This SL mini-lesson is the AI heartland: sampling methods and data, measures of centre & spread, correlation & regression, probability (Venn/tree diagrams, conditional), the binomial and normal distributions, and the χ² test for independence.
AI flavour: statistics is the largest strand — you design samples, run tests on your GDC and interpret results in context.
Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Every number on the calculation screens has been re-derived and checked. Press Start when you are ready.
Data & sampling
Sampling methods
Simple random — every member equally likely; needs a sampling frame.
Systematic — every k-th member from a list.
Stratified — sample each subgroup in proportion to its size.
Quota / convenience — quick but potentially biased.
Bias makes a sample unrepresentative — watch for self-selection and undercoverage.
Centre & spread
Averages & standard deviation
The mean is the balance point; the standard deviation σ measures spread. For data 4, 7, 7, 9, 10, 13:
2For X ~ B(10, 0.3), find P(X = 4) to 4 decimal places using the binomial formula (or GDC binompdf).
Hint: 10C4 × 0.3⁴ × 0.7⁶.
Normal
The normal distribution
A continuous, symmetric, bell-shaped model X ~ N(μ, σ²). Areas under the curve are probabilities (use GDC normalcdf / inverse normal).
Worked example
X ~ N(50, 8²).
P(X < 60) = 0.8944
P(45 < X < 60) = 0.6284
90th percentile (inverse normal) = 60.25
Calculate
Your turn — normal probability
3For X ~ N(50, 8²), find P(X < 60) to 4 decimal places (GDC normalcdf, lower = −1E99).
Hint: standardise z = (60 − 50) ÷ 8 = 1.25, then read the area.
χ² test
Chi-square test for independence
The χ² test checks whether two categorical variables are independent. From a contingency table of observed O, compute expected E = (row total × column total) ÷ grand total, then:
χ²calc = Σ (O − E)² ÷ Edegrees of freedom = (rows − 1)(columns − 1)
Worked example — 2×3 table
Observed: 20,30,10 / 30,20,40 (grand total 150).
χ²calc = 16.67, df = (2−1)(3−1) = 2
Critical value at 5% = 5.991. Since 16.67 > 5.991, reject H₀ — the variables are associated.
Calculate
Your turn — degrees of freedom
4A χ² test uses a 3 × 3 contingency table. State the number of degrees of freedom, (r − 1)(c − 1).
Hint: (3 − 1) × (3 − 1).
Calculate
Your turn — χ² decision
5A χ² test gives χ²calc = 16.67 with critical value 5.991 at the 5% level. Enter 1 if you reject H₀ (association exists), or 0 if you do not.
Hint: reject H₀ when χ²calc is greater than the critical value.
Sort it
Sort the statistics idea
Tap a term, then the strand it belongs to.
🎲 Probability
🔔 Distribution
🧪 Hypothesis test
Quick check
χ² conclusion
?In a χ² test for independence, you reject H₀ when:
Quick check
Stratified sampling
?A school has 60% junior and 40% senior students. A stratified sample of 50 should contain how many juniors?
Match it
Match the tool to its job
Tap an item on the left, then its match on the right.
Item
Match
Correlation vs causation
Interpreting correlation with care
A strong r shows association, not cause. Confounding variables (a hidden third factor) can create correlation without any causal link.
In your exam, state associations cautiously and avoid claiming one variable causes the other.
Quick check
Correlation caution
?Ice-cream sales and drowning rates are strongly positively correlated. The best explanation is: