IGCSE Maths · Edexcel 4XMA1 · Unit 1 Higher · Statistics

Two-Way Tables

A two-way table sorts data by two features at once, such as year group and how students travel. Edexcel asks you to complete them, design them from words, and read probabilities from them. These are quick marks if you use the totals.

1What a two-way table shows

Each row is one category of the first feature, each column is one category of the second, and every cell counts the items that fit both. The last row and column hold the totals.

	Walk	Bus	Car	Total
Year 10	12	19	9	40
Year 11	13	15	12	40
Total	25	34	21	80

Reading it: 15 Year 11 students take the bus; 25 students walk altogether; 80 students were surveyed in total.

Key ideaEvery row adds to its row total, every column adds to its column total, and both sets of totals add to the grand total in the corner.

2Completing a two-way table

Look for any row or column with only one missing value and fill it in. Each value you find unlocks another, so keep going until the table is complete.

Worked example

Complete the table.

	Walk	Bus	Car	Total
Year 10	12		9	40
Year 11		15
Total	25			80

Year 10 row: bus = 40 − 12 − 9 = 19.
Total column: Year 11 = 80 − 40 = 40.
Walk column: Year 11 = 25 − 12 = 13.
Year 11 row: car = 40 − 13 − 15 = 12.
Bus total = 19 + 15 = 34; car total = 9 + 12 = 21. Check: 25 + 34 + 21 = 80 ✓

Bus: 19, 15, total 34; Car: 9, 12, total 21; Year 11: 13, 15, 12, total 40

3Designing a table from words

When the information comes as sentences, draw the empty table first, label the rows and columns, then put each fact in its cell. Then complete it as before.

Worked example

120 students each chose one of French, Spanish or Mandarin. 64 are girls. 23 girls chose French. 31 boys chose Spanish. 40 students chose Mandarin, and 18 of them are boys. How many girls chose Spanish?

Boys = 120 − 64 = 56.
Boys row: French = 56 − 31 − 18 = 7.
Mandarin column: girls = 40 − 18 = 22.
Girls row: Spanish = 64 − 23 − 22 = 19.

19 girls chose Spanish

	French	Spanish	Mandarin	Total
Boys	7	31	18	56
Girls	23	19	22	64
Total	30	50	40	120

4Two-way tables for grouped data

The categories can be groups rather than single values, such as age bands or mark ranges. You complete and read the table in exactly the same way.

Age (years)	Cinema	Streaming	Neither	Total
0–17	14	9	3	26
18–39	11	18	6	35
40+	5	12	22	39
Total	30	39	31	100

From this table, 18 of the people aged 18–39 prefer streaming, and 39 of the 100 people are aged 40 or over.

5Probability from a two-way table

Probability = the cell you want ÷ the total you are choosing from. Read the question carefully to see which total that is.

Worked example

Using the travel table in Section 1, a student is chosen at random. Find (a) P(Year 11 and bus) (b) P(walks, given the student is in Year 10).

(a) Choosing from all 80 students: P = 1580 = 316.
(b) Choosing only from the 40 Year 10 students, 12 walk: P = 1240 = 310.

(a) 3/16 (b) 3/10

Exam tip“Given that …” or “one of the Year 10 students is chosen” means the denominator is a row or column total, not the grand total.

6Two-way tables and Venn diagrams

A 2 × 2 two-way table holds exactly the same information as a two-set Venn diagram. Each cell matches one region.

	Cat	No cat	Total
Dog	6	10	16
No dog	14	10	24
Total	20	20	40

Cat and dog (6) is the overlap; cat, no dog (14) is “cat only”; dog, no cat (10) is “dog only”; and neither (10) is outside both circles.

Common mistakes

Forgetting to fill in the totals row and column, which are often part of the marks.
Using the grand total as the denominator when the question restricts the choice to one group.
Not checking that the row totals and the column totals both add to the grand total.
Copying values into the wrong cell when designing a table from words. Label rows and columns clearly first.

★Key Vocabulary Recap

Two-way table: A table showing how data falls into categories of two different features.
Row / column total: The sum of a row or a column of a two-way table.
Grand total: The total of all the data; the bottom-right cell.
Grouped data: Data sorted into classes or ranges, such as 18–39 years.
Relative frequency: Frequency ÷ total, used as an estimate of probability.

Specification reference (Pearson Edexcel 4XMA1, Unit 1 Higher)

Design and use two-way tables for discrete and grouped data.
Use information provided to complete a two-way table.
Find probabilities from two-way tables (supports the Probability topic).

Next stepReady to practise? Try the 11 exam-style questions, then check your working against the worked solutions.

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