts, average, spread, percentiles, box plots, outliers |
| Understand chance | 5–7 | The normal distribution, probability, common distributions, the central limit theorem |
| Draw conclusions | 8–10 | Estimation, hypothesis testing, statistical tests, relationships between variables |
The ten parts, in order:
- What statistics is
- Describing data with tables and charts
- Centre and spread
- Percentiles, quartiles and box plots
- The normal distribution
- Probability
- Probability distributions
- Estimation and hypothesis testing
- Statistical tests
- Relationships between variables
6 Who is this for?
- Beginners in data science and data analysis
- Anyone preparing for interviews that ask basic statistics questions
- Learners who want a strong base before moving on to machine learning
7 What you need
- School maths: averages, fractions, percentages, squares and square roots
- Curiosity about data
That’s all for now. We’ll set up the software when we reach the practical lessons.
8 How each lesson works
Each lesson begins with a one-sentence definition. It then explains the idea with a simple example, turns the idea into a formula, and works the formula out by hand on small numbers. At the end, you get a few small things to try yourself.
9 Try it yourself
- If one student’s mark were 20 instead of 66, would the class average go up or down? Take a guess before calculating.
- Write one question about your own class that is descriptive, and one that is inferential.
- Name two pieces of numeric data and two pieces of categorical data you could collect about your class.
10 Key takeaways
- Statistics helps us make decisions from evidence.
- Data can be numbers or categories.
- Descriptive statistics summarizes the data you have.
- Inferential statistics uses a small group to say something about a larger group, with some uncertainty.
Next: Lesson 1 · Installing software →