Statistics: describes data (what you see). Probability: models uncertainty (what you don’t know yet).
Summarise a dataset using central tendency and variability
Explain core probability ideas using simple examples
Apply the axioms of probability
Distinguish mutually exclusive vs independent events
flowchart TD
A[Dataset] --> B[Central Tendency]
A --> C[Variability]
B --> B1[Mean]
B --> B2[Median]
B --> B3[Mode]
C --> C1[Range]
C --> C2[Variance]
C --> C3[Standard Deviation]
C --> C4[IQR]
Central tendency tells you where the “middle” of the data is.
Describes a set of scores with a single number that describes the PERFORMANCE of the group.
Probability models uncertainty:
what you don’t know yet, but want to reason about.
Key takeaway:
Probability is a number between 0 and 1 that measures how likely an event is.
The whole topic is about defining events clearly and applying a few core rules consistently.
Probability quantifies uncertainty: a number between 0 and 1.
Probability often changes when we learn new information.
Conditional probability and Bayes’ theorem give a structured way to update beliefs using evidence.
Conditional probability updates probabilities after observing an event.
Bayes’ theorem lets you estimate a hidden cause from observed evidence.
Naïve Bayes turns Bayes’ theorem into a practical classifier by assuming conditional independence of features given the class.
flowchart TD
A[Conditional<br/>probability] -->|foundation| B[Bayes<br/>theorem]
D[Independent<br/>events] -->|implies| C[Independence]
C -->|simplifies| A
E[Prior] -->|with likelihood| B
F[Likelihood] -->|updates| H[Posterior]
G[Evidence] -->|normalises| B
B -->|yields| H
I[Naïve<br/>Bayes] -->|uses| B
J[Naïve<br/>assumption] -->|assumes| C
K[Features] -->|given class| J
L[Class] -->|conditions| J
I -->|predicts| M[Classification]
M -->|selects| L
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