Tabulation, Diagrams & Representation (Edexcel GCSE Statistics: Foundation): Exam Questions

Leyla wants to find out how often people in her town eat in a restaurant.

She asked a sample of 30 people how many times they had eaten in a restaurant during the last week.

Here are Leyla’s results.

Fill in the tally chart for this information and complete the frequency column.

Write down the mode.

Work out the number of people in Leyla’s sample who had eaten in a restaurant fewer than 4 times during the last week.

Suggest a suitable diagram that Leyla could use to represent her data.

Richard works in an animal rescue centre.

Richard has collected data on the weights, in kilograms, of 10 male cats and the weights, in kilograms, of 10 female cats at the centre.

Richard wants to compare the average weight of the male cats with the average weight of the female cats.

Richard thinks that he should use either the mean or the median.

Which one of the mean or the median do you think he should use?
Give a reason for your answer.

Richard plans to use a scatter diagram in order to compare the weights of the male cats with the weights of the female cats.

Discuss whether or not a scatter diagram would be a suitable diagram to use.

The incomplete multiple bar chart shows information about the numbers of UK films first shown in 2013 and in 2014 for some types of film.

9 UK action films were first shown in 2013

7 UK action films were first shown in 2014

Complete the multiple bar chart.

The number of UK films first shown in 2013 was 17 for two types of film.

Which two types of film?

Work out the total number of drama films that were first shown in these two years.

Compare the numbers of UK films of the different types that were first shown in 2013 with those first shown in 2014

Explain why it would not be appropriate to display the information from the multiple bar chart in a time series graph.

The bar chart gives information about the amounts of different types of fuel, in Mtoe (millions of tonnes of oil equivalent), that were used in the United Kingdom in the year 2000

Ignoring ‘other fuels’,

write down the type of fuel that used the least amount of Mtoe in the year 2000

One type of fuel used one quarter of the amount of Mtoe used by natural gas in the year 2000

Which type of fuel was this?

The pie chart shows information about the amounts of different types of fuel, in Mtoe, that were used in the United Kingdom in the year 2013

The amount of natural gas used, in Mtoe, was the greatest in both 2000 and 2013

Explain how the bar chart and the pie chart show this.

Juanita says that more diesel was used in 2013 than in 2000

Explain whether or not the information given in the two diagrams can be used to support this statement.

Razwan collected data about the methods used to get to work that morning by the 25 people who work at his company.

The bar chart shows information about the methods used.

Which method was used by the greatest number of people?

Which method was used by half as many of the people who got to work by bus?

Razwan concludes that travelling to work by car is the most popular method used to get to work in his city.

Give one limitation of Razwan's conclusion.

Rebecca collected information about the type of accommodation that 30 people stayed in the last time they went on holiday.

She drew this diagram to show her results.

Write down three things that could be misleading or that are wrong in Rebecca's diagram.

The time series graphs show information about the numbers of students taking A Level Physics and A Level French in each of the years from 2008 to 2016

Work out an estimate for the difference in the number of students taking A Level Physics and the number of students taking A Level French in the year 2008

Explain why the answer to part (a) is an estimate.

Describe the trend in the number of students taking A Level French from 2008 to 2016

Alizee is going to give a presentation to students at a school. She wants to show her target audience that Physics is the most popular subject at A Level.

Explain whether or not it would be appropriate for Alizee to use the time series graph to show this.

Ivan is going to give a presentation to students at a school. He wants to show his target audience that the number of students taking A Level Physics is decreasing.

Explain how Ivan can use information from the time series graph to show this.

Lionel wants to use the time series graphs to predict the number of students taking A Level Physics and the number of students taking A Level French in 2020

Discuss whether or not it would be appropriate to do so.

27 adults were each asked to count the number of times they could bounce a ball on a bat.

Here are the results.

Complete the stem and leaf diagram for this information.

Work out the interquartile range of the results.

The median of the results for 27 children is 9.

The interquartile range of the results for these children is 6.

Alex thinks these results show that adults are better than children at bouncing a ball on a bat.

Do you agree with Alex?
You must give reasons for your answer.

Archaeologists divided a field into 36 squares of equal size.

The number of Roman roof tiles found in each square was recorded.

The choropleth map below was drawn using this information.

Use the choropleth map to describe where in the field the greatest number of roof tiles was found.

Give a statistical reason for your answer.

Tomoyo found the weight, in grams, of each of 100 cherries.

Circle the two words from the list that best describe the data Tomoyo found.

quantitative    qualitative    discrete    continuous    bivariate    ordinal    categorical

Tomoyo grouped the weights and she then drew this diagram for her results.

The incomplete frequency table shows some information about her results.

(i) Complete the frequency column in the table.

(2)

(ii) Calculate an estimate of the mean weight of the 100 cherries.

........................ g

(3)

The editor of a home magazine collects information about the types of washing machines people use.

She uses statistical software to represent the results in three different ways.

Way 1: Table.

Way 2: Bar chart.

Way 3: Pie chart.

For each of the ways, comment on why the editor might choose this way to represent the results in the magazine.

Way 1 ..........................

Way 2 ..........................

Way 3 ..........................

The incomplete pictogram gives information about the flavour and number of ice creams sold at Pradeep’s cafe one Saturday morning.

20 chocolate ice creams were sold on Saturday morning.

Complete the pictogram for the number of chocolate ice creams sold.

Work out the total number of ice creams sold on Saturday morning.

The pictogram below gives information about the flavour and number of ice creams sold at Pradeep’s cafe one Sunday morning.

Compare the number of vanilla ice creams sold in the cafe on Saturday morning with the number of vanilla ice creams sold in the cafe on Sunday morning.

Give a reason for your answer.

Pradeep wants to use the collected data to estimate how many ice creams of each flavour she will sell for the whole of next week.

Considering Pradeep’s data decide if this is appropriate.

The incomplete multiple bar chart gives information about the home country of visitors to a theme park in 2003 and in 2013

In 2003, 39% of the visitors were from France.

(i) On the multiple bar chart complete the label for the horizontal axis.

(1)

(ii) On the multiple bar chart complete the label for the vertical axis.

(1)

In 2003, 6% of the visitors were from Germany.
In 2013, 3% of the visitors were from Germany.

Complete the multiple bar chart for visitors from Germany.

Compare the change in the percentage of visitors to the theme park from France in 2003 and in 2013 with the change in the percentage of visitors to the theme park from the United Kingdom in 2003 and in 2013

John is investigating how the total number of visitors to the theme park has changed from 2003 to 2013

Comment on whether or not it is appropriate to use this multiple bar chart for his investigation.

The pie charts give information about the different types of properties that were for sale in July 2020 in Harrogate and in July 2020 in South Shields.

Compare the proportion of different types of properties for sale in Harrogate in July 2020 with the proportion of different types of properties for sale in South Shields in July 2020

Adam also drew two pie charts showing the different types of properties that were for sale in July 2021 in Harrogate and in July 2021 in South Shields.

Both pie charts have the same size angle for bungalows.
Adam uses this information to reach the following conclusion.

“The numbers of bungalows for sale in Harrogate in July 2021 and in South Shields in July 2021 were the same.”

Assess the validity of Adam’s conclusion.

A fjord is a deep and narrow part of a sea with steep land on three sides.

Emily is investigating the length of fjords in Norway. She collects some data from the internet and puts the data into a grouped frequency table.

The grouped frequency table below shows information about the results she collected.

(Source: https://en.wikipedia.org/wiki/List_of_Norwegian_fjords (opens in a new tab))

Work out the number of fjords that have a length of at least 100km.

(i) Calculate an estimate of the mean length of these fjords.
Give your answer to 1 decimal place.

......................... km (3)

(ii) Explain why your answer to part (b)(i) is only an estimate.

(1)

(iii) How could Emily have improved the accuracy of her answer to part (b)(i)?

(1)

Emily plans to use a frequency polygon to represent the lengths of the fjords.

Discuss whether or not a frequency polygon would be an appropriate diagram to use.

The two population pyramids give information about the percentage of the population who are male and who are female for each age group in France and in Italy in 2010

Tommy is investigating how the populations of Italy and France differ in 2010. He uses the two population pyramids to reach the following two conclusions.

• The percentage of people aged 50–54 was lower in France than the percentage of people aged 50–54 in Italy.

• The number of males aged 40–44 in France was greater than the number of males aged 40–44 in Italy.

Assess Tommy's two conclusions.
You should show clearly the value of any statistics you use in your answer.

The time taken, in minutes, for some runners to complete a 5 km run was recorded. The incomplete histogram and incomplete grouped frequency table give information about the times taken, in minutes, for these runners to complete the 5 km run.

(Source: www.parkrun.org.uk (opens in a new tab))

Use the information in the histogram to complete the table.

Estimate the number of runners that took less than or equal to 23 minutes to complete the race.

Identify and interpret the skew shown on the histogram.

Jenny is investigating how many days per week people use a gym.

She asks the 40 people in her fitness group how often they use the gym each week. Jenny draws this bar chart for her data.

One of these people is chosen at random.

Find the probability that this person uses the gym exactly 2 days per week.

What is the modal number of days to use the gym each week?

Jenny thinks that there are a lot of people in her fitness group who are exercising less than 2 days per week as there is a total of 10 people who used the gym on 0 days or 1 day per week.

Explain why Jenny might not be correct.

Ben is researching information about the number of British swimming medals won at the Olympics.

Here are his results, giving the number of British swimming medals won at the Olympics from 1900 to 2016

(Source: www.teamgb.com (opens in a new tab))

Fill in the tally chart for Ben’s results and complete the frequency column.

Suggest a suitable diagram that could be used for Ben’s results.

Write down the mode or modes.

Work out the median.

Ben wants to use an average to summarise the data.

Which of the mode or the median would be more appropriate?
Give a reason for your answer.

Ana collected information about the Scottish Football Championship results for the 2021/2022 season.

The composite bar chart gives some information about the number of points scored by nine of the teams.

Points are scored from wins or draws.

Raith Rovers scored 36 points from wins and 14 points from draws.

Complete the composite bar chart for Raith Rovers.

What does the overall height of each bar represent?

Compare the points scored by Dunfermline Athletic with the points scored by Queen of the South.

Chris is a manager at a theme park.

He wants to find out what food options visitors would like to be able to buy in the theme park.

State the population for this investigation.

Chris decides that he will take a convenience sample of visitors in the section of the park selling food.

Explain what is meant by a convenience sample.

Give one disadvantage of using a convenience sample.

Chris plans to use the data collection sheet below.

Discuss whether this data collection sheet is appropriate.

You should consider how Chris might use the data and describe any problems he might have when he uses the data collection sheet.

Chris suggests using a stem and leaf diagram to represent the data that he collects.

Discuss whether or not this would be a suitable diagram to represent his data.

Mobeen is investigating whether there is a difference in the amount of time spent reading by pupils in Green Park school and pupils at Golden Plains school.

He uses a census of all of the pupils at each school.
Each pupil is asked to record the amount of time spent reading in a week.

Mobeen then collects this information from each student through an online database.

Part of the database is shown below.

Give two reasons why the data should be cleaned before processing.

Mobeen wants to compare the data for Green Park school with the data for Golden Plains school.

Once the data has been cleaned Mobeen plans to use all of the times to draw a single box plot.

Explain why this is not an appropriate thing to do.

Matthew is investigating average household income for different states in the USA.

Give a reason why it is appropriate to use secondary data for this.

Matthew creates a choropleth map giving information about the mean household income by state for the USA in 2023

Mean annual household income in $ thousands.

Which three states have the lowest mean household income?

Matthew concludes that the mean household incomes are highest on the West coast and the East coast.

Does the choropleth map support this conclusion?
Give a reason for your answer.

Some researchers investigated the hand span, in centimetres, of adult pianists by their level – international, national and amateur.

The box plots below give information about the hand spans for national level and amateur level pianists.

Circle the word in the list below that describes hand span, in centimetres, as a type of data.

qualitative     ordinal     continuous     bivariate

The table gives information about the hand spans of the international level pianists.

Using the information in the table, draw on the grid above a box plot for the hand spans of the international level pianists.

Compare the three distributions of hand spans.
Give three comparisons and interpret two of your comparisons.

Pavel owns a music shop.
He wants to investigate the keyboard sizes used by pianists with different hand spans.
He collects data about the hand spans of the pianists who use his shop.

The table gives information about the number of these pianists with hand spans in each of four size categories.

Pavel plans to sample 20 of these pianists stratified by hand span size.

Explain how Pavel can obtain his stratified sample.
You should include details of any calculations he should use.

The cumulative frequency graph gives information about the ages, in years, of the 650 members of the UK Parliament in 2017

Using the cumulative frequency diagram, find an estimate of the median age for the members of the UK Parliament in 2017

................... years

In 2017 the German Parliament had 51.6% of members of Parliament aged between 45 and 60 years old.

(Source: https://www.dw.com/en/germanys-new-bundestag-who-is-who-inparliament/a-41082379 (opens in a new tab))

Compare this figure to the percentage of members of the UK Parliament with ages between 45 and 60 years in 2017

The table shows the average heights, to the nearest cm, of Adult Males and Adult Females who were born in the year 1996 in some countries of the world.

Write down the average height of Adult Males in Italy.

Write down the country in the table in which the Adult Females have the greatest average height.

Afzal thinks that the country in the table with the greatest difference in average heights between Adult Males and Adult Females is Italy.

Is Afzal correct?
Give a reason for your answer.

Using the table, compare the average height of Adult Males in Australia, with the average height of Adult Males in Zimbabwe.

Afzal suggests drawing a time series graph to represent the data in the table.

Explain whether or not this is an appropriate graph to use.

A newspaper reporter completed some research into the percentage of household waste that was recycled in the London Borough of Hackney in 2018 and 2019

The newspaper reporter drew the following bar chart to show this information.

Give two reasons why the bar chart could be misleading or wrong

Kyle is investigating the heights and the weights of professional basketball players.

He found the weight, in kilograms, of some professional basketball players from 1950 to 1959

Choose the word in the list below that describes weight, in kilograms, as a type of data.

The incomplete histogram and incomplete grouped frequency table give information about the weights, in kilograms, of the professional basketball players from 1950 to 1959

Use the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

Kyle also drew a histogram for the weights of professional basketball players from 2000 to 2009
This histogram was negatively skewed.

Interpret the negative skew of the weights of professional basketball players from 2000 to 2009

Kyle also collected data about the heights of professional basketball players from 1950 to 1959 and the heights of professional basketball players from 2000 to 2009

The grouped frequency table below gives information about the heights of professional basketball players from 2000 to 2009

The estimate of the mean height for professional basketball players from 1950 to 1959 is calculated to be 190.9cm to one decimal place.

(i) Calculate an estimate of the mean height of basketball players from 2000 to 2009

....................................................... cm

[3]

(ii) Comment on how the mean height of professional basketball players has changed between the two sets of data.

[1]

The incomplete comparative bar chart shows the total number of medals won by three of the countries that took part in the 2014 and 2018 Winter Olympics.

The total number of medals won by Sweden in the 2018 Winter Olympics was 14

Complete the comparative bar chart for Sweden.

Work out how many more medals were won by Sweden than Great Britain in the 2014 Winter Olympics.

Compare the total number of medals won by Sweden, Great Britain and Switzerland in the 2014 Winter Olympics.

Thomas says that the data displayed in the comparative bar chart is quantitative data.

Explain what is meant by quantitative data.

Norbert asked each of the students in his class to name their favourite fruit from Apple, Banana, Orange or Pear.

The results are shown below.

Fill in the tally chart for this information and complete the frequency column.

How many students are in the class?

Find the probability that this student’s favourite fruit is Orange.

Compare the number of students whose favourite fruit is Apple to the number of students whose favourite fruit is Pear.

Norbert decides to find the favourite fruit that is the mode.

Explain why the mode is an appropriate average for Norbert to find for this type of data.

Give one advantage of the tally chart over the raw data.

Norbert wants to draw a diagram to represent his results.

Choose the type of diagram from the list below that is most suitable for him to draw.

Rose is investigating the number of brothers and sisters that students in her secondary school have.

To investigate this she asks 10 students in Year 8 and 10 students in Year 11 how many brothers and sisters they each have.

Assess Rose’s method for her data collection.

The vertical line graph shows the data that she collected.

How many students have 2 or more brothers and sisters?

Write down the mode.

Rose uses her vertical line graph to conclude that no student in her school has 5 or more brothers or sisters.

Assess whether or not Rose’s conclusion is appropriate.

Linzi is the owner of a coffee shop and makes afternoon teas for customers.

The customers have an option of egg or ham sandwiches and an option of plain or fruit scones.

The incomplete two‑way table shows information about the number of afternoon teas she makes one Saturday

Complete the two‑way table.

Write down the probability that this customer

(i) ordered a plain scone,

[1]

(ii)ordered an egg sandwich and a fruit scone,

[1]

(iii) did not order a ham sandwich.

[2]

Linzi needs to place an order for scones for the next Saturday.

Use the information in the table to help her decide if she should order more fruit scones than plain scones. Give a reason for your answer

Grace asked a sample of 60 people in her town if they had ever visited France or Spain.
17 people visited both France and Spain
23 people visited Spain only
33 people visited France

Draw a Venn diagram to represent this information.

Grace says

• more than half of the people in her sample have visited France

• therefore more than half of the people in her town have visited France

Discuss the validity of each of Grace’s comments.

The cumulative frequency step polygon shows information about the number of goals scored in each of 28 matches played by the German women’s national football team.

(Source: www.worldfootball.net/teams/deutschland‑frauen‑team/)

Give a reason why a cumulative frequency step polygon is used to represent this information rather than a cumulative frequency curve.

Find the mode of the number of goals scored.

Find the number of these matches where

(i) exactly 6 goals were scored,

[1]

(ii) more than 6 goals were scored.

[2]

In 24 matches fewer than n goals were scored.

Find the value of n

Klara tries to calculate the interquartile range of the number of goals scored.

She gets an answer of 14

Explain how you know that her answer is incorrect.

The choropleth map below represents a park that has been divided into 25 squares of equal area.

Arthur has collected data about litter in the park.

The number of pieces of litter collected in each square on one Saturday morning is shown.

Use the information in the choropleth map to calculate an estimate of the total number of pieces of litter that were collected that day.

Arthur works in this park. He has been asked to decide where a new bin should be placed in the park to help reduce the amount of litter. He concludes that the new bin should be placed in the corner of the park represented by the bottom right of the choropleth map.

Assess the validity of Arthur’s conclusion with reference to the choropleth map.

Ian suggests that the method Arthur used to collect his data is not suitable to reach a reliable conclusion.

Assess whether Ian’s suggestion is correct.

Give a reason for your answer.