KS3 Maths · Year 8 · Chapter 4: Using data · Lesson 2

Two-way tables

Year 8About 60 minutesNo calculator45 marks

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Date

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Quick questions to start.

A1
Last lesson
As the temperature goes up, sales of hot drinks go down. What type of correlation is this?
[1 mark]
Answer
A2
Needed today
A bag holds $7$ red counters and $13$ blue counters. One is taken at random. What is the probability that it is red?
[1 mark]
Answer
A3
Needed today
Write $27$ out of $60$ as a percentage.
[1 mark]
Answer
A4
From chapter 2
Expand $4 (2 x - 3)$ .
[1 mark]
Answer

Example, then your turn

Year 8

Your teacher works through each example with you. Then try the one beside it.

Example 1

The two-way table shows where $60$ students chose to go on a trip. Complete the table.

Hint Start with a row or a column that has only one gap.

B1
The two-way table shows how $70$ students in Year 7 (Y7) and Year 8 (Y8) have lunch. Work out the numbers $a$ , $b$ , $c$ and $d$ .
[3 marks]
Answer $a = \dots$ $b = \dots$ $c = \dots$ $d = \dots$

Example 2

The table shows the pets of $50$ students. A student is picked at random. Work out the probability that the student is (i) a girl with a cat, (ii) without a dog.

Hint The probability is the number who fit, out of the

50

students.

B2
The table shows the activity that each of $80$ people at a club chose (None means neither). A person is picked at random. Work out the probability that the person is a child who does not swim.
[2 marks]
Answer

Example 3

The table shows the cost of sending a parcel by its weight in kg ( $1$ to $2$ means over $1$ and up to $2$ ). Mo sends parcels of $0.6$ kg and $1.8$ kg by standard post. How much would he save by sending them as one parcel?

Hint Work out the cost of the two parcels on their own, then the cost of one parcel of

0.6 + 1.8

kg.

B3
Use the table in Example 3. Ria sends parcels of $0.7$ kg and $2.6$ kg by express post. How much would she save by sending them as one parcel?
[2 marks]
Answer $£ \dots\dots$

Example 4

There are $80$ people at a concert. $45$ are women. $28$ of the men are over $30$ . $31$ of the people are aged up to $30$ . How many of the women are over $30$ ?

Hint Draw a two-way table: men and women across, over

30

and up to

30

down. Fill in the facts, then the gaps.

B4
Year 8 has $120$ students. $54$ are boys. Each studies French or Spanish. $41$ girls study French. $63$ students study Spanish. How many boys study French?
[3 marks]
Answer

Practice

Year 8

C1
The table shows the percentage of boys and the percentage of girls who own a phone, at each age. Comment on the difference between boys and girls, and on the trend as age goes up.
[2 marks]
C2
Part of a bus timetable is shown. Kai is at the Library. He must be at the Station by $9 : 05$ . Write down the latest time he can catch a bus at the Library, and how long his journey takes.
[2 marks]
Answer

C3
The chart shows the distances in miles between four towns. Work out the length of a trip from Ayton to Cole to Dale and back to Ayton.
[2 marks]
Answer $\dots\dots$ miles
C4
The table shows the bikes sold each month by shops A and B. In which month was the difference between them greatest? Give the difference.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
The two-way table shows the favourite sport of some students. Sam says, "More boys than girls chose football, so a boy is more likely to choose football than a girl."
Use the table to show that Sam is wrong.
[3 marks]

D2
A café sold $150$ drinks one day. Each drink was a tea or a coffee, small or large. $64$ of the drinks were coffee. $52$ of the teas were large. $39$ of the drinks were small coffees.
(a)
Complete the two-way table.
[3 marks]
(b)
A drink is picked at random. Work out the probability that it is a large coffee or a small tea.
[2 marks]
Answer
Total for D2: 5 marks
D3
The table shows the prices of one swim at a pool. A family of two adults aged $38$ and $41$ , two children aged $9$ and $13$ , and a grandparent aged $66$ want to swim. How much would they save by swimming at an off-peak time instead of a peak time? You must show your working.
[4 marks]
Answer $£ \dots\dots$
D4
The table shows the heights of $40$ boys and $40$ girls.
(a)
Write down the modal class for the boys and for the girls.
[2 marks]
Answer
(b)
Make two comparisons between the heights of the boys and the heights of the girls.
[2 marks]
(c)
A girl is picked at random. Work out the probability that she is under $160$ cm tall.
[2 marks]
Answer
Total for D4: 6 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A club has $108$ members. The ratio of men to women is $4 : 5$ . $\frac{3}{4}$ of the men and $\frac{2}{3}$ of the women can swim. A member is picked at random. Work out the probability that the member cannot swim. Give your answer in its simplest form.
[5 marks]
Hint 1 · What to try
Draw a two-way table: men and women, can swim and cannot swim. Fill in the totals first.
Hint 2 · The first line
$108 \div 9 = 12$ , so there are $4 \times 12 = 48$ men and $5 \times 12 = 60$ women.
Hint 3 · The full method
Men who cannot swim: $48 - 36 = 12$ . Women who cannot swim: $60 - 40 = 20$ . So $\frac{32}{108}$ , then simplify.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can complete a two-way table from what I am told.
I can work out a probability from a two-way table.
I can read and compare the data in a two-way table, timetable or chart.

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