Course · Data Analytics

Statistics and Probability from Scratch

A practical course in statistics and probability for analysts: descriptive statistics (mean, median, variance, IQR), probability and conditional probability (Bayes' theorem, the base rate fallacy), counting, distributions (binomial, normal, the 68–95–99.7 rule), sampling and the CLT, confidence intervals, and hypothesis testing. A companion to the Data Analytics course.

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PepelenCourse author

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Unit 1. Descriptive statistics

Lesson 1: Mean, median, and mode — and when to use which

8 exercises · Calculate the mean, median, and mode of a small data set and choose a measure deliberately, understanding how sensitive the mean is to outliers.

Lesson 2: Spread — range, variance, standard deviation, IQR

8 exercises · Calculate the range, variance, and standard deviation, find the quartiles and the IQR, and understand what each measure says about spread.

Lesson 3: Outliers, resistance, and sample vs. population

6 exercises · Distinguish a sample (n) from a population (N), understand Bessel's correction (n−1), and choose measures that are resistant to outliers.

Unit 2. Probability basics

Lesson 1: Outcomes, events, and probability from 0 to 1

7 exercises · Define the sample space and an event, and calculate P(A) as the proportion of favorable outcomes, a number from 0 to 1.

Lesson 2: The addition rule and overlapping events

7 exercises · Apply the addition rule P(A or B)=P(A)+P(B)−P(A and B), correctly accounting for the intersection of the events.

Lesson 3: The multiplication rule and independence

7 exercises · Apply the multiplication rule and check whether events are independent using P(A and B)=P(A)·P(B).

Unit 3. Conditional probability, Bayes, and counting

Lesson 1: Conditional probability P(A|B)

7 exercises · Calculate the conditional probability P(A|B)=P(A and B)/P(B) and understand how a new condition changes a probability.

Lesson 2: Bayes' theorem and the base rate fallacy

7 exercises · Update a probability with Bayes' theorem and recognize the base rate fallacy, without confusing P(A|B) and P(B|A).

Lesson 3: Counting — arrangements, permutations, combinations

7 exercises · Calculate arrangements, permutations, and combinations, and choose the formula by asking “does order matter?”

Unit 4. Distributions

Lesson 1: Random variables and expected value

7 exercises · Distinguish discrete from continuous random variables and calculate the expected value of a discrete random variable.

Lesson 2: The binomial distribution

7 exercises · Apply the binomial distribution to find the probability of k successes in n independent trials with probability p.

Lesson 3: The normal distribution, the 68–95–99.7 rule, and z-scores

7 exercises · Use the normal distribution and the 68–95–99.7 rule, and calculate a z-score to standardize a value.

Unit 5. Sampling, the CLT, and confidence intervals

Lesson 1: Random sampling and sampling bias

6 exercises · Tell a random sample from a biased one and recognize sources of bias in how data are collected.

Lesson 2: The Central Limit Theorem and standard error

7 exercises · Explain the Central Limit Theorem and calculate the standard error of the mean SE=SD/√n.

Lesson 3: Confidence intervals and how to read them correctly

6 exercises · Understand what a confidence interval means and interpret a 95% CI as a property of the procedure, not as a probability for a particular interval.

Unit 6. Hypothesis testing and its pitfalls

Lesson 1: Null and alternative hypotheses, α, and the p-value

7 exercises · State H0/H1, understand the significance level α, and interpret the p-value correctly.

Lesson 2: Type I and Type II errors, statistical vs. practical significance, correlation ≠ causation

7 exercises · Tell Type I and Type II errors apart, distinguish statistical significance from practical significance, and avoid confusing correlation with causation.

Lesson 3: Capstone case — drawing a sound statistical conclusion

4 exercises · Draw a sound statistical conclusion about a real-world situation using concepts from the whole course, and check yourself against a checklist.