THE CURVE READER— Estimating Median & IQR
Cumulative Frequency · Syllabus 6.2 A, D · Higher Tier
▸ Panel A — Quartile Scanner
n = 80 students▸ Panel B — Logic Track
Click a quartile button to activate the laser scanner →
Key Formulae
Median position = n ÷ 2
LQ position = n ÷ 4
UQ position = 3n ÷ 4
IQR = Q₃ − Q₁
▸ Panel C — Dynamic Solver · IQR Extractor
Given: Total frequency n = 80
Step 1 — Median Position
Median = n ÷ 2 = 80 ÷ 2 = 40th value
Step 2 — Quartile Positions
LQ = n ÷ 4 = 80 ÷ 4 = 20th value
UQ = 3n ÷ 4 = 3 × 80 ÷ 4 = 60th value
Step 3 — Read from Curve
Q₁ ≈ 12.9
Median ≈ 18.7
Q₃ ≈ 24.4
Step 4 — IQR
IQR = Q₃ − Q₁ = 24.4 − 12.9 = 11.5
⚠️ Examiner Trap Vault
Trap #1 — Wrong Position
❌ Using n/2 = 40, then reading CF = 40 as the median VALUE directly.
✅ CF = 40 is the position on the y-axis. Read across to the curve, THEN drop to the x-axis to get the value.
Trap #2 — IQR vs Range
❌ Calculating Range = max − min instead of IQR = Q₃ − Q₁.
✅ The question will say "estimate the interquartile range." IQR measures the middle 50% spread, NOT the full range.
Trap #3 — Ignoring "Estimate"
❌ Giving an exact answer without the word "estimate" or using class boundaries wrong.
✅ All values read from a CF curve are ESTIMATES. Always write ≈ and show your reading method for method marks.
Mark Scheme Tip (AO1)
✓ M1 — Correct CF position identified (n/2, n/4, 3n/4)
✓ A1 — Correct value read from CF graph (± tolerance)
✓ A1 — Correct IQR = Q₃ − Q₁ calculated
▸ Bridge Strategy Progress
Phase 1 · Anchor
Read median from equal-width CF diagram. Total frequency given.
Grade 4–5
Phase 2 · Twist
Scan all three quartiles. Calculate IQR. Interpret spread in context.
Grade 6–7
Phase 3 · Killer
Compare IQR of two distributions. Justify which is more consistent using statistical reasoning.
Grade 8–9
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