Outcome frequencies and frequency trees
OCR Statistics across J560/02, /03, /05 and /06 routinely sets frequency-tree questions. They reward clear branch labelling and consistent use of fractions or decimals.
Frequency tables
A frequency table records how often each outcome occurs.
| Score on die | Frequency |
|---|---|
| 1 | 4 |
| 2 | 7 |
| 3 | 5 |
| 4 | 8 |
| 5 | 3 |
| 6 | 3 |
Total trials = 4 + 7 + 5 + 8 + 3 + 3 = 30.
Relative frequency = frequency / total. For score 4: 8/30 ≈ 0.27.
This is an estimate of the experimental probability — useful when theoretical probability is unknown or when you want to test fairness.
Frequency trees (OCR-specific)
A frequency tree branches by category, splitting the total into sub-counts. Different from a probability tree (which uses probabilities).
Example: 200 students surveyed about whether they cycle or walk to school, and whether they like PE.
The first split: 120 cycle, 80 walk. Among cyclists, 90 like PE; among walkers, 50 like PE.
┌── Like PE: 90
Cycle ──┤
(120) └── Don't like: 30
─────
Walk ───┬── Like PE: 50
(80) └── Don't like: 30
Total who like PE = 90 + 50 = 140.
Two-way tables
A two-way table records two categorical variables simultaneously:
| Like PE | Don't like PE | Total | |
|---|---|---|---|
| Cycle | 90 | 30 | 120 |
| Walk | 50 | 30 | 80 |
| Total | 140 | 60 | 200 |
Frequency trees and two-way tables hold the same information. OCR sometimes asks you to convert between them.
Analysing frequency data
Typical OCR question types:
- "Complete the frequency tree." → Compute missing branches by subtraction.
- "What is the probability that a randomly chosen student cycles?" → 120/200 = 0.6.
- "Given that a student likes PE, what is the probability they walk?" → 50/140 (conditional).
- "Estimate the number from a different total of N." → scale: (count/total) × N.
OCR mark scheme conventions
- Frequency tree completion: M1 for one correct missing value, A1 for all correct.
- Probability answer: B1 for the correct fraction; equivalent decimal/percentage accepted.
- Conditional probability: M1 for using the correct conditional total in the denominator, A1 for value.
⚠Common mistakes
- Mixing probability and frequency on the same tree (frequency trees show counts, not probabilities).
- For conditional probability, dividing by the total instead of by the conditional sub-total.
- Forgetting to add up across BOTH branches when finding "total who like PE".
- Rounding too early in scaling questions.
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves