Tables, charts and diagrams

David collected data about 34 players on the 2022–2023 Manchester United Premier League football team.

Each player has a playing position identified as goalkeeper or defender or midfielder or forward.

The bar chart shows information about the playing positions of these players.

Which playing position has the greatest number of players?

Which playing position has twice as many players as the goalkeeper position?

David concludes that there are more defenders than midfielders who play for Premier League football teams.

Give one limitation of David’s conclusion.

Johan sells tickets for a walking tour, a boat tour and a bus tour.

The pictogram shows the number of people who chose each type of tour one Saturday morning in June.

Write down the modal type of tour.

How many more people chose the boat tour than the bus tour on this morning?

Johan thinks that the number of people choosing each type of tour will change in July compared to June.

He wants to investigate the number of people choosing each type of tour.

Write down a hypothesis that he could use for this investigation.

Suggest two things that Johan should do when collecting his data to ensure that he can compare his results for July with the results for June.

A company offers a number of activities for its employees. Yusra wants to investigate what employees at the company think about the activities.

Here is her plan for data collection, for calculations and for diagrams.

Discuss whether Yusra’s plans for data collection, for calculations and for diagrams are appropriate.

The time series graph gives information about the revenue, in $ billion, for the skiing resort of Vail each quarter from Quarter 1, 2018 to Quarter 1, 2023

For which year and quarter was the revenue the greatest?

The 4‑point moving averages for the data and the trend line are also plotted on the grid.

Explain why it is appropriate to calculate 4‑point moving averages for this set of data.

Describe and interpret the trend shown by the time series graph.

Compare and interpret the seasonal variation for each quarter of the revenue for the years 2018 to 2022

Benjamin collected data on the results for the male competitors in the Ironman Canada competition in 2022

The incomplete histogram and incomplete grouped frequency table give information about the times taken, in hours, for these competitors to complete the competition.

Time (t hours)	Frequency
8 t 9	2
9 t 10	23
10 t 11	58
11 t 12	134
12 t 13	188
13 t 14	183
14 t 15	..................
15 t 16	..................
16 t 17	102

Use the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

Benjamin also collected data about the results of the male competitors in the Ironman UK competition in 2022

The histogram below gives information about the times taken, in hours, for these competitors to complete the Ironman UK competition.

Identify and interpret the type of skew shown in this histogram of the times for these competitors in the Ironman UK competition.

The time taken, in hours, for each competitor to complete the competition was recorded when the digital tag worn by the competitor passed the finish line.

Discuss the reliability of any conclusions made based on this method of data collection. Give a reason for your answer.

Benjamin wants to find out how competitors prepare for Ironman competitions. He plans to give a questionnaire to the finishers of his local competition. There are 1200 people in the competition. Benjamin intends to use systematic sampling and ask every 10th competitor who crosses the finish line.

Comment on the appropriateness of this plan for data collection.

The choropleth map gives information about the percentage change in the mileage driven in Great Britain for each region from 2020 to 2021

Percentage change in mileage driven in 2020 to 2021

(Source: https://roadtraffic.dft.gov.uk)

The table shows the number of miles driven in London in 2020 and in 2021

Show that London has been shaded correctly on the choropleth map.

Which region had the lowest percentage change in the mileage driven between 2020 and 2021?

Amy concludes that the percentage change in the mileage driven between 2020 and 2021 is the same for Wales and South West England.

Explain why Amy may not be correct.

Tom concludes that the number of motor vehicles using the roads has increased the most in Scotland between 2020 and 2021

Explain whether or not the choropleth map supports this conclusion.

Tsena is researching the ages of Oscar winners.

She has collected data from the internet about the ages of the winners of the Best Actor and Best Actress categories from 2000 to 2022

Data from the internet is an example of secondary data.

Explain what is meant by secondary data.

Here are the ages of the winners of the Best Actor category from 2000 to 2022

40 36 47 29 43 37 38 45 50 48 60 50

39 55 44 32 41 41 59 37 83 53 54 (Source: www.openintro.org and www.oscars.org)

The stem and leaf diagram gives the ages of the winners of the Best Actress category from 2000 to 2022

Complete the stem and leaf diagram with the ages of the winners of the Best Actor category. You should also complete the key.

(Source: www.openintro.org and www.oscars.org)

Work out the median age for the winners of the Best Actress category from 2000 to 2022

Michelle thinks it is more appropriate to use the interquartile range than the range as a measure of spread for these sets of data.

Give a reason why Michelle may think this.

Work out the interquartile range for the winners of the Best Actress category from 2000 to 2022

The table gives information about the ages of the winners of the Best Actor and Best Actress categories before 2000 It also gives information about the ages of the winners of the Best Actor category from 2000 to 2022

Compare the distribution of ages for the winners of the Best Actor category with the distribution of ages for the winners of the Best Actress category. You may use the blank column in the table to record your answers to parts (c) and (e) to help you. You should interpret your comparisons in context.

Rebecca collected data from the internet about the litter size of wild boar in France and in Italy. The frequency polygons give information about the litter sizes.

(Source: www.academic.oup.com and www.researchgate.net) Rebecca concludes that the average wild boar litter size in France is bigger than in Italy.

Do the frequency polygons support Rebecca’s conclusion? Give a reason for your answer.

Give another comparison of the distributions of the wild boar litter sizes in France and in Italy.

Discuss how the data collection could reduce the reliability of these conclusions.

The choropleth map gives information about the percentage change in the mileage driven in Great Britain for each region from 2020 to 2021

Percentage change in mileage driven in 2020 to 2021

(Source: https://roadtraffic.dft.gov.uk)

The table shows the number of miles driven in London in 2020 and in 2021

Show that London has been shaded correctly on the choropleth map.

Which region had the lowest percentage change in the mileage driven between 2020 and 2021?

Amy concludes that the percentage change in the mileage driven between 2020 and 2021 is the same for Wales and South West England.

Explain why Amy may not be correct.

Tom concludes that the number of motor vehicles using the roads has increased the most in Scotland between 2020 and 2021

Explain whether or not the choropleth map supports this conclusion.

Tsena is researching the ages of Oscar winners.

She has collected data from the internet about the ages of the winners of the Best Actor and Best Actress categories from 2000 to 2022

Data from the internet is an example of secondary data.

Explain what is meant by secondary data.

Here are the ages of the winners of the Best Actor category from 2000 to 2022

40 36 47 29 43 37 38 45 50 48 60 50

39 55 44 32 41 41 59 37 83 53 54 (Source: www.openintro.org and www.oscars.org)

The stem and leaf diagram gives the ages of the winners of the Best Actress category from 2000 to 2022

Complete the stem and leaf diagram with the ages of the winners of the Best Actor category. You should also complete the key.

(Source: www.openintro.org and www.oscars.org)

Work out the median age for the winners of the Best Actress category from 2000 to 2022

Michelle thinks it is more appropriate to use the interquartile range than the range as a measure of spread for these sets of data.

Give a reason why Michelle may think this.

Work out the interquartile range for the winners of the Best Actress category from 2000 to 2022

The table gives information about the ages of the winners of the Best Actor and Best Actress categories before 2000 It also gives information about the ages of the winners of the Best Actor category from 2000 to 2022

Compare the distribution of ages for the winners of the Best Actor category with the distribution of ages for the winners of the Best Actress category. You may use the blank column in the table to record your answers to parts (c) and (e) to help you. You should interpret your comparisons in context.

Agatha is investigating the times taken in the 2022 Olympic Women’s Skiathlon race.

There are two parts to the Skiathlon race. There is a 7.5 km classic stage and a 7.5 km free stage.

Agatha thinks there may be a relationship between the time taken by each skier to complete the classic stage and the time taken by each skier to complete the free stage. She suggests calculating a correlation coefficient to check.

Discuss the appropriateness of this suggestion. You should consider the type of data in your answer.

Agatha found the times taken for the event by all the skiers.

The incomplete histogram and incomplete grouped frequency table give information about the times taken, in minutes, to complete the 7.5 km classic stage of the race.

Use the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

Agatha also drew this histogram for the overall times for the race.

Agatha concludes that the median is in the 50 t ≤ 52 minute time interval.

Does the histogram support Agatha’s conclusion? Show calculations to support your answer.

A ski manufacturer produces wax used on skis.

It has made a new type of wax and wants to find out if using this wax improves the skiers’ times.

Agatha thinks a matched pairs approach should be used to find out if the wax improves the time taken to complete the race.

Agatha suggests matching skiers based on the type of ski that they use and their times in the race. One skier in each pair would use their original wax and the other skier would use the new wax.

Comment on the appropriateness of this suggestion. Give a reason for your answer.

The table shows information about the percentage of teenagers who used different types of devices in 2015 and in 2022

(Source: www.pewresearch.org)

Sapna created a visual representation of these data.

73% 95% 87% 90% 81% 80%

Discuss whether or not Sapna’s visual representation was an appropriate way to represent this information.

Mandeep visited Marple Wood Farm and tallied the types of animals he saw.

Circle the word in the list below that best describes the type of data for the types of animals.

Quantitative Discrete Continuous Categorical

The incomplete tally chart and incomplete bar chart give some information about Mandeep’s results.

Complete the tally chart and the bar chart.

This is a sign at the entrance to the farm.

Mandeep tallied 55 animals during his visit. Using his results, Mandeep claims that the most common animal in the farm is a chicken.

Give two reasons why Mandeep’s claim may be incorrect.

A teacher wants to investigate how many hours students spent revising for a test.

20 students have to complete a short questionnaire before they begin the test.

This is a copy of the questionnaire.

State one advantage of using a short questionnaire instead of interviewing each student.

State the type of question used as Question 2

The table below shows the data collected for Question 2

Give a reason why this data needs to be cleaned.

The teacher cleans the data. The teacher wants to display information about the test mark each student got compared to the number of hours this student revised.

The teacher plans to draw a diagram for this information. The diagram will be shown on a poster where these students can see it.

From the list below, circle the type of diagram it would be best to use for this target audience.

Box plot Pie chart Scatter diagram Cumulative frequency chart

A store manager wants to show the employees which department is making the most profit.

The store manager presents the data in this pie chart.

Explain why the use of a pie chart may not be appropriate to show which department is making the most profit.

The raw data is summarised in the table.

Suggest a more appropriate diagram to represent and compare the profits made in the different departments.

The diagram shows information about managers in Australia from 2016 to 2017

Managers in Australia 2016–17

18 16 14 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18

State the name of this type of diagram.

Find the age group that the greatest proportion of managers are from. You should justify your answer.

Divyesh is investigating the number of games won by two Los Angeles basketball teams, the Clippers and the Lakers. He collects some data from the NBA website.

Complete the sentence with an appropriate statistical word.

Divyesh has collected data from the internet and so this is_........ data.

Using the information in the bar chart to compare the number of games won by each team over the four years,

write down one comparison between the two teams,

describe the trend in the number of games won by the Lakers over the four seasons.

The table contains information about the number of games won by the Clippers in the 2022–23 season.

Complete the table. Give your answers correct to the nearest whole number.

The line graph shows the cumulative games played and the cumulative percentage of games won by the Lakers in the same season.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Each team played 82 games in the 2022–23 season.

Which team won the most games by the end of the 2022–23 season? You should justify your answer.

The cumulative frequency diagram gives information about the lengths, in mm, of a sample of 80 pike, caught in the Yukon River in Alaska. The pike were put back into the river.

Estimate how many of these pike had a length of 440 mm or more.

These data were collected using opportunity sampling.

State an advantage of using opportunity sampling.

The box plot below shows information about the lengths of the pike sampled from the Yukon River.

Here are the summary statistics, in mm, for a sample of pike caught in the Chena River in Alaska.

On the grid above, draw a box plot for the lengths of the pike caught in the Chena River.

Give three comparisons between the distribution of the lengths of pike from the Yukon River and the distribution of the lengths of pike from the Chena River. Interpret one of these comparisons in context.

Divyesh is investigating the number of games won by two Los Angeles basketball teams, the Clippers and the Lakers. He collects some data from the NBA website.

Complete the sentence with an appropriate statistical word.

Divyesh has collected data from the internet and so this is_........ data.

Using the information in the bar chart to compare the number of games won by each team over the four years,

write down one comparison between the two teams,

describe the trend in the number of games won by the Lakers over the four seasons.

The table contains information about the number of games won by the Clippers in the 2022–23 season.

Complete the table. Give your answers correct to the nearest whole number.

The line graph shows the cumulative games played and the cumulative percentage of games won by the Lakers in the same season.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Each team played 82 games in the 2022–23 season.

Which team won the most games by the end of the 2022–23 season? You should justify your answer.

The cumulative frequency diagram gives information about the lengths, in mm, of a sample of 80 pike, caught in the Yukon River in Alaska. The pike were put back into the river.

Estimate how many of these pike had a length of 440 mm or more.

These data were collected using opportunity sampling.

State an advantage of using opportunity sampling.

The box plot below shows information about the lengths of the pike sampled from the Yukon River.

Here are the summary statistics, in mm, for a sample of pike caught in the Chena River in Alaska.

On the grid above, draw a box plot for the lengths of the pike caught in the Chena River.

Give three comparisons between the distribution of the lengths of pike from the Yukon River and the distribution of the lengths of pike from the Chena River. Interpret one of these comparisons in context.

The pie charts show information about the proportion of livestock in 2021 for Finland and for Norway.

Marcus concludes that there are more turkeys in Finland than there are in Norway.

Explain why Marcus might be wrong.

The pie chart for Finland represents 2 341 780 livestock.

Work out the number of cattle represented in the pie chart for Finland.

In 2021, the total number of cattle, sheep, turkeys and pigs in Denmark was 14 888 487

Marcus plans to draw comparative pie charts for Finland and Denmark. The pie chart for Finland will have a radius of 5 cm.

Calculate the radius he should use for the pie chart for Denmark. Give your answer correct to one decimal place.

The population pyramid shows the age distribution of the world population in the year 1960

Each percentage is given correct to one decimal place.

10% 8% 6% 4% 2% 0% 2% 4% 6% 8% 10%

Work out the percentage of males aged 65 or over in 1960

Kiran is carrying out research into how the population of Finland is changing. She uses the data for Finland in 2023

	Finland 2023
Age (y years)	Percentage of the population (%)
0 y 15	14.91
15 y 30	17.13
30 y 45	19.52
45 y 60	18.39
60 y 75	18.88
75 y	11.17

Use linear interpolation to work out an estimate of the median age in Finland in 2023

In 1960, the median age in Finland was 27 years correct to the nearest year. Kiran claims that Finland’s population is getting older.

Explain whether or not Kiran’s claim is correct. You should justify your answer.

On a website, Kiran reads that the median age in Finland in 2023 was 42.8 years. (Source: www.worldometers.info)

Suggest a reason why the median of 42.8 from the website and a median found using linear interpolation would be different.

In world athletics, an athlete’s personal best results in different track and field events are recorded.

Zara wants to compare a sample of athletes’ longest recorded long jump against their height. She is going to present this information on a scatter diagram.

Explain why it is appropriate to use a scatter diagram.

Zara plotted the athletes’ heights on the x‑axis.

Give a reason why plotting the heights on the x‑axis is appropriate.

Zara selects 12 athletes ranked as some of the world’s best long jumpers. She calculates the Pearson Product Moment Correlation Coefficient (PMCC) for their personal best long jump distances against their heights.

The PMCC value is 0.02 (Source: www.worldathletics.org)

Describe the correlation shown by the PMCC.

Using data for the same 12 athletes, Zara compares their personal best long jump distances (m metres) to their fastest times in a 100 metre race (t seconds).

She calculates the PMCC to be –0.5

Describe and interpret the relationship between the athletes’ personal best long jump distances and their personal best 100 metre race times in context.

The data for the 12 athletes is shown in the table below.

World rank April 2023	Long jump athlete	Personal best long jump distance (m metres)	Personal best 100 m race time (t seconds)
1	M Tentoglou	8.60	10.70
3	M Dendy	8.42	10.31
4	S Ehammer	8.45	10.46
5	T Montler	8.38	10.49
8	E Cáceres	8.37	10.37
10	T Gayle	8.69	10.13
11	E Lasa	8.28	11.03
15	H Frayne	8.34	10.96
16	Y Hashioka	8.36	10.53
17	R Ju ka	8.31	11.07
26	C Mitrevski	8.21	10.27
30	H Santos	8.19	11.77

(Source: www.worldathletics.org)

The linear regression line for these data is t = 25 – 1.7m

In April 2023, M Massó was ranked number 2 in the world for the long jump. His personal best long jump distance was 8.39 m.

Zara uses this regression line to predict that M Massó could run the 100 m race in 10.7 seconds.

Comment on the reliability of this prediction in context.

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.

Length of fjord (lkm)	Frequency
0 l 50	199
50 l 100	17
100 l 150	12
150 l 200	3
200 l 250	1

(Source: https://en.wikipedia.org/wiki/List_of_Norwegian_fjords)

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

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

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

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

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.

Time taken to run 5 km (t minutes)

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.

Roberta is investigating how the ages of brides getting married in the UK has changed from 2003 to 2013 She collects official data from the internet using the website ‘Office for National Statistics’.

Explain why this website will give reliable data.

Roberta wrote the following hypothesis before she collected her data,

Has the age of brides increased between 2003 and 2013?

Explain why it is not appropriate to use this as a hypothesis.

The table gives information about the data that Roberta collected.

Roberta wants to compare the proportion of brides in each age group and the total number of brides in each age group by presenting the results in charts for 2003 and 2013 She discusses how to present the results with Andria.

Andria thinks that they should use pie charts.

Roberta thinks that they should use comparative pie charts.

What advice would you give to Andria and to Roberta on their choice of charts?

Roberta used a circle with a radius of 4 cm for her comparative pie chart for 2003

Calculate the radius of the circle for her comparative pie chart for 2013 Give your answer correct to 2 decimal places.

Roberta is going to present her comparative pie charts to non-statisticians.

What extra information could she include on her pie charts to help the non-statisticians make comparisons?

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)

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.

Claire is planning an investigation into the length of time that a learner has to wait for a driving test. She wants to find out about how waiting time varies in different regions of the UK.

Here is her plan for data collection, for calculations and for diagrams.

Discuss whether Claire’s plans for data collection, for calculations and for diagrams are appropriate.

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.

Timur is investigating the heights and weights of rugby players. He collected data from the internet about the heights and weights of players from the Wales rugby squad.

The players from the Wales rugby squad are classed as Forwards or Backs. Timur draws a scatter diagram for the heights and weights of some of the Backs from the Wales rugby squad.

Explain why a scatter diagram is appropriate for the type of data Timur collected.

The data for three of the players was not plotted on the scatter diagram. The height and weight of each of these players is given in the table below.

Complete the scatter diagram by plotting the points for players A, B and C.

Describe and interpret the type of correlation shown by the scatter diagram.

The double mean point for the heights and weights of all of the Backs is (184, 92).

Draw a line of best fit through the double mean point.

Timur also collected the heights and weights of players from the England rugby squad. He found the Spearman’s rank correlation coefficient for the heights and weights of the Forwards from the England rugby squad.

The correlation coefficient was 0.00

Interpret this correlation coefficient in context.

Timur used statistical software to find the following information about the heights (x cm) and weights (y kg) of the Backs from the Wales rugby squad and the Backs from the England rugby squad.

Compare the Spearman’s rank correlation coefficients and interpret this comparison in the context of the question.

Timur uses the information in the table to conclude that the weight of the England rugby squad Backs increases faster than the weight of the Wales rugby squad Backs as their height increases.

Assess the validity of Timur’s conclusion with reference to the statistical results.

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.

2.

5.

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.

Hand span (cm)	A B C D (less than 19) (19 span 22) (22 span 24) (24 or more)
Number of pianists	24 65 57 14

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

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-in- parliament/a-41082379)

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

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.

2.

5.

10.

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.

Hand span (cm)	A B C D (less than 19) (19 span 22) (22 span 24) (24 or more)
Number of pianists	24 65 57 14

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 snow depth, in centimetres, at Whistler Mountain was measured daily in February, in March and in April 2022

The table gives information about the snow depths for these 89 days.

Draw a cumulative frequency diagram for this information.

Find an estimate for the number of these days where the snow depth was between 195 cm and 215 cm.

Zack is comparing the players from the England Rugby Union team with the players from the Welsh Rugby Union team. The players are listed as Rugby Union Forwards or Rugby Union Backs.

Here are the weights, in kilograms, of the England Rugby Union team players who are listed as Backs.

(Source: www.englandrugby.com/england/senior‑men#squad)

The back‑to‑back stem and leaf diagram gives the weights, in kilograms, of the Welsh Rugby Union Backs.

Complete the back‑to‑back stem and leaf diagram with the weights, in kilograms, of the England Rugby Union Backs.

(Source: www.wru.wales/fixtures‑and‑teams/teams/wales/)

Work out the median weight for the Welsh Rugby Union Backs.

Work out the interquartile range for the Welsh Rugby Union Backs.

The table gives information about the weights for the England Rugby Union Backs.

Zack thinks that the Welsh Rugby Union Backs are heavier and have less consistent weights than the England Rugby Union Backs.

Do the statistics support these conclusions? You must give reasons for your answer.

Amy wants to use the median and interquartile range statistics in a news article for a sports magazine. The article will compare the players on the two teams who are Backs.

Comment on the appropriateness of using the median and the interquartile range in the article.

Give a limitation of using Zack’s statistics to compare all the players on the two teams.

Roxann wants to investigate the resting heart rates for members of her running club.

She believes that the resting heart rates will be normally distributed.

Here is the plan for her investigation.

Discuss whether Roxann’s plans for collecting and presenting data are appropriate.

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.

A town council is proposing to build a new leisure centre. Michelle is going to carry out a survey to find out what all the people in the town think of the proposal.

Michelle thinks that she should take a sample rather than a census.

Give two reasons why Michelle might think this.

Michelle plans to use the electoral register as the sampling frame.

Explain what you understand by the term sampling frame.

Give one problem Michelle may have using the electoral register as the sampling frame.

Michelle intends to conduct a pilot study.

Give two reasons why it is a good idea to conduct a pilot study.

Michelle is writing a plan for her investigation into people’s views on the leisure centre proposal.

Write down what Michelle should include in her plan. You should include each of the following

• a sampling method

• a question she could ask in her questionnaire

• a statistical diagram she could use to show the results of the survey.

Explain why each of the things you have written down is appropriate.

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

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

discrete continuous ordinal categorical

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

Weight (w kilograms)
Frequency

65 w 70	5
70 w 75	15
75 w 80	61
80 w 85	81
85 w 90
90 w 95
95 w 100	35
100 w 105	14
105 w 110	9
110 w 115	1

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

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

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

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

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.

Number of medals won in 2014 and 2018 Winter

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.

Banana Orange Apple Banana Pear Apple

Apple Banana Orange Pear Apple Banana Apple

Apple Apple Orange Apple Pear Banana Banana

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

How many students are in the class?

One of the students is chosen at random.

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.

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.

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.

Logan is investigating the heights of male adult giraffes and the heights of female adult giraffes.

He records the height, in metres, of each of a sample of male adult giraffes and the height, in metres, of each of a sample of female adult giraffes.

He draws the box plot below for the recorded heights of the male adult giraffes.

The table gives information about the recorded heights of the female adult giraffes.

Logan makes the following two conclusions.

1. Male adult giraffes are generally taller than female adult giraffes.

2. The heights of the female adult giraffes are more consistent than the heights of the male adult giraffes.

Assess Logan’s two conclusions. You should show clearly the values of any statistics you use in your answer.

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

exactly 6 goals were scored,

more than 6 goals were scored.

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.

The incomplete pictogram gives information about the numbers of cars sold from a garage in August and in September.

In October, 25 cars were sold from the garage.

Complete the pictogram for October.

Compare the number of cars sold from the garage in August to the number of cars sold from the garage in September. Give a reason for your answer.

In November, 17 cars were sold from the garage.

Explain why the use of this key may not be appropriate for representing 17 cars in the pictogram.

The time series graph shows the percentages of households in the United Kingdom with

(Source: Office for National Statistics)

Write down an estimate for the percentage of households with internet access in

2000

2018

The percentage of households with internet access in 2019 was 93%

Plot this information on the time series graph.

Write down the first year where the percentage of households with internet access was greater than 50

Using the information given in the time series graph,

compare the change in percentage of households with internet access from 2001 to 2005 with the change in percentage of households with internet access from 2015 to 2019

You must show how you get your answer.

Complete the labelling on the frequency axis.

20 employees work in the warehouse in the Rotherham branch.

Complete the key.

In the York branch, 25 employees work in the office and 10 employees work in the warehouse.

Complete the composite bar chart for the York branch.

Find the total number of employees who work in the offices of Northern Stationery Supplies.

Northern Stationery Supplies has a total of 125 employees.

One employee from Northern Stationery Supplies is chosen at random.

Find the probability that this employee works in the warehouse in the Manchester branch.

Mrs Singh is the Headteacher of a school with 1200 students.

She wants to find out about the ways the students at her school use the internet to complete their homework.

She is going to write a plan for her enquiry.

Write down one thing Mrs Singh should include in her plan for each of

• data collection

• choice of sampling method

• a diagram to represent the data collected.

Explain why each of the things you have written down is appropriate.

The population pyramid gives information about the percentages of the population of the United Kingdom who are male and who are female in each age group for 2017

Each percentage is given correct to one decimal place.

United Kingdom 2017
Population: 65 511 097

Write down the percentage of the population who are female in the age group 50–54

Work out the percentage of the population who are male in the age group 10–19

In 2017, the number of people age 100 and older (100+) in the United Kingdom was 13 310 (Source: Office for National Statistics)

Using the information above and information from the population pyramid,

explain why the percentage of the population in the age group 100+ is given as 0.0% on the population pyramid. You must show your working.

Jamie is carrying out research into the ages of people in the United Kingdom. He uses the information in the population pyramid to claim,

“In the United Kingdom in 2017 the number of males who were older than 40 was greater than the number of females who were older than 40”

Explain whether or not Jamie’s claim is correct.

Weronika works for a road traffic organisation. One day she is investigating the speeds of cars and the speeds of motorcycles along a motorway.

Here is part of the spreadsheet that Weronika used to record her results.

Speed (s miles per hour)	Percentage of cars	Percentage of motorcycles
30 s 40	3	0
40 s 50	18	two
50 s 60	42	7
60 s 70	27	124
70 s 80	6	56
80 s 90		11
Total	100	100

Give a reason why Weronika will need to clean the data.

Weronika concludes that the value of 124 in the spreadsheet must be wrong.

Explain why.

Here is the information about motorcycles from the spreadsheet with the data cleaned.

Speed (s miles per hour)	Percentage of motorcycles
30 s 40	0
40 s 50	2
50 s 60	7
60 s 70	24
70 s 80	56
80 s 90	11
Total	100

Use linear interpolation to work out an estimate of the median speed of the motorcycles.

The frequency polygon for the speeds of cars has been drawn on the grid.

On the same grid, draw the frequency polygon for the speeds of the motorcycles.

Using the two frequency polygons, compare the skew of the distribution of the speeds of the cars with the skew of the distribution of the speeds of the motorcycles. Explain what your comparison means in context.

The choropleth map gives information about the numbers of orangutans living in the forests of the Malaysian state of Sabah in northern Borneo. Some regions of the state are shaded and labelled with a number.

Write down the number of a shaded region where there are not more than 100 orangutans.

Regions 15 and 16 are protected forest regions.

Adam claims that in a protected forest region there is a greater number of orangutans.

Does the choropleth map support Adam’s claim? You must give a reason for your answer.

The population pyramid gives information about the percentages of the population of the United Kingdom who are male and who are female in each age group for 2017

Each percentage is given correct to one decimal place.

United Kingdom 2017
Population: 65 511 097

Write down the percentage of the population who are female in the age group 50–54

Work out the percentage of the population who are male in the age group 10–19

In 2017, the number of people age 100 and older (100+) in the United Kingdom was 13 310 (Source: Office for National Statistics)

Using the information above and information from the population pyramid,

explain why the percentage of the population in the age group 100+ is given as 0.0% on the population pyramid. You must show your working.

Jamie is carrying out research into the ages of people in the United Kingdom. He uses the information in the population pyramid to claim,

“In the United Kingdom in 2017 the number of males who were older than 40 was greater than the number of females who were older than 40”

Explain whether or not Jamie’s claim is correct.

Weronika works for a road traffic organisation. One day she is investigating the speeds of cars and the speeds of motorcycles along a motorway.

Here is part of the spreadsheet that Weronika used to record her results.

Speed (s miles per hour)	Percentage of cars	Percentage of motorcycles
30 s 40	3	0
40 s 50	18	two
50 s 60	42	7
60 s 70	27	124
70 s 80	6	56
80 s 90		11
Total	100	100

Give a reason why Weronika will need to clean the data.

Weronika concludes that the value of 124 in the spreadsheet must be wrong.

Explain why.

Here is the information about motorcycles from the spreadsheet with the data cleaned.

Speed (s miles per hour)	Percentage of motorcycles
30 s 40	0
40 s 50	2
50 s 60	7
60 s 70	24
70 s 80	56
80 s 90	11
Total	100

Use linear interpolation to work out an estimate of the median speed of the motorcycles.

The frequency polygon for the speeds of cars has been drawn on the grid.

On the same grid, draw the frequency polygon for the speeds of the motorcycles.

Using the two frequency polygons, compare the skew of the distribution of the speeds of the cars with the skew of the distribution of the speeds of the motorcycles. Explain what your comparison means in context.

David is investigating the prices of houses in Streetly, which is in the West Midlands.

David took a sample of 41 houses in Streetly from a property website and recorded the price of each of these houses.

The cumulative frequency table shows information about the prices of these houses.

Draw a cumulative frequency diagram for this information.

In David’s sample there were N houses with a price in the interval 300 < P ≤ 350

Find an estimate for the value of N.

David wants to use his investigation to predict the number of houses in Central London that have a price between £300 000 and £350 000

Assess whether or not it is sensible for David to make this prediction using the results of his investigation.

Gaby is researching the final position of a football team in the English Premier League and the mean value of all the players in the team.

Suggest a diagram that Gaby could draw to see if there is an association between the final position and the mean value.

The table gives information about the data for the 2018–2019 season that Gaby used.

(Source: www.transfermarket.com)

Calculate Spearman’s rank correlation coefficient for the information in the table. You may complete the d column and d² column of the table to help you.

Interpret your answer to part (b) in the context of Gaby’s research. You should refer to the effects of any anomalous data.

Amelia suggests that Pearson’s product moment correlation coefficient should be used instead of Spearman’s rank correlation coefficient to measure the correlation between the data Gaby is researching.

Discuss whether or not Amelia’s suggestion is appropriate.

For a survey, Kayleigh counted the number of people in each of the 20 cars that arrived at her office car park one morning.

Here are her results.

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

Write down the mode.

At Kayleigh’s office there is a scheme to reduce the number of cars arriving at the office car park which have only 1 person in the car.

Kayleigh concludes from her survey that the scheme is not working.

Explain whether or not Kayleigh’s results support her conclusion.

John suggests that Kayleigh’s results are not suitable for her to reach a reliable conclusion.

Give one reason why John may be correct.

The table shows information about the results of a survey into ‘Charitable Giving and Social Activity’ over a four week period.

For example, 40% of all of those surveyed said that they had donated money to charity, but for 16 – 24 year olds this was only 26%

Some people in the survey said that they took part in more than one of the given activities.

7% of those aged 16 – 24 took part in one of the activities.

Which activity?

Of those who Volunteered for a charity, which age group had the greatest percentage?

One of the people surveyed is selected at random. This person had Bought an ethical product.

Describe the most likely gender and age group for this person.

Describe the relationship suggested by the data between age and having Given goods to charity.

Laura is going to do a Sponsored bike ride for charity.

She uses the information in the table to suggest that more than half the people who sponsor her will be female.

Explain how the information in the table supports this suggestion.

Nikola asks 50 male and 50 female drivers arriving at a car park if the type of car they are driving is petrol, diesel or electric.

The two-way table shows some information about her results.

Complete the two-way table.

Nikola wants to compare her results for male drivers with her results for female drivers. To do this she uses the information she collected to draw the two pie charts shown below.

Work out the angle for electric cars in the pie chart for male drivers. You must show the calculation.

Nikola told Seb how she collected her data. She then gave Seb a copy of each of her two pie charts and asked him to tell her what they showed. Seb used the pie charts to reach the following conclusions.

The most common type of car is diesel.

Males are more likely than females to be drivers of electric cars.

Use the information in the pie charts to assess Seb’s two conclusions. You should also consider how Nikola’s data collection method affects the reliability of Seb’s conclusions.

A garden centre has a register of 400 loyalty card members. The owner of the garden centre wants to find out information about the distribution of the amount of money spent by each loyalty card member on each visit to the garden centre.

The owner decides on the following plan.

• Record the amount of money spent by each of the first 50 customers to the garden centre on Monday morning.

• Draw a bar chart for the amounts of money spent.

• Find the mean of the amounts of money spent.

Discuss whether the manager’s plan is likely to be effective.

You should comment on both the collection of data and on the analysis of results.

Where appropriate you should suggest improvements to the plan.

Bill investigated the heights of females competing in different sports.

Using data from the internet, he recorded the height, in cm, of each female in a sample of 15 female rugby players and the height, in cm, of each female in a sample of 15 female basketball players.

He drew the box plot below for the recorded heights of the 15 female basketball players.

(Source: englandrugby.com, gbbasketball.com)

The table gives information about the recorded heights of the 15 female rugby players.

Using the information in the table, draw on the grid above a box plot for the recorded heights of the 15 female rugby players.

Compare the two distributions of heights. Give three comparisons and interpret one of your comparisons.

Considering the method that Bill used to collect his data, comment on the reliability of your comparisons in part (b).

Irina is investigating whether the percentage of the population of a country living in urban areas has an effect on the life expectancy in that country.

Suggest a hypothesis Irina could use for her investigation.

Irina collected the following information about 10 countries.

The Urban population (%) refers to the percentage of the population of the country who live in urban areas.

Irina used statistical software to draw a scatter diagram for the information in the table.

Give a reason why a scatter diagram is an appropriate diagram to use.

For this investigation, which variable is the explanatory variable? Give a reason for your answer.

The scatter diagram from the statistical software is shown below.

Explain, giving a statistical reason, whether or not this scatter diagram supports your hypothesis in part (a).

For these 10 countries, the double mean point of the data is (63.9, 77.8).

Using this information, draw a line of best fit on the scatter diagram.

Using statistical software, Irina finds that the gradient of the line of best fit should be 0.19

Interpret the gradient of the line of best fit.

Irina now finds that South Africa has Urban population 65% and Life expectancy 63 years.

Determine how this information for South Africa fits with the relationship shown in the scatter diagram for the other countries.

Bill investigated the heights of females competing in different sports.

Using data from the internet, he recorded the height, in cm, of each female in a sample of 15 female rugby players and the height, in cm, of each female in a sample of 15 female basketball players.

He drew the box plot below for the recorded heights of the 15 female basketball players.

(Source: englandrugby.com, gbbasketball.com)

The table gives information about the recorded heights of the 15 female rugby players.

Using the information in the table, draw on the grid above a box plot for the recorded heights of the 15 female rugby players.

Compare the two distributions of heights. Give three comparisons and interpret one of your comparisons.

Considering the method that Bill used to collect his data, comment on the reliability of your comparisons in part (b).

Irina is investigating whether the percentage of the population of a country living in urban areas has an effect on the life expectancy in that country.

Suggest a hypothesis Irina could use for her investigation.

Irina collected the following information about 10 countries.

The Urban population (%) refers to the percentage of the population of the country who live in urban areas.

Irina used statistical software to draw a scatter diagram for the information in the table.

Give a reason why a scatter diagram is an appropriate diagram to use.

For this investigation, which variable is the explanatory variable? Give a reason for your answer.

The scatter diagram from the statistical software is shown below.

Explain, giving a statistical reason, whether or not this scatter diagram supports your hypothesis in part (a).

For these 10 countries, the double mean point of the data is (63.9, 77.8).

Using this information, draw a line of best fit on the scatter diagram.

Using statistical software, Irina finds that the gradient of the line of best fit should be 0.19

Interpret the gradient of the line of best fit.

Irina now finds that South Africa has Urban population 65% and Life expectancy 63 years.

Determine how this information for South Africa fits with the relationship shown in the scatter diagram for the other countries.

Three types of sausage are sold in a farm shop, pork, beef and vegan.

The comparative pie charts show information about the number of packs of these sausages sold in the farm shop in May 2015 and in May 2019

The pie charts are drawn accurately and the angles for the vegan sectors are shown.

The radius of the pie chart for May 2019 is greater than the radius of the pie chart for May 2015

Explain what can be deduced from this information.

30 packs of vegan sausages were sold in the farm shop in May 2015

Work out the number of packs of vegan sausages that were sold in the farm shop in May 2019

The pictogram shows information about the number of rugby balls sold in a shop each day from Monday to Wednesday last week.

How many rugby balls were sold on Monday?

On Thursday, the number of rugby balls sold was 8

Show this information on the pictogram.

Brian begins to draw the pictogram below to show the number of tennis rackets sold in the shop on Friday and on Saturday last week.

On Saturday, the number of tennis rackets sold was 22

Explain why the key for the pictogram is not suitable.

The time series graphs show information about the numbers of births recorded in England and Wales for girls named Chloe and for girls named Evelyn in the years 2000 to 2017

(Source: Office for National Statistics)

For the year 2017, write down the number of births recorded for girls named Evelyn.

For the year 2017, there were more births recorded for girls named Evelyn than for girls named Chloe.

How many more?

For the years 2000 to 2017, describe the trend for

girls named Chloe,

girls named Evelyn.

Julie asked 20 of her friends how many days last week they each played a sport.

Here are her results.

3 4 5 3 2 2 3 3 2 5 1 0 1 0 2 3 3 2 5 3

Which word from the list below best describes Julie’s data before it is processed?

Julie draws the following tally chart for her results.

Write down two things that could be misleading or are wrong with Julie’s tally chart.

The median for Julie’s results is 3

Interpret this value in context.

Julie says the mode of her results is 7

Is Julie correct? Give a reason for your answer.

Albert groups Julie’s results and then draws the following bar chart.

Assess whether or not Albert’s way of presenting Julie’s results is appropriate. Give two reasons for your answer.

The multiple bar charts show information about the percentages of the population in each of Japan and of Kenya that are in each of five different age groups.

(Source: https://www.cia.gov/library/publications/the-world-factbook)

One person is selected at random from the population of Japan.

Work out the probability that this person is not in the age group 15–24

Compare the percentage of the population of Japan aged 0–14 with the percentage of the population of Kenya aged 0–14 Justify your answer using values from the multiple bar charts.

There are two statements below.

Decide whether each statement is true for Japan only or for Kenya only or for both countries or for neither country. Justify each answer using information from the multiple bar charts.

“The age group 55–64 has more than 10% of the population.”

The statement is true for_........

“There is only one age group with a smaller population than the age group 55–64”

The statement is true for_........

Craig thinks that the information in the multiple bar charts could be represented using a population pyramid.

Explain whether or not this would be a suitable diagram for Craig to use.

Aminah collected information about the mean daily temperature, in C, in August in Scotland for the years 1910 to 2018

The table shows a summary of the data produced by statistical software.

(Source: https://www.metoffice.gov.uk/climate/uk/summaries/datasets)

On the grid below, draw a box plot for the information in the table.

Calculate the interquartile range for the data in the table. You must show your working.

Describe the skew of the distribution represented by the box plot. Give a reason for your answer.

The cumulative frequency graph gives information about the area, in square kilometres, of the 48 counties in England.

(Source: https://en.wikipedia.org/wiki/List_of_ceremonial_counties_of_England)

Find an estimate of the 75th percentile of this information.

_........ square kilometres

Interpret this value in context.

Half of the counties in England have an area between 2000 square kilometres and k square kilometres.

Work out an estimate for the value of k.

An activity centre sells Adult tickets and Child tickets. A ticket can be a Day pass or a Weekend pass.

The incomplete two‑way table gives some information about the number of each type of ticket sold last Saturday.

Complete the two‑way table.

One of the people at the activity centre last Saturday with an Adult ticket is selected at random.

Write down the probability that their ticket is a Day pass.

Compare the number of Day passes sold and the number of Weekend passes sold. You should make two comparisons.

The manager of an art shop wants to find out about the shopping habits of customers in his shop. He wants to find out how many customers leave the shop without buying anything.

For the next four weeks he plans to record how many customers leave the shop without buying anything each Monday.

Give one problem with the manager’s plan for data collection.

The manager asks his staff to record the number of people served at the till each hour.

‘Number of people served’ is an example of which type of data?

The staff record the number of people served per hour. Here is the completed table.

Identify two problems with this completed table.

The manager also collected data on the type of art that his customers produce.

The incomplete bar chart shows information about the type of art produced by some of his customers.

Photography is the type of art produced by 11 customers.

Complete the bar chart.

Which type of art is produced by half as many customers as those who produce paintings?

Shona and Luke are investigating housing.

Shona wants to find out about the types of house in which people live. She plans to collect data by asking people to tell her in which type of house they each live.

Complete the sentence with an appropriate statistical word.

Shona is collecting the data herself and so this is_........ data.

Design a data collection sheet for Shona to use.

Luke has collected data about the number of people living in each of the 12 houses in his street.

Here is his data.

2 2 3 3 3 4 4 4 4 5 5 11

Luke wants to work out the average of the number of people living in each house in his street.

Which average, mean or median, would it be more appropriate for Luke to use? Give a reason for your answer.

There is one outlier in the data.

Excluding the outlier, work out the range of the number of people living in the houses in the street.

Shona has collected data about the number of people living in each of the houses in her street. She has collected data for 2014 and for 2019

The table gives the range of the number of people living in the houses in Shona’s street

Compare the range for 2014 with the range for 2019 and interpret your comparison in context.

On the grid, use this information to complete the composite bar chart for Year 3

How many retirement cakes were sold in Year 2?

Describe how the numbers of retirement cakes sold changed over the three years.

Simas is investigating what students like to do in their spare time.

He collected data by asking the students at a primary school and at a secondary school what they like to do in their spare time.

Simas asked each student at the two schools which of reading, watching television, playing computer games or playing outside they like best to do in their spare time.

The pie charts show information about the students’ answers.

What does the pie chart for the primary school students show about what they like best to do in their spare time? Give one conclusion.

Compare what primary school students like best to do in their spare time with what the secondary school students like best to do in their spare time. Give two comparisons.

Ruth is investigating the results of the Six Nations rugby competition.

She finds the following summary information for the Six Nations rugby competition in 2018 and in 2019

In 2018, which two teams had fewer ‘points scored for’ than ‘points scored against’?

Two teams finished in the same final position in 2019 as they had finished in 2018

Write down the names of these two teams.

Which team won 2 matches in 2018 and 3 matches in 2019?

Ruth concludes that in 2018 and in 2019 Wales had a more successful rugby team than Scotland.

Does the information in the tables support her conclusion? Give a reason for your answer.

Ruth found from a newspaper the age of each player from the England team for a 2019 Six Nations rugby match.

Here are the ages.

20 24 25 25 26 26 26 27 27 28 28 28 28 29 29

(Source: www.irishtimes.com)

Find the mode of the ages.

Ruth plans to use a stem and leaf diagram to represent the ages.

Discuss whether or not a stem and leaf diagram would be an appropriate diagram to use.

Tim is writing an article for university lecturers on literacy rates in Africa.

He uses the following choropleth map to display the literacy rates in the countries of mainland Africa and Madagascar.

No data 0% 20%
40%
60%
80% 95% 100%

Discuss whether or not this is a suitable diagram to use for the readers of his article.

In his article, Tim concludes that the south of Africa has higher literacy rates than other parts of Africa.

Does the choropleth map support this conclusion? Give statistical reasons for your answer.

Anne is investigating the effect of caffeine on reaction times.

Here is what Anne has written down for her hypothesis and how she plans to collect, process and present her data.

Discuss whether Anne’s hypothesis and her plans for collecting, processing and presenting data are appropriate.

Tim is writing an article for university lecturers on literacy rates in Africa.

He uses the following choropleth map to display the literacy rates in the countries of mainland Africa and Madagascar.

No data 0% 20%
40%
60%
80% 95% 100%

Discuss whether or not this is a suitable diagram to use for the readers of his article.

In his article, Tim concludes that the south of Africa has higher literacy rates than other parts of Africa.

Does the choropleth map support this conclusion? Give statistical reasons for your answer.

Anne is investigating the effect of caffeine on reaction times.

Here is what Anne has written down for her hypothesis and how she plans to collect, process and present her data.

Discuss whether Anne’s hypothesis and her plans for collecting, processing and presenting data are appropriate.

Emily and Jess work in the head office of a chain of restaurants.

The menu in all of the restaurants has recently been changed. Emily and Jess have been asked to find out the effect of these changes.

They are going to start by finding out what the kitchen staff think of the new menu.

Emily thinks that they should use a cluster sample of kitchen staff in the restaurants. The restaurants would be the clusters.

Jess thinks that they should use judgement sampling. The head chef of the company would be asked to select suitably experienced kitchen staff for the judgement sample.

Discuss whether these two sampling methods are suitable for Emily and Jess to use.

A website gives diners the opportunity to rate their dining experience at restaurants. Here is one of the questions that diners are asked to answer.

Poor Excellent

1 2 3 4 5 Mark with a cross (X) on the scale, one of the numbers 1 (poor), 2, 3, 4, 5 (excellent) to show how you rate your meal at the restaurant.

Emily recorded the mean ratings, correct to one decimal place, for meals at each of the 28 restaurants in the chain.

The stem and leaf diagram gives information about Emily’s recorded mean ratings.

Emily picks at random one of the restaurants.

Find the probability that the mean rating recorded by Emily for meals at this restaurant is less than 2.5

Jess separates the ratings into those that were made for meals from the previous menu and those that were made for meals from the new menu.

Jess uses her data to draw a percentage composite bar chart in order to compare the ratings for the previous menu and the ratings for the new menu.

The table below gives the percentages for each rating for the new menu.

Use the information in the table to complete the percentage composite bar chart for the new menu.

Use information from the composite percentage bar charts to describe what conclusions can be made about the effects of the changes to the menu.

Jon is investigating the colour of the eyes of all the students at his school. He recorded the colour of the eyes of a sample of 20 students in his class.

Work out how many of these students do not have brown eyes.

One of these students is selected at random.

Describe the likelihood that this student has grey eyes.

For Jon’s investigation, which statistical term best describes all of the students at Jon’s school?

Explain whether or not Jon could use his results to determine the most common colour of the eyes of teachers in his school.

Dalia works in a cafe. One Monday morning she recorded what type of milk each customer wanted in their coffee.

The tally chart gives the number of customers who wanted whole milk or skimmed milk or soya milk or no milk.

The list below gives the type of milk wanted by each of the other customers.

oat oat almond oat almond almond oat almond almond almond almond

Complete the tally chart.

Write down the type of milk that is the mode.

On Tuesday, Dalia again recorded what type of milk each customer wanted in their coffee.

The table below gives information about her results.

Determine whether or not both days have the same mode. You must give a reason for your answer.

The table shows information about the mean amount of water used per person per day in each of five countries.

(Source: United Nations Development Program

Here is a visual representation of the data.

Discuss whether or not this is an appropriate way to represent this information.

Some students in Year 9, in Year 10 and in Year 11 at a school were asked to name their favourite meal.

The two-way table gives some information about the favourite meal of each of these students.

Write down the number of Year 9 students whose favourite meal is lunch.

Complete the two-way table.

One of the students is selected at random.

Which meal is least likely to be this student’s favourite meal?

Write down the probability that this student is in Year 11

Find the probability that this student’s favourite meal is either lunch or dinner.

Given that this student is in Year 9, find the probability that this student’s favourite meal is breakfast.

People who completed higher education were asked what they were doing six months after they graduated.

The table shows information about the answers given by those who completed higher education in the UK for the years 2013 to 2017

(Source: Higher Education Statistics Agency

Write down the number of people in 2016 who answered Overseas work.

Write down all years in which the number of Non-response was greater than 120 000

Between which two consecutive years did the greatest increase in the number of people answering Further study take place?

For one of the categories in the table, the number of people decreased each year from 2013 to 2017

Write down this category.

Here are two methods that could have been used to collect this information.

Method 1: Conduct a face to face interview with each person who completed higher education.

Method 2: Send an email to each person who completed higher education inviting them to complete an online survey.

State which of Method 1 or Method 2 is the more appropriate method to use. Give a reason for your answer.

Explain how the pie chart shows that fish made up the largest proportion of the total pet population of the UK in 2017

_........

The total pet population in the UK in 2017 was estimated to be 54 million.

Calculate an estimate for the number of fish in the total pet population of the UK in 2017

Melanie takes a random sample of 30 pet owners in her town and records the number of pets they each have.

She produced the following table for her results.

For Melanie’s sample, find the upper quartile of the number of pets owned.

Give an interpretation of the value of the upper quartile.

From this sample, Melanie concluded that everyone in her town owns at least 1 pet.

Comment on the validity of Melanie’s conclusion.

The time series graph shows information about the annual inflation rate in the UK each

Quarter and Year (Source: ONS

Describe and interpret the trend in the annual inflation rate from 2015 to 2017

The table gives the annual inflation rate for the first two quarters of 2018

Plot this information on the time series graph.

Show that the first 4-point moving average for the data values in the time series graph is 0.375

Alex wants to use the time series graph to describe the changes in the annual inflation rates.

He subtracts the annual inflation rate of the first data point from the annual inflation rate of the last data point on the time series graph.

Explain whether or not this is an appropriate method for Alex to use.

The map below gives information about the percentage change in the number of police officers in each of the 42 different police force regions of England and Wales between 2014 and 2015

Write down the percentage change in the number of police officers in region 17

In how many of the 42 regions did the number of police officers increase?

Sadiq thinks that the map shows that there was a decrease in the overall number of police officers in England and Wales between 2014 and 2015

Explain why Sadiq may not be correct.

Write down the statistical name for the type of map used in this question.

The composite bar chart shows information about the number of new car registrations for the first quarter of 2018 in the UK and in Italy for each fuel type.

(Source: European Automobile Manufacturers Association)

In total, there were more new car registrations in the UK than in Italy.

Work out an estimate for how many more.

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

For each fuel type, compare the number of new car registrations in the UK with the number of new car registrations in Italy.

The table below shows the number of alternative fuel new car registrations in the UK for the first quarter of each year from 2015 to 2017

Michael says that the information in the table shows that the total number of alternative fuel new car registrations in the UK for 2015 to 2017 increased each year.

Explain why Michael’s conclusion may not be valid.

Joel is investigating the heights of buildings in Paris and in London. He collects data on the heights of the tallest buildings in Paris and in London.

Joel decides to remove the height of the tallest building from each of his two data sets before carrying out the investigation.

Suggest a reason why it may be appropriate for Joel to do this.

The cumulative frequency diagram shows information about the heights, in metres, of a sample of 50 of the tallest buildings in Paris.

The box plot shows information about the heights, in metres, of a sample of 50 of the tallest buildings in London.

­ Height (metres)

Compare the distribution of the heights of the tallest buildings in Paris with the distribution of the heights of the tallest buildings in London.

You should give the value of any statistic that you use in your comparisons.

The map below gives information about the percentage change in the number of police officers in each of the 42 different police force regions of England and Wales between 2014 and 2015

Write down the percentage change in the number of police officers in region 17

In how many of the 42 regions did the number of police officers increase?

Sadiq thinks that the map shows that there was a decrease in the overall number of police officers in England and Wales between 2014 and 2015

Explain why Sadiq may not be correct.

Write down the statistical name for the type of map used in this question.

The composite bar chart shows information about the number of new car registrations for the first quarter of 2018 in the UK and in Italy for each fuel type.

(Source: European Automobile Manufacturers Association)

In total, there were more new car registrations in the UK than in Italy.

Work out an estimate for how many more.

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

For each fuel type, compare the number of new car registrations in the UK with the number of new car registrations in Italy.

The table below shows the number of alternative fuel new car registrations in the UK for the first quarter of each year from 2015 to 2017

Michael says that the information in the table shows that the total number of alternative fuel new car registrations in the UK for 2015 to 2017 increased each year.

Explain why Michael’s conclusion may not be valid.

The table shows information from a survey about train passengers’ satisfaction with 10 categories of train facilities in spring 2018

In which of the 10 categories was

the ‘% satisfied or good’ the least?

the ‘% dissatisfied or poor’ the greatest?

How many people said ‘satisfied or good’ for punctuality?

Michelle claims that the percentages for ‘Cleanliness of the inside’ are the most reliable for these 10 categories.

Using the information in the table, suggest why she might think this.

The cumulative frequency graph shows information about the maximum daily temperature, in °C, in Bingley for the 30 days of June 2018

Find the 90th percentile.

Interpret your 90th percentile in context.

For Bingley in June 2018, the lowest maximum daily temperature was 13 °C and the greatest maximum daily temperature was 28 °C.

Show that the greatest maximum daily temperature in June is not an outlier.

The box plot below shows information about the maximum daily temperature, in °C, in Aultbea for each day of June 2018

On the grid above, draw a box plot for the maximum daily temperatures in June 2018 for Bingley.

Compare the distributions of maximum daily temperatures in June 2018 for Aultbea and for Bingley.

Reeta read a report that said that these days more 18 to 24 year olds find out what is happening in the news from social media than find out by watching TV. She decided to investigate how the 12 000 students at her university find out what is happening in the news. Reeta wrote the following as a hypothesis: Do more students get their news from social media than from other sources?

Comment on whether it is appropriate to use this as a hypothesis.

Reeta planned to use a sample of the students at her university stratified by gender and by age.

Explain why this method of sampling would be appropriate.

Reeta found that she could not get a list of all the students at her university to use for her stratified sample. Instead she decided she would question students in the university cafeteria. Here is the data collection sheet Reeta plans to use.

Discuss whether Reeta’s data collection sheet is appropriate for her to use. You should consider how Reeta might use the responses and describe any problems she may have when she uses the data collection sheet.

Reeta’s friend George is at a different university with 18 000 students.

George carried out a similar investigation at his university so that he and Reeta could compare their results.

They each questioned the same percentage of students at the university they each attend.

They decided to compare their results by using comparative pie charts.

Explain why comparative pie charts would be appropriate.

Reeta used a circle with diameter 10 cm for her pie chart.

Calculate the diameter of the circle that George used for his pie chart.