📈 Intro to Statistics · Lesson 1 of 7
Data, variables and sampling
Categorical vs. quantitative, populations, samples and bias.
Types of variables
| Categorical | Groups or labels: major, state, yes/no |
|---|---|
| Quantitative | Numbers you can average: height, GPA, minutes of sleep |
| Discrete vs. continuous | Counts (number of siblings) vs. measurements (weight) |
Population and sample
The population is everyone you want to learn about (all US college students). A sample is the group you actually measure (500 students). A number describing a population is a parameter; one describing a sample is a statistic. We use statistics to estimate parameters.
Good and bad samples
| Simple random sample | Everyone has an equal chance — the gold standard |
|---|---|
| Stratified | Random samples from each group (e.g., each class year) |
| Convenience sample | Whoever is easy to reach — often biased |
| Voluntary response | People choose to answer — strong opinions over-represented |
Studies vs. experiments
In an observational study you only observe; you can find associations but not prove cause. In an experiment you randomly assign treatments, so differences can be attributed to the treatment. “Correlation is not causation” starts here.
Tip
💡 Before trusting any statistic, ask: who was measured, how were they chosen, and how many?
✏️ Practice: your turn
- Classify 6 variables from a survey as categorical or quantitative
- Identify the population and sample in a news article about a study
- Explain why an online poll is a voluntary response sample
- Decide: was a study you read observational or an experiment?
✏️ Scientific calculator with a statistics tab (mean, median, standard deviation)
🧠 Quick quiz
Answer all 4 questions correctly to mark this lesson as done.
0 of 4 correct
All lessons in Intro to Statistics
- 🎲 1. Data, variables and samplingCategorical vs. quantitative, populations, samples and bias
- 🎯 2. Mean, median and modeMeasures of center, and which one to use when data are skewed
- ↔️ 3. Spread: range, IQR and standard deviationHow spread out the data are, and how to read a box plot
- 🔔 4. The normal curve and z-scoresThe 68–95–99.7 rule and comparing values on different scales
- 📉 5. Correlation and regressionScatterplots, r, the line of best fit — and causation
- 🎯 6. Confidence intervalsEstimate ± margin of error, and what “95% confident” means
- ⚗️ 7. Hypothesis tests and p-valuesNull and alternative, the p-value, significance and errors