Recording outcomes — tables and frequency trees

Edexcel introduces frequency trees on Foundation papers and uses two-way tables on both tiers. The skill being tested is systematic counting: every outcome must appear once and only once, and totals must match.

Frequency tables

A frequency table records how often each outcome occurs.

Score on dice	Frequency
1	4
2	6
3	5
4	7
5	5
6	3
Total	30

Always include and check the total row.

Frequency trees (Edexcel-specific style)

Edexcel diagrams these as branching boxes (not probability trees with fractions). Each box holds a frequency. The left split is by some category (e.g. boys/girls), the right split is by another category (e.g. passed/failed).

Example: 80 students. 35 are boys. 12 of the boys passed. 50 students passed in total.

Frequency tree fills as:

• Boys: 35 → split into Pass = 12, Fail = 23.
• Girls: 80 − 35 = 45 → Pass = 50 − 12 = 38, Fail = 45 − 38 = 7.

Check: 12 + 23 + 38 + 7 = 80 ✓.

A typical Edexcel question asks you to "complete the frequency tree" (3–4 marks) and then "find the probability that a randomly chosen student is a girl who failed" — answer 7/80.

Two-way tables

Two categorical variables along axes; cells hold frequencies. Every row and column has its own total, plus a grand total.

	Likes maths	Dislikes maths	Total
Year 9	18	12	30
Year 10	22	8	30
Total	40	20	60

Probabilities from frequencies

P(event) = frequency of event ÷ grand total.

From the table above: P(Year 10 likes maths) = 22/60 = 11/30.

Common Edexcel exam tips

• Always work systematically — fill in given values first, then deduce the remaining cells using row/column totals.
• For a frequency tree, the left branches sum to the grand total; the right branches at each split also sum to that branch's frequency.
• When the question switches from frequencies to probability, divide by the grand total (not the row total) unless explicitly told otherwise (then it is conditional probability — see P9).