Statistics
This section covers Statistics. The exam tests the mean, median, and mode of grouped data, cumulative frequency, and interpretation of ogives.
Core rules
- Direct mean: x̄ = Σfᵢxᵢ/Σfᵢ, where xᵢ is the class mark.
- Median for grouped data: median = l + [(N/2 - cf)/f]×h, where l is the lower class boundary of the median class, cf is the cumulative frequency before it, f is its frequency, and h is the class width.
- Mode for grouped data: mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)]×h, using the modal class.
- An ogive plots cumulative frequency against class boundaries; the median is read at N/2.
Worked example
Classes 0–10, 10–20, 20–30, 30–40 have frequencies 5, 8, 12, 5. N = 30, so N/2 = 15. Cumulative frequencies are 5, 13, 25, 30; the median class is 20–30. Here l = 20, cf = 13, f = 12, h = 10. Median = 20 + [(15 - 13)/12]×10 = 20 + 20/12 = 21.67 approximately.
Traps
Use class boundaries, not class midpoints, in the median formula. The cumulative frequency before the median class excludes that class. For the mode, identify the modal class first and keep f₀, f₁, f₂ in order. Do not mix grouped-data formulas with ungrouped-data shortcuts.