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3.2 Two-way Tables

GCSE Maths Foundation · Edexcel · Chapter 3: Graphs, tables and charts

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: reading, completing and drawing two-way tables, and using distance charts. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Read information from a two-way table
  • Complete a two-way table using row and column totals
  • Design and fill a two-way table from information given in words
  • Read distance charts and use them to plan journeys

Key words

  • Two-way table: A table that sorts data by two things at once, e.g. gender and favourite sport.
  • Row: A line of cells going across the table.
  • Column: A line of cells going down the table.
  • Total: The sum of a row or a column. The bottom-right cell is the grand total.
  • Distance chart: A table that shows the distance between each pair of places.

Reading a two-way table

Each cell is where a row meets a column. Find the right row and the right column, then read the number where they cross. Totals are at the end of each row and the bottom of each column.

Worked example: reading the trip table

(a) How many girls chose the museum? Girls row, Museum column: 14
(b) How many students chose the beach? Beach column total: 27
(c) What fraction of the boys chose the zoo? 12 out of 35 boys

Answer: (a) 14 (b) 27 (c) 12/35

Completing a two-way table

Each row adds up to its row total and each column adds up to its column total. Look for a row or column with only one missing number and fill that in first.

Worked example: filling the gaps

Year 7 dog: 60 − 18 − 17 = 25
Year 8 cat: 40 − 18 = 22. Year 8 none: 31 − 17 = 14
Year 8 total: 115 − 60 = 55. Dog total: 25 + 19 = 44
Check: 22 + 19 + 14 = 55 ✓ and 40 + 44 + 31 = 115 ✓

Answer: 25, 22, 14, 55, 44

Key fact: Always check your table: the row totals and the column totals must both add up to the grand total.

Making a two-way table from information

When the information is in words, draw the table first with labels and a Total row and column. Put in every number you are told, then complete it.

Worked example: gym classes

80 people go to a gym class. Each does yoga or spin. 45 of them are women. 18 men do yoga. 30 people do spin. How many women do yoga?
Men = 80 − 45 = 35. Men doing spin = 35 − 18 = 17.
Women doing spin = 30 − 17 = 13. Women doing yoga = 45 − 13 = 32.

Answer: 32 women do yoga

  • Men; Yoga 18; Spin 17; Total 35
  • Women; Yoga 32; Spin 13; Total 45
  • Total; Yoga 50; Spin 30; Total 80

Distance charts

A distance chart is a special two-way table. To find the distance between two places, go down from one name and across from the other until they meet.

Worked example: planning a round trip

A van driver goes from Ashby to Carlow, then to Denham, then straight back to Ashby. How far does she drive?
Ashby–Carlow 37, Carlow–Denham 28, Denham–Ashby 52.
37 + 28 + 52 = 117

Answer: 117 miles

Common mistakes

  • Reading the wrong row or column. Put a finger on the row label and the column label and slide them together.
  • Using the grand total when the question asks for a fraction of one group, e.g. "what fraction of the boys" uses the boys total.
  • Forgetting to check that both the rows and the columns add up.
  • Not drawing the table first when the information is in words.

Revision questions

Try these, then check your answers below each one.

Question 1. A two-way table shows the lunch choices of 60 students. Boys: hot dinner 14, sandwich 11, packed lunch 5. Girls: hot dinner 12, sandwich 8, packed lunch 10. How many girls chose a packed lunch?

Answer: 10

Working: Girls, packed lunch: 10.

Question 2. A two-way table shows the lunch choices of 60 students. Boys: hot dinner 14, sandwich 11, packed lunch 5. Girls: hot dinner 12, sandwich 8, packed lunch 10. How many students chose a hot dinner?

Answer: 26

Working: 14 + 12 = 26.

Question 3. A two-way table shows the lunch choices of 60 students. Boys: hot dinner 14, sandwich 11, packed lunch 5. Girls: hot dinner 12, sandwich 8, packed lunch 10. How many boys are there?

Answer: 30

Working: 14 + 11 + 5 = 30 boys.

Related lessons

Continue in the full course

This lesson is section 3.2 (EGCMF0302) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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