GCSE Maths · Higher · Chapter 3: Statistical diagrams and averages · Lesson 1

Representing data

Grades 4–6About 50 minutesCalculator allowed32 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/gcse-representing-data/

NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

Grades 4–6

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

Example 1

60 people chose a fruit: apples 22, bananas 15, grapes 14, pears 9. Work out the pie chart angles.

Hint Work out

360 \div 60

first. The angles must add up to

36 0^{\circ}

B1
40 students named their pet: dog 13, cat 11, fish 7, none 9. Work out the pie chart angles.
[3 marks]
Answer

Grades 5–6

C1
The dual bar chart shows the number of cakes sold at two shops from Monday to Thursday. On which day was the difference between the shops greatest, and what was the difference?
[2 marks]
Answer $\dots\dots$ difference $\dots\dots$
C2
The composite bar chart shows how students in two year groups travel to school. How many Year 11 students travel by bus?
[2 marks]
Answer

C3
The bar chart shows the number of bikes a shop sold in two years. The axis starts at $400$ . How many times as tall as the 2023 bar is the 2024 bar? Work out the real percentage increase in sales, to 1 decimal place.
[2 marks]
Answer $\dots\dots$ times $\dots\dots %$
C4
The line graph shows the depth of water in a tank, read every hour. Estimate the depth at 11:30 am.
[1 mark]
Answer
C5
In a pie chart, a sector of $5 4^{\circ}$ stands for 15 people. How many people does the whole chart show?
[2 marks]
Answer
C6
A pie chart has three sectors. Their angles are in the ratio $2 : 3 : 7$ . Work out the size of the largest angle.
[2 marks]
Answer

Grades 5–6

D1
Ana is drawing a pie chart for 25 people. She says, "Each person gets $1 5^{\circ}$ , because $360 \div 25$ is about 15."
Explain why Ana's pie chart will not work, and give the correct angle for one person.
[2 marks]

D2
160 people were asked where they spent their main holiday. The pie chart shows the results.
(a)
How many people chose a beach holiday?
[2 marks]
Answer
(b)
How many more people chose a beach holiday than camping?
[2 marks]
Answer
(c)
In a second survey, 85 out of 250 people chose a beach holiday. Which survey had the greater percentage choosing a beach holiday? Show how you decide.
[2 marks]
Total for D2: 6 marks
D3
Pie chart A shows the favourite subjects of $180$ pupils. Pie chart B shows the favourite subjects of $300$ pupils. The music sector is $6 0^{\circ}$ in chart A and $4 8^{\circ}$ in chart B. Zak says, "More pupils chose music in chart A, because its sector is bigger."
Show that Zak is wrong.
[3 marks]

Grade 7 and beyond

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

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out the angles of a pie chart and read a number from a sector.
I can compare data in bar charts and spot an axis that does not start at 0.
I can read an estimate from a line graph.

The worked answers and the full mark scheme are free with a Mathswariz account. Teachers and students can both sign up.