Types of Data - Worksheets, Questions and Revision

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GCSE · Statistics

S04 Types of Data

EDEXCEL 1ST0 · Calculator allowed · about 90 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Data can be described as either qualitative or quantitative, depending on what is being recorded.

(a)Define what is meant by qualitative data.(1)

(b)Define what is meant by quantitative data.(1)

(c)A vet records information about 4 variables for every animal at a clinic. For each variable, write down whether it is qualitative or quantitative.

Variable	Type (qualitative or quantitative)
Breed of animal
Mass of animal (kg)
Colour of coat
Number of visits this year

(4)

(Total for Question 1 is 6 marks)

Quantitative data can be further described as discrete or continuous.

(a)Define what is meant by discrete data.(1)

(b)Define what is meant by continuous data.(1)

(c)For each variable, write down whether it is discrete or continuous.

Variable	Discrete or continuous
Shoe size
Height of a plant (cm)
Number of siblings
Time taken to run 100 m (seconds)
Mass of a bag of sugar (kg)

(5)

(Total for Question 2 is 7 marks)

Data can also be classified by where it comes from: primary data or secondary data.

(a)Define what is meant by primary data.(1)

(b)Define what is meant by secondary data.(1)

(c)For each scenario, write down whether primary or secondary data is being used.

Scenario	Primary or secondary
A student times her own class doing a memory test.
A researcher uses population figures published by the Office for National Statistics.
A shop owner counts how many customers enter her shop each day.
A student uses last year's weather records from the Met Office website.

(4)

(Total for Question 3 is 6 marks)

For each variable, circle the word that correctly describes it.

(a)Number of pets owned by a family:(1)

Qualitative
Quantitative

(b)Favourite colour of paint:(1)

Qualitative
Quantitative

(c)Time taken to solve a puzzle, in seconds:(1)

Discrete
Continuous

(d)Number of goals scored in a match:(1)

Discrete
Continuous

(e)A student's own measurements taken during a science experiment:(1)

Primary
Secondary

(f)Rainfall figures taken from a government website:(1)

Primary
Secondary

(Total for Question 4 is 6 marks)

Complete each sentence using one word from the box. Each word may be used once, more than once, or not at all.

qualitative, quantitative, discrete, continuous, primary, secondary

(a)Data that describes a quality and cannot be measured numerically is called ______ data.(1)

(b)Data that is numerical and can be counted or measured is called ______ data.(1)

(c)______ data can only take exact, separate values, such as the number of cars in a car park.(1)

(d)______ data can take any value within a range, such as the exact time taken to complete a race.(1)

(e)Data collected first-hand, for a specific purpose, is called ______ data.(1)

(f)Data that has already been collected by someone else, for a different purpose, is called ______ data.(1)

(Total for Question 5 is 6 marks)

For each statement about types of data, write down whether it is True or False.

(i)Continuous data can only take whole-number values.(1)

(ii)The number of pets a family owns is discrete data.(1)

(iii)Secondary data is always less reliable than primary data.(1)

(iv)Nominal data has categories that can be placed in a meaningful order.(1)

(v)Bivariate data involves two variables recorded for each individual or item in a data set.(1)

(Total for Question 6 is 5 marks)

Amir wants to find the average monthly rainfall in the UK over the last 20 years, to use in a geography project.

(a)State whether Amir should collect primary data or use secondary data for this investigation.(1)

(b)Give two reasons to justify your answer to part (a).(2)

(c)State one disadvantage of Amir using secondary data for this project.(1)

(Total for Question 7 is 4 marks)

Primary and secondary data both have advantages and disadvantages.

(a)Give one advantage of using primary data.(1)

(b)Give one disadvantage of using primary data.(1)

(c)Give one advantage of using secondary data.(1)

(d)Give one disadvantage of using secondary data.(1)

(e)A company wants to compare its own weekly sales figures against sales trends for the whole of the UK retail sector. State whether the company needs primary or secondary data to find out about UK-wide retail trends, and explain your answer.(2)

(Total for Question 8 is 6 marks)

Categorical (qualitative) data can be further divided into nominal data and ordinal data.

(a)Define what is meant by nominal data.(1)

(b)Define what is meant by ordinal data.(1)

(c)For each variable, write down whether it is nominal or ordinal.

Variable	Nominal or ordinal
Eye colour
T-shirt size (S, M, L, XL)
Exam grade achieved (9, 8, 7, ..., 1, U)
Postcode
Favourite type of music

(5)

(d)Explain why exam grade is an example of ordinal data rather than nominal data.(1)

(Total for Question 9 is 8 marks)

Bivariate data is data in which two variables are recorded for each individual or item, so that any relationship between them can be investigated. The scatter graph shows the height and arm span of 8 students in a class.

(a)Define what is meant by bivariate data.(1)

(b)State the two variables that have been recorded to create this scatter graph.(2)

(c)Give one other example of a pair of variables that would produce bivariate data if recorded for the same group of people.(1)

(Total for Question 10 is 4 marks)

Data can be recorded as raw (ungrouped) data, or it can be organised into grouped data.

(a)Define what is meant by raw (ungrouped) data.(1)

(b)Define what is meant by grouped data.(1)

(c)The raw ages, in years, of 15 people at a gym class are shown below.

23, 45, 31, 29, 52, 38, 41, 27, 33, 49, 36, 44, 28, 55, 32

Complete the grouped frequency table.

Age (years)	Frequency
20 - 29
30 - 39
40 - 49
50 - 59

(3)

(d)Give one advantage and one disadvantage of grouping this data.(2)

(Total for Question 11 is 7 marks)

A courier company grouped the weights of 30 parcels delivered in one day. The bar chart shows the results.

(a)Use the bar chart to write down the number of parcels with weight in the interval 4 - <6 kg.(1)

(b)Explain why the horizontal axis is labelled using class intervals (such as 2 - <4 kg) rather than the exact weight of each parcel.(2)

(Total for Question 12 is 3 marks)

A student is carrying out a statistical investigation into the question: 'Do students who spend more time revising get higher test scores?' She plans to follow the statistical enquiry cycle: plan, collect, process, interpret.

(a)At the plan stage, state two variables the student should record for each student in her sample.(2)

(b)Classify the data type of each variable named in part (a).(2)

(c)At the collect stage, state whether the student should use primary or secondary data, and give a reason for your answer.(2)

(d)At the interpret stage, the student's sample only includes students from one class in her year group. Explain one way this could limit the conclusions she can draw.(1)

(Total for Question 13 is 7 marks)

The table shows 8 variables collected in a school survey about travel to school and lifestyle. For each variable, write down whether it is qualitative, discrete quantitative, or continuous quantitative.

Variable	Data type
Mode of transport to school
Distance travelled to school (km)
Number of school bags carried
Time taken to travel to school (minutes)
T-shirt size worn (S, M, L, XL)
Favourite school subject
Height of each pupil (cm)
Number of days absent this term

(Total for Question 14 is 8 marks)

A supermarket manager wants to decide whether to start stocking a new brand of oat milk. She is considering two options: (1) survey her own customers in-store, or (2) look at national sales reports for oat milk published by a market research company.

(a)Which option, (1) or (2), would produce primary data? Give a reason.(2)

(b)Give one advantage of the manager using option (2) instead of option (1).(1)

(c)Give one disadvantage of the manager using option (2) instead of option (1).(1)

(d)State which option you would recommend, with a reason.(1)

(Total for Question 15 is 5 marks)

In a survey, students are asked which of three school clubs they attend. Their answers are recorded using codes: 1 = Drama club, 2 = Sports club, 3 = Art club.

(a)Explain why this data is qualitative, even though it has been recorded using numbers.(2)

(b)Is this an example of nominal or ordinal data? Give a reason.(1)

(Total for Question 16 is 3 marks)

Ffion wants to find out whether taller students tend to have bigger shoe sizes. She asks 5 of her friends their height and records their shoe size using the categories 'small', 'medium' or 'large' rather than an exact shoe size.

(a)State the two variables involved in Ffion's investigation, and say whether the data she is collecting is bivariate.(2)

(b)Explain why recording shoe size as 'small', 'medium' or 'large' loses information compared with recording the exact shoe size.(2)

(c)Give one further limitation of Ffion's data collection method.(1)

(d)Suggest one improvement Ffion could make to her data collection.(1)

(Total for Question 17 is 6 marks)

A gardener grouped the heights of 50 sunflowers into class intervals, as shown.

Height (cm)	Frequency
100 - 119	8
120 - 139	19
140 - 159	17
160 - 179	6

(a)Explain why the gardener can only estimate the mean height of the sunflowers from this table, rather than calculate it exactly.(2)

(b)State one way the gardener could have collected the data so that the exact mean height could be found.(1)

(Total for Question 18 is 3 marks)

Complete the table below, classifying each variable in two ways.

(a)

Variable	Qualitative or quantitative	Discrete or continuous (or N/A)
Number of pets owned
Time to complete a marathon (hours)
Breed of dog

(5)

(b)Explain why 'discrete or continuous' does not apply to the variable 'breed of dog'.(1)

(Total for Question 19 is 6 marks)

A student is planning an investigation and is comparing primary and secondary data collection using the table below. Complete the missing cells.

Factor	Primary data	Secondary data
Typical cost	usually higher
Typical time to obtain		usually quicker
How well it matches the exact research question		may not match exactly

(a)Complete the missing cells in the table above.(3)

(b)A student is short on time before a coursework deadline. State, with a reason, which type of data she should prioritise using.(2)

(Total for Question 20 is 5 marks)

A national charity is investigating the question: 'Has the average distance people commute to work changed over the last 10 years?' The charity obtains commuting-distance figures from a government transport survey published every year since 2005, rather than surveying commuters itself.

(a)State whether the government transport survey data used by the charity is primary or secondary data. Give a reason.(2)

(b)The variable 'commuting distance (km)' is quantitative. State, with a reason, whether it is discrete or continuous.(2)

(c)The charity also records the year of each survey alongside the average commuting distance for that year, so that a trend can be studied. Explain why this makes the data set bivariate.(2)

(d)Evaluate one limitation of using this secondary data set to answer the charity's question, and suggest how the charity could address it.(2)

(Total for Question 21 is 8 marks)

Mark scheme · S04 Types of Data

Question 1

(a) B1 data that describes a quality/characteristic and is not numerical oe
(a) Answer: Qualitative data describes a quality or characteristic of something and is not numerical (for example colour or opinion).
(b) B1 data that is numerical and can be counted or measured oe
(b) Answer: Quantitative data is numerical data that can be counted or measured (for example height or number of pets).
(c) B1 Breed of animal: qualitative
(c) B1 Mass of animal (kg): quantitative
(c) B1 Colour of coat: qualitative
(c) B1 Number of visits this year: quantitative
(c) Answer: Breed of animal - qualitative; Mass of animal (kg) - quantitative; Colour of coat - qualitative; Number of visits this year - quantitative.

Question 2

(a) B1 data that can only take specific, separate values (often whole numbers obtained by counting) oe
(a) Answer: Discrete data can only take specific, separate values, often whole numbers obtained by counting.
(b) B1 data that can take any value within a range and is usually obtained by measuring oe
(b) Answer: Continuous data can take any value within a range and is usually obtained by measuring.
(c) B1 Shoe size: discrete
(c) B1 Height of a plant (cm): continuous
(c) B1 Number of siblings: discrete
(c) B1 Time taken to run 100 m (seconds): continuous
(c) B1 Mass of a bag of sugar (kg): continuous
(c) Answer: Shoe size - discrete; Height of a plant - continuous; Number of siblings - discrete; Time to run 100 m - continuous; Mass of a bag of sugar - continuous.

Question 3

(a) B1 data collected first-hand by the person or organisation using it, for their own specific purpose oe
(a) Answer: Primary data is collected first-hand by the person or organisation that will use it, for their own specific purpose.
(b) B1 data that already exists, collected by someone else, usually for a different purpose oe
(b) Answer: Secondary data already exists and was collected by someone else, usually for a different purpose.
(c) B1 Timing her own class: primary
(c) B1 Using ONS population figures: secondary
(c) B1 Counting her own customers: primary
(c) B1 Using Met Office records: secondary
(c) Answer: Timing her own class - primary; ONS population figures - secondary; Counting her own customers - primary; Met Office records - secondary.

Question 4

(a) B1 Quantitative cao
(a) Answer: Quantitative
(b) B1 Qualitative cao
(b) Answer: Qualitative
(c) B1 Continuous cao
(c) Answer: Continuous
(d) B1 Discrete cao
(d) Answer: Discrete
(e) B1 Primary cao
(e) Answer: Primary
(f) B1 Secondary cao
(f) Answer: Secondary

Question 5

(a) B1 qualitative
(a) Answer: qualitative
(b) B1 quantitative
(b) Answer: quantitative
(c) B1 discrete
(c) Answer: discrete
(d) B1 continuous
(d) Answer: continuous
(e) B1 primary
(e) Answer: primary
(f) B1 secondary
(f) Answer: secondary

Question 6

(i) B1 False cao
(i) Answer: False
(ii) B1 True cao
(ii) Answer: True
(iii) B1 False cao
(iii) Answer: False
(iv) B1 False cao
(iv) Answer: False
(v) B1 True cao
(v) Answer: True

Question 7

(a) B1 secondary cao
(a) Answer: Secondary data.
(b) B1 collecting 20 years of rainfall data himself would take far too long and is impractical oe
(b) B1 reliable rainfall records already exist (e.g. from the Met Office), so there is no need to collect it again oe
(b) Answer: It would take Amir far too long to record rainfall himself for 20 years, and reliable records already exist (e.g. from the Met Office), so he should use those instead.
(c) B1 the data may have been collected in a different way, for a different region, or for a different purpose, so it may not exactly match what Amir needs oe
(c) Answer: The secondary data may not exactly match what Amir needs, for example if it covers different regions or was recorded in a different way to what his project requires.

Question 8

(a) B1 collected for the exact purpose needed and the researcher controls how it is collected oe
(a) Answer: Primary data is collected for the exact purpose needed, and the researcher has control over how it is collected.
(b) B1 can take a long time and cost more to collect oe
(b) Answer: Collecting primary data can take a long time and cost more than using data that already exists.
(c) B1 usually quicker and cheaper to obtain, since it already exists oe
(c) Answer: Secondary data already exists, so it is usually quicker and cheaper to obtain than primary data.
(d) B1 may not exactly match the purpose needed, may be out of date, or its reliability cannot be checked oe
(d) Answer: Secondary data may not exactly match the purpose it is being used for, may be out of date, or its reliability cannot always be checked.
(e) B1 secondary data
(e) B1 because it would be impractical, too costly and too time-consuming for the company to survey the whole UK retail sector itself oe
(e) Answer: Secondary data - the company cannot realistically survey every retailer in the UK itself, so it should use existing published sales figures for the sector.

Question 9

(a) B1 categorical data with no natural order between the categories oe
(a) Answer: Nominal data is categorical data whose categories have no natural order (for example, eye colour).
(b) B1 categorical data that has a natural order or ranking between the categories oe
(b) Answer: Ordinal data is categorical data whose categories have a natural order or ranking (for example, T-shirt size).
(c) B1 Eye colour: nominal
(c) B1 T-shirt size: ordinal
(c) B1 Exam grade achieved: ordinal
(c) B1 Postcode: nominal
(c) B1 Favourite type of music: nominal
(c) Answer: Eye colour - nominal; T-shirt size - ordinal; Exam grade achieved - ordinal; Postcode - nominal; Favourite type of music - nominal.
(d) B1 the grades have a natural order or ranking (a grade 9 is higher than a grade 8, and so on), unlike a nominal variable such as eye colour where no category is 'higher' than another oe
(d) Answer: Exam grades have a clear order or ranking (grade 9 is higher than grade 8, which is higher than grade 7, and so on), whereas nominal categories such as eye colour have no such order.

Question 10

(a) B1 data in which two variables are recorded for each individual or item, so a relationship between them can be studied oe
(a) Answer: Bivariate data is data in which two variables are recorded for each individual or item, so that a relationship between them can be investigated.
(b) B1 height (of each student)
(b) B1 arm span (of each student)
(b) Answer: Height and arm span.
(c) B1 any sensible related pair of variables recorded for the same items/people, e.g. age and shoe size, or hours of revision and test score oe
(c) Answer: For example, age and shoe size, or hours spent revising and test score.

Question 11

(a) B1 individual data values listed separately, not organised into class intervals or groups oe
(a) Answer: Raw (ungrouped) data is a list of individual data values, with each one recorded separately.
(b) B1 data organised into class intervals (groups of values), usually shown with a frequency for each interval oe
(b) Answer: Grouped data is data that has been organised into class intervals, usually shown with a frequency for each interval.
(c) B1 20 - 29 = 4 and 30 - 39 = 5, both correct
(c) B1 40 - 49 = 4
(c) B1 50 - 59 = 2, with all four frequencies summing to 15
(c) Answer: 20 - 29: 4, 30 - 39: 5, 40 - 49: 4, 50 - 59: 2
(d) B1 advantage: e.g. it is easier to see the overall pattern, and simpler to display in a table or chart oe
(d) B1 disadvantage: e.g. the original, exact individual ages are lost, so the exact mean or exact range can no longer be found oe
(d) Answer: Advantage: it is easier to see the overall pattern of ages and to display the data in a chart. Disadvantage: the exact individual ages are lost, so an exact mean cannot be calculated from the grouped table alone.

Question 12

(a) B1 9 cao
(a) Answer: 9
(b) B1 weight (mass) is continuous data, so parcels can take any value and are very unlikely to share exactly the same weight oe
(b) B1 grouping into class intervals lets the data be organised and displayed sensibly, rather than having up to 30 separate individual values oe
(b) Answer: Weight is continuous data, so almost every parcel could have a slightly different exact weight. Grouping the weights into class intervals allows the data to be organised and displayed sensibly, instead of showing up to 30 separate individual values.

Question 13

(a) B1 time spent revising (e.g. in hours)
(a) B1 test score (e.g. out of 100)
(a) Answer: Time spent revising, and test score.
(b) B1 time spent revising: continuous quantitative data
(b) B1 test score: discrete quantitative data (assuming whole-number marks) oe
(b) Answer: Time spent revising is continuous quantitative data; test score is discrete quantitative data.
(c) B1 primary
(c) B1 because she needs data specific to her own sample of students and no existing data set matches her exact question oe
(c) Answer: Primary data - she needs to collect data specific to her own sample of students, and no existing data set matches her exact research question.
(d) B1 the sample may not be representative of all students (e.g. in other classes or schools), so the conclusion may not generalise oe
(d) Answer: A sample from only one class may not be representative of all students, so her conclusion might not apply more widely.

Question 14

B1 Mode of transport to school: qualitative
B1 Distance travelled to school (km): continuous quantitative
B1 Number of school bags carried: discrete quantitative
B1 Time taken to travel to school (minutes): continuous quantitative
B1 T-shirt size worn: qualitative
B1 Favourite school subject: qualitative
B1 Height of each pupil (cm): continuous quantitative
B1 Number of days absent this term: discrete quantitative
Answer: Mode of transport - qualitative; Distance travelled - continuous quantitative; Number of school bags - discrete quantitative; Time taken to travel - continuous quantitative; T-shirt size worn - qualitative; Favourite school subject - qualitative; Height of each pupil - continuous quantitative; Number of days absent - discrete quantitative.

Question 15

(a) B1 (1)
(a) B1 because the manager would be collecting the data herself, first-hand, for her own specific purpose oe
(a) Answer: Option (1), because the manager collects the data herself, first-hand, for her own specific purpose.
(b) B1 e.g. it is quicker and cheaper than running her own survey, and covers a much larger, national sample oe
(b) Answer: It is quicker and cheaper than running her own survey, and gives information from a much larger, national sample.
(c) B1 e.g. the national report may not reflect the preferences of her own local customers oe
(c) Answer: The national report may not reflect the preferences of her own local customers.
(d) B1 either option accepted, provided a valid supporting reason relevant to cost, time or relevance to her own customers is given
(d) Answer: Either option can be recommended, provided the reason given is a valid comparison of cost, time or relevance to her own customers.

Question 16

(a) B1 the numbers are just labels/codes for categories (Drama, Sports, Art), not numerical quantities that can be measured or counted oe
(a) B1 it would not make sense to carry out arithmetic with the codes, e.g. finding an 'average club code' would be meaningless oe
(a) Answer: The numbers 1, 2 and 3 are just labels for the categories Drama, Sports and Art - they do not represent a measurable quantity. It would not make sense to calculate something like an 'average club code', which shows the data is really qualitative.
(b) B1 nominal, because the three clubs have no natural order or ranking oe
(b) Answer: Nominal, because there is no natural order or ranking between Drama club, Sports club and Art club.

Question 17

(a) B1 height and shoe size
(a) B1 yes, it is bivariate, because two variables are being recorded for each friend oe
(a) Answer: Height and shoe size - yes, this is bivariate data, because two variables are recorded for each friend.
(b) B1 the exact numerical (discrete quantitative) shoe size is lost, and it becomes ordinal qualitative data instead oe
(b) B1 two friends with different exact shoe sizes could end up in the same category, so detail and precision are lost oe
(b) Answer: By using 'small', 'medium' or 'large', the exact numerical shoe size is lost and the data becomes ordinal qualitative data instead of discrete quantitative data. Two friends with genuinely different shoe sizes could be placed in the same category, so precise detail is lost.
(c) B1 e.g. a sample of only 5 friends is very small and may not be representative, so no reliable conclusion can be drawn oe
(c) Answer: A sample of only 5 friends is very small and may not be representative of students generally, so no reliable conclusion can be drawn.
(d) B1 e.g. record the exact shoe size, for a larger sample of students, not just her own friends oe
(d) Answer: She could record the exact shoe size for a larger, more representative sample of students, not just her own friends.

Question 18

(a) B1 the exact individual heights are not known, since they have been lost once grouped into intervals oe
(a) B1 only the interval each sunflower falls into is known, so a midpoint has to be used to represent each group, which introduces some inaccuracy oe
(a) Answer: Once the heights are grouped, the exact individual measurements are no longer known - only which interval each sunflower falls into. To estimate the mean, a midpoint has to be used for each interval, which is not exactly correct for every sunflower, so the result can only be an estimate.
(b) B1 record/keep the exact (raw, ungrouped) height of each individual sunflower, rather than only recording which interval it falls into oe
(b) Answer: Record the exact height of every individual sunflower as raw, ungrouped data, instead of only recording which class interval it falls into.

Question 19

(a) B1 Number of pets owned: quantitative
(a) B1 Number of pets owned: discrete
(a) B1 Time to complete a marathon (hours): quantitative, continuous (both needed)
(a) B1 Breed of dog: qualitative
(a) B1 Breed of dog: N/A (not applicable) for discrete/continuous
(a) Answer: Number of pets owned - quantitative, discrete. Time to complete a marathon - quantitative, continuous. Breed of dog - qualitative, N/A.
(b) B1 breed of dog is qualitative (categorical), not quantitative, and only quantitative data can be discrete or continuous oe
(b) Answer: Breed of dog is qualitative data, not quantitative, and the discrete/continuous classification only applies to quantitative data.

Question 20

(a) B1 Typical cost, secondary data: usually lower/cheaper oe
(a) B1 Typical time to obtain, primary data: usually longer/takes more time oe
(a) B1 Matches the exact research question, primary data: matches exactly, since the researcher designs the collection themselves oe
(a) Answer: Secondary data is usually cheaper; primary data usually takes longer to obtain; primary data matches the exact research question, since the researcher designs how it is collected.
(b) B1 secondary data
(b) B1 because it already exists and can usually be obtained more quickly than collecting primary data from scratch oe
(b) Answer: Secondary data, because it already exists and can usually be obtained more quickly than collecting primary data from scratch.