OCR GCSE Maths
Topic questions Statistics Tables, charts and diagrams
60 questions · 300 marks · about 4.5 hours
Also involves Angle facts
The pie chart shows the proportion of games won by a sports team.
The sports team won 9 games.
Work out how many games the sports team played.
The ratio of the number of games drawn by the sports team to the number of games lost by the sports team was 2: 1.
Complete the pie chart above.
The bar chart shows the number of hours per month Riley spends at the gym in each of January, February and March.
How many hours did Riley spend at the gym in February?
Find how many more hours Riley spent at the gym in January compared to March.
In April, Riley spent a total of 18 hours at the gym.
Complete the bar chart for April.
Riley says,
I spent 50% less time at the gym in April than in March.
Is Riley correct? Show how you decide.
Riley is........ because........
A school has three terms, Autumn, Spring and Summer.
In class A there were 90 absences in the Autumn term, 120 absences in the Spring term and 40 absences in the Summer term.
Compared to class A, class B had:
• 
fewer absences in the Autumn term
• 5% more absences in the Spring term
• 7 more absences in the Summer term.
Design and complete a two-way table to show this information.
The price of a laptop is reduced in a January sale from £450 to £382.50.
Work out the percentage reduction in the price of the laptop.
The graph shows the price of the laptop in the months before the January sale.
Explain why this graph is misleading.
A school has three terms, Autumn, Spring and Summer.
In class A there were 90 absences in the Autumn term, 120 absences in the Spring term and 40 absences in the Summer term.
Compared to class A, class B had:
• fewer absences in the Autumn term
• 5% more absences in the Spring term
• 7 more absences in the Summer term.
Design and complete a two-way table to show this information.
The price of a laptop is reduced in a January sale from £450 to £382.50.
Work out the percentage reduction in the price of the laptop.
The graph shows the price of the laptop in the months before the January sale.
Explain why this graph is misleading.
200 students at a school were asked how they travel to school. The pictogram shows the results for four of the ways they travel to school.
How many students walk to school?
How many more students travel by car to school than travel by tram to school?
The rest of the 200 students cycle to school.
Complete the pictogram to show the number of students who cycle to school.
The total number of students at the school is 800.
What fraction of the students at the school were asked how they travel to school? Give your answer in its simplest form.
The vertical line chart shows the rainfall, in millimetres (mm), in March and April.
Write down the rainfall in March.
In May there was 55 mm of rainfall.
Complete the vertical line chart for May.
Work out the total rainfall for March, April and May.
A school is deciding on a charity to support. Each student at the school votes for one of four charities, A, B, C or D. The results are to be shown in a pie chart.
This pie chart shows the sector for charity A. Twice as many students voted for charity C than charity B. Twice as many students voted for charity D than charity C.
Show that the sector for charity B will have an angle of 44°.
Complete the pie chart.
39 students voted for charity A.
Calculate the total number of students at the school.
The school asks 80 of the students to choose a new logo from three designs G, H and J. The same results are shown in a pie chart and in a bar chart.
Give one advantage of using the pie chart rather than the bar chart.
Give one disadvantage of using the pie chart rather than the bar chart.
Also involves The four operations
At an adventure park, all children participate in three activities, choosing exactly one activity from each of three options.
| Option | Activity |
| 1 | football or golf |
| 2 | bowling or climbing |
| 3 | rafting or swimming or tennis |
On one Monday morning, 100 children visited the adventure park.
The frequency tree shows the number of children choosing some of the activities.
Option 1
Option 2
Option 3
........
Complete the frequency tree.
Which was the most popular activity out of rafting, swimming and tennis? Show how you decide.
One of the 100 children is picked at random.
Find the probability that this child chose bowling.
Alex says
45% of all children coming to the adventure park choose football.
What assumption has Alex made?
The graph shows a household’s average daily electricity usage, in kilowatt hours (kWh).
Give two different reasons why this graph is misleading.
A school is deciding on a charity to support. Each student at the school votes for one of four charities, A, B, C or D. The results are to be shown in a pie chart.
This pie chart shows the sector for charity A. Twice as many students voted for charity C than charity B. Twice as many students voted for charity D than charity C.
Show that the sector for charity B will have an angle of 44°.
Complete the pie chart.
39 students voted for charity A.
Calculate the total number of students at the school.
The school asks 80 of the students to choose a new logo from three designs G, H and J. The same results are shown in a pie chart and in a bar chart.
Give one advantage of using the pie chart rather than the bar chart.
Give one disadvantage of using the pie chart rather than the bar chart.
The graph shows a household’s average daily electricity usage, in kilowatt hours (kWh).
Give two different reasons why this graph is misleading.
Also involves Angle facts
The table shows the results for a sports club’s ‘A’ team.
| Result | Frequency |
| Win | 18 |
| Draw | 10 |
| Lose | 12 |
| Total | 40 |
Complete a labelled pie chart to show these results.
Here are the results for the sports club’s ‘B’ team and ‘C’ team.
‘B’ team
‘C’ team
The ‘C’ team manager says
The pie charts show that the ‘C’ team won more games than the ‘B’ team.
Referring to the pie charts, explain why the ‘C’ team manager may not be correct.
Also involves The four operations
The bar chart shows the rainfall, in millimetres (mm), for a city in the first three months of the year.
Write down the amount of rainfall in February.
Write in its simplest form the ratio amount of rainfall in February: amount of rainfall in March.
The total amount of rainfall in January and February was the same as the total amount of rainfall in March and April.
Work out the amount of rainfall in April.
A sales representative and a manager discuss this graph of sales over the last year.
The sales representative says
I can tell from the graph that, over the last year, sales have risen every month.
Is the sales representative correct? Give a reason for your answer.
The manager says
I can tell from the graph that sales are now more than double what they were at the start of the year.
Is the manager correct? Give a reason for your answer.
The graph shows the value of sunscreen products sold in a shop for each quarter from quarter 1 of 2021 to quarter 4 of 2023.
| 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
| 2021 | 2022 | 2023 |
Year and quarter
Make one comment about the annual variation shown in this graph.
In one of these years, quarter 3 was very cloudy. Write down which year this is most likely to be. Give a reason for your answer.
The manager of the shop says that the value of sales in quarter 4 of 2024 will be £3100. What assumption has the manager made?
The table shows the results for a sports club’s ‘A’ team.
| Result | Frequency |
| Win | 18 |
| Draw | 10 |
| Lose | 12 |
| Total | 40 |
Complete a labelled pie chart to show these results.
Here are the results for the sports club’s ‘B’ team and ‘C’ team.
‘B’ team
‘C’ team
The ‘C’ team manager says
The pie charts show that the ‘C’ team won more games than the ‘B’ team.
Referring to the pie charts, explain why the ‘C’ team manager may not be correct.
A sales representative and a manager discuss this graph of sales over the last year.
The sales representative says
I can tell from the graph that, over the last year, sales have risen every month.
Is the sales representative correct? Give a reason for your answer.
The manager says
I can tell from the graph that sales are now more than double what they were at the start of the year.
Is the manager correct? Give a reason for your answer.
A store carries out a satisfaction survey on a sample of its customers. The bar chart shows the results.
Work out how many customers were in the sample.
The store manager decides to display the results in a pictogram.
Complete the final row of the pictogram and the key.
Alex draws a bar chart to show the age of the young people attending a youth club.
Make one criticism of Alex’s bar chart.
Also involves The four operations
The bar chart shows the number of points scored by some quiz players.
How many points were scored by Ellis?
How many more points were scored by Alex than Dan?
Clara scored 13 points.
Complete the bar chart to show this information.
The pictogram shows the number of students absent from a school in a particular week.
Harper says
The pictogram shows 2 circles for Monday. Therefore 2 students were absent on Monday.
Explain what Harper has done wrong. Write down the correct number of students who were absent on Monday.
5 students were absent on Friday.
Complete the pictogram above to show this information.
Also involves The four operations
The graph shows information about the population of a village.
The population of the village in 2021 was 4740.
Plot this point on the graph.
Work out the increase in the population of the village between 2016 and 2018.
Rowan says that there was a huge increase in the population of the village between 2015 and 2020.
Describe how Rowan may have been misled by the graph.
Blake says that the population of the village will be greater than 4800 in 2022.
Write down an assumption Blake has made.
The graph shows information about the population of a village.
The population of the village in 2021 was 4740.
Plot this point on the graph.
Work out the increase in the population of the village between 2016 and 2018.
Rowan says that there was a huge increase in the population of the village between 2015 and 2020.
Describe how Rowan may have been misled by the graph.
Blake says that the population of the village will be greater than 4800 in 2022.
Write down an assumption Blake has made.
This graph shows the number of mobile phones sold by a shop in June, July and August.
Give two reasons why the graph is misleading.
Taylor has collected data on the number of students who were absent from their school last week. The bar chart shows the results for the first four days.
On Friday there were 54 students who were absent from the school.
Show this information on the bar chart.
Taylor says
On Monday 150% of the students were absent from my school.
Could this be true? Explain how you decide.
There are 600 students in Taylor’s school. Find the percentage of students who were absent from Taylor’s school on Thursday.
Also involves Fractions
Some students were asked how they travel to school. Each student gave one answer. The pie chart shows the proportion who travel by bus, by train or walk.
All of the remaining students travel to school either by bike or by car. The ratio of the number who travel by bike to the number who travel by car is 2: 3.
Complete the pie chart.
You must show your working.
Which way of travelling to school is the mode?
A student is researching the difference in how much exercise adults and children do. To collect their data, the student interviews the first 25 people found in the High Street at 11 am on one Monday morning.
Make three different criticisms of the student’s method of collecting data.
Here is the data collection table that the student used.
Make one criticism of the student’s table.
Two pupils are given data that shows the estimated number of computer tablet users worldwide from 2014 to 2018.
Li creates this pie chart to show the data.
Number of computer tablet users (billions)
Write down two reasons why Li’s pie chart is not suitable to represent the data.
Amaya creates this line graph to show the same data.
Work out the percentage increase in the number of computer tablet users from 2014 to 2018.
Also involves The four operations
In a survey, some students chose their favourite type of film from a list of five. The bar chart shows the results.
(a)(i)........
How many Year 11 students chose Action films?
What type of film was chosen by the most Year 10 students?
How many Year 10 students took part in the survey?
45 students took part in the survey.
Write the ratio
number of Year 10 students taking part: number of Year 11 students taking part
in its simplest form.
Also involves Fractions
A sports team played the same number of matches in 2019 and 2020. The two pie charts summarise their results.
What fraction of the matches did the team win in 2019?
Did the team’s results improve in 2020? Explain how you know.
Also involves The four operations
Reece asked some friends what type of programme they watch most on television. The bar chart shows some of his results.
10 people answered Film.
Complete the bar chart to show this information.
Complete these sentences.
........ was chosen by the most people.
........ people chose News.
........ fewer people chose Nature than Comedy.
This is Nadia’s bar chart to show the number of goals scored by four teams during November.
Blake says
Nadia’s bar chart shows that United scored twice as many goals as City.
Is Blake correct? Give a reason for your answer.
Give one way in which Nadia can improve her bar chart.
Kareem says
Out of these four teams, United achieved the highest mean number of goals per game during November.
What assumption has Kareem made?
The graph shows the number of umbrellas sold in Ling’s shop for each quarter from quarter 1 of 2017 to quarter 3 of 2019.
The shop sold 32 umbrellas in quarter 4 of 2019.
Complete the graph.
Make one comment about the seasonal variation shown in this graph.
Make one comment about the annual variation shown in this graph.
Ling predicts that she will sell 50 umbrellas in quarter 1 of 2020.
What assumption has she made?
The masses, m kg, of some parcels are shown below.
4 15 14 11 12 3 1 18 13 2 16 10
Jack constructs this grouped frequency table to record the masses.
Explain why Jack’s table is unsuitable to record the masses.
The histogram summarises the times taken, in minutes, by some students to complete a
Show that 70 students took between 45 and 70 minutes to complete the race.
Calculate an estimate of the mean time taken to complete the race. Show your working.
Also involves The four operations
A theme park asked 900 people to choose their favourite activity from a list of five. The pictogram shows the results for four of the activities.
How many people chose entertainment?
How many more people chose water rides than family rides?
All 900 people chose one of the five activities.
Complete the pictogram for children’s rides.
Will plays a game at the theme park. There are 20 cards numbered from 1 to 20. Will takes a card at random. He wins if the card he chooses shows a prime number.
Work out the probability that Will wins. Give your answer as a fraction in its simplest form.
A family ticket for the theme park costs £68. If the ticket is bought online it costs 15% less.
How much does it cost to buy a family ticket online?
30 students each own one pet. The pie chart shows the proportion of each type of pet owned by the 30 students.
Which type of pet is the mode?
Use the information in the pie chart to complete this bar chart.
The pie chart shows how Jack spent his time one evening.
On which activity did Jack spend most time?
Jack says
Show that he is not correct.
The pie chart represents 5 hours.
Find the time, in hours and minutes, that Jack spent reading.
Also involves The four operations
Megan’s Cafe sells ice cream. Customers choose to have a tub or a cone, and a wafer or no wafer. They can choose vanilla, lemon or chocolate ice cream.
This frequency tree shows the number of people making some of the choices.
Anaya buys an ice cream.
One choice she can make is
a cone, no wafer and vanilla.
How many different choices can she make?
Complete the frequency tree.
Which flavour of ice cream was most popular? Show how you decide.
This spinner has two grey sections, two white sections and one black section.
Vlad says The probability of the spinner landing on black is 
Explain why Vlad is not correct.
The graph shows the cost of a litre of petrol for the last six months of 2017.
Explain why this graph is misleading.
This spinner has two grey sections, two white sections and one black section.
Vlad says The probability of the spinner landing on black is 
Explain why Vlad is not correct.
The graph shows the cost of a litre of petrol for the last six months of 2017.
Explain why this graph is misleading.
Jodie asked some people to choose from six countries where they would most like to go on holiday. The bar chart shows her results for five of the countries.
14 people answered Spain.
Show this information on the bar chart.
Complete these sentences.
........ was chosen by the fewest people.
........ people chose France.
........ more people chose Italy than Mexico.
This graph shows the cost of buying potatoes from a farm.
How much does it cost to buy 70 kg of potatoes?
What weight of potatoes can be bought for £38?
The cost per kilogram of potatoes is the same for any weight of potatoes.
How much will it cost to buy 180 kg of potatoes from the farm?
This graph shows the annual profits, in thousands of pounds, of the farm between 2013 and 2017.
Describe one misleading feature of the graph.
Also involves The four operations
The table shows the number of computers sold in Tom’s shop each quarter from 2015 to 2017.
| 2015 | 2016 | 2017 | ||||||||||
| Quarter | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
| Number of computers sold | 13 | 31 | 29 | 45 | 20 | 32 | 25 | 47 | 27 | 40 | 30 | 58 |
Complete this graph using the information for 2017.
Tom adds the three results for quarter 1 and he adds the three results for quarter 4. Tom says
The ratio of the total number of computers sold in quarter 1 compared to quarter 4 is 2: 5.
Is he correct? Show your reasoning.
Make two comments about Tom’s sales over the period 2015 to 2017.
Tom predicts that he will sell more than 60 computers in the 4th quarter of 2018.
What assumption has he made?
Also involves The four operations
In a survey, people were asked to choose their favourite type of pizza. The pictogram shows some of the results.
8 people chose Margherita.
Complete the key.
How many people chose Pepperoni?
There were 36 people in the survey. All of these people chose one of the pizzas in the pictogram.
Complete the pictogram for Veggie.
Also involves Angle facts
30 people choose their favourite sport. Matt wants to show their choices in a pie chart. 4 of the people chose ‘tennis’.
Work out the angle of the sector for ‘tennis’.
In a dance competition, two judges each award scores out of 30. The scatter diagram shows the scores awarded to the first 10 dancers.
Here are the scores for the next two dancers.
| Judge A | 21 | 7 |
| Judge B | 18 | 8 |
Plot their scores on the scatter diagram.
Dancers who are awarded a score of more than 20 by both judges receive a medal.
For the 12 dancers, express the ratio of medal winners to non-medal winners in its simplest form.
This chart shows the types of dance performed by the 12 dancers.
3 performed a street dance, 8 performed a jazz dance and 1 performed a tap dance.
Why is this diagram misleading?
Also involves The four operations
The table shows the number of computers sold in Tom’s shop each quarter from 2015 to 2017.
| 2015 | 2016 | 2017 | ||||||||||
| Quarter | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
| Number of computers sold | 13 | 31 | 29 | 45 | 20 | 32 | 25 | 47 | 27 | 40 | 30 | 58 |
Complete this graph using the information for 2017.
Tom adds the three results for quarter 1 and he adds the three results for quarter 4. Tom says
The ratio of the total number of computers sold in quarter 1 compared to quarter 4 is 2: 5.
Is he correct? Show your reasoning.
Make two comments about Tom’s sales over the period 2015 to 2017.
Tom predicts that he will sell more than 60 computers in the 4th quarter of 2018.
What assumption has he made?
In a dance competition, two judges each award scores out of 30. The scatter diagram shows the scores awarded to the first 10 dancers.
Here are the scores for the next two dancers.
| Judge A | 21 | 7 |
| Judge B | 18 | 8 |
Plot their scores on the scatter diagram.
Dancers who are awarded a score of more than 20 by both judges receive a medal.
For the 12 dancers, express the ratio of medal winners to non-medal winners in its simplest form.
This chart shows the types of dance performed by the 12 dancers.
3 performed a street dance, 8 performed a jazz dance and 1 performed a tap dance.
Why is this diagram misleading?
Also involves The four operations
This bar chart shows the average monthly expenditure, by category, of households in a particular town in 2005 and 2015.
Utility bills Transport Housing Entertainment Food
In which category was there a decrease in the average monthly expenditure between 2005 and 2015?
How much more was the average monthly expenditure on housing in 2015 than in 2005?
The total average monthly expenditure in 2005 was £1200.
What percentage of this was spent on transport?
Two groups of students go on a water sport holiday. Each student chooses one activity.
Students in Group A choose from Diving, Swimming, Paddleboarding and Kayaking. Their choices are to be shown in a pie chart.
Complete this table for Group A.
| Activity | Number of students | Angle of sector |
| Diving | 5 | 60 |
| Swimming | 120 | |
| Paddleboarding | ||
| Kayaking | 9 | 108 |
Complete the pie chart for Group A.
One student in Group A changes activity. There is now a new modal activity for Group A.
Write down the student’s original activity and new activity.
original activity........
The choices made by Group B are shown in this pie chart.
A teacher thinks more students chose Diving in Group B than in Group A.
Give a reason why the teacher may be wrong.
Percy sells paint in standard tins and large tins. The standard tin covers 40 m2 and the large tin covers 60 m2.
Percy publishes this chart showing the area that can be covered with each tin of paint.
Explain why the chart is misleading.
The standard tin and the large tin are mathematically similar. The volume of the large tin is 50% more than the volume of the standard tin. Both tins are cylinders. The radius of the standard tin is 10 cm.
Calculate the radius of the large tin.
Also involves Angle facts
This pie chart shows how the employees of a business travel to work.
Find the ratio of the number of employees who cycle to work to the number of employees who walk to work. Give your answer in its simplest form.
80 employees travel to work by car.
Work out the number of employees who cycle to work and the number of employees who walk to work.
Also involves Fractions
Jorge recorded the scorers of 120 goals. He started to draw a pie chart to show the results.
How many goals did Simon score?
The table shows the other players who scored goals.
| Name of scorer | Number of goals | Angle of sector |
| Wayne | 48 | 144° |
| Harry | 5 | |
| Obi | 72° | |
| Antony |
Complete the table.
Complete the pie chart.
The table shows the average number of customers per day entering a shop.
| 2015 | 2016 | |||||||
| Months | Jan- Mar | Apr- Jun | July- Sep | Oct- Dec | Jan- Mar | Apr- Jun | July- Sep | Oct- Dec |
| Average number of customers per day | 119 | 264 | 368 | 172 | 130 | 304 | 381 | 192 |
Complete the time series graph below.
Make two different comments comparing the number of customers entering the shop in 2015 and 2016.
George recorded all the different types of tree in a wood.
His results are shown in this table.
Complete the table.
| Type of tree | Tally | Frequency |
| Alder | I I I I I I I | 8 |
| Beech | I I I I I I I I I I I I | 15 |
| Oak | I I I I I I I I I I I I I I I | 18 |
| Rowan | I I I I I | |
| Other | 13 |
Complete the bar chart to show George’s results.
George found 60 trees altogether in the wood.
What percentage of the trees were oak trees?
The owner of a tourist attraction records the amount of rainfall, in millimetres, and the number of visitors each day. The results for 10 days are shown in the scatter diagram.
Circle the outlier on the scatter diagram.
The owner claims that he would expect around 320 visitors on a day with 2 mm of rainfall.
Does the scatter diagram support his statement? Explain how you made your decision.
Explain why the scatter diagram should not be used to estimate the number of visitors on a day with 9 mm of rainfall.
The pie chart summarises information about the visitors to the tourist attraction on a different
Explain why the pie chart cannot be used to work out how many adults visited on that day.
The table shows the average number of customers per day entering a shop.
| 2015 | 2016 | |||||||
| Months | Jan- Mar | Apr- Jun | July- Sep | Oct- Dec | Jan- Mar | Apr- Jun | July- Sep | Oct- Dec |
| Average number of customers per day | 119 | 264 | 368 | 172 | 130 | 304 | 381 | 192 |
Complete the time series graph below.
Make two different comments comparing the number of customers entering the shop in 2015 and 2016.
The owner of a tourist attraction records the amount of rainfall, in millimetres, and the number of visitors each day. The results for 10 days are shown in the scatter diagram.
Circle the outlier on the scatter diagram.
The owner claims that he would expect around 320 visitors on a day with 2 mm of rainfall.
Does the scatter diagram support his statement? Explain how you made your decision.
Explain why the scatter diagram should not be used to estimate the number of visitors on a day with 9 mm of rainfall.
The pie chart summarises information about the visitors to the tourist attraction on a different
Explain why the pie chart cannot be used to work out how many adults visited on that day.
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