Statistics Module
Beginner to Advanced.
Master data handling, probability, and inferential statistics — fully aligned to the CAPS curriculum for Grade 8–12.
Beginner — Grade 8–10
Build a solid foundation in data collection, representation, and basic probability.
Beginner Topics
Worked Examples
Step-by-step solutions — the same method your teacher and the NSC memo use.
The ages of 8 learners are: 14, 15, 15, 16, 17, 17, 17, 18. Find the mean, median, mode, and IQR.
Mean = (14+15+15+16+17+17+17+18) ÷ 8 = 129 ÷ 8 = 16.125
Median = average of 4th and 5th values = (16+17) ÷ 2 = 16.5
Mode = 17 (appears 3 times)
Q1 = median of lower half {14,15,15,16} = (15+15)÷2 = 15
Q3 = median of upper half {17,17,17,18} = (17+17)÷2 = 17
IQR = Q3 − Q1 = 17 − 15 = 2
A sample of 36 students has a mean exam score of 68 and a standard deviation of 12. Construct a 95% confidence interval for the true population mean.
Identify: x̄ = 68, σ = 12, n = 36, z* = 1.96 (for 95% CI)
Calculate margin of error: E = z* × (σ/√n) = 1.96 × (12/√36) = 1.96 × 2 = 3.92
Lower bound: 68 − 3.92 = 64.08
Upper bound: 68 + 3.92 = 71.92
95% CI: (64.08 ; 71.92)
Interpretation: We are 95% confident the true population mean lies between 64.08 and 71.92.
Test the hypothesis that a coin is fair. In 100 flips, 62 heads are observed. Use α = 0.05.
H₀: p = 0.5 (coin is fair) | H₁: p ≠ 0.5 (two-tailed test)
Test statistic: z = (p̂ − p₀) / √(p₀(1−p₀)/n) = (0.62 − 0.5) / √(0.25/100)
z = 0.12 / 0.05 = 2.4
Critical value at α = 0.05 (two-tailed): z* = ±1.96
Since |2.4| > 1.96, we REJECT H₀
Conclusion: There is sufficient evidence at the 5% level to conclude the coin is not fair.
Formula Sheet
All the key formulae you need — organised by category.
Mean (ungrouped)
x̄ = Σx / n
Mean (grouped)
x̄ = Σ(f·m) / Σf
Practice Sets
Targeted question sets to build confidence and exam readiness.
Probability Foundations
Venn Diagrams, Addition Rule, Complementary Events
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