The Statistical Enquiry Cycle - Worksheets, Questions and Revision

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GCSE · Statistics

S02 The Statistical Enquiry Cycle

EDEXCEL 1ST0 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A statistical enquiry always follows the same four stages, in the same order, before the cycle can begin again.

Complete each sentence by writing in the missing stage.

(a)In the ______ stage, a suitable hypothesis is written and a method of collecting data is decided.(1)

(b)In the ______ stage, the data described in the plan is gathered.(1)

(c)In the ______ stage, the collected data is organised, calculated and presented, for example using tables, charts and averages.(1)

(d)In the ______ stage, conclusions are drawn from the processed data and compared back to the original hypothesis.(1)

(Total for Question 1 is 4 marks)

For each statement about the statistical enquiry cycle, write down whether it is True or False.

(i)The four stages of the statistical enquiry cycle can be carried out in any order.(1)

(ii)Once the interpret stage is complete, the enquiry cycle can begin again with a new plan stage.(1)

(Total for Question 2 is 2 marks)

The four stages of the statistical enquiry cycle are listed below, in the wrong order.

A Interpret
B Plan
C Process
D Collect

Write down the letters A, B, C and D in the correct order.

(Total for Question 3 is 2 marks)

Match each statistical term to its correct definition.

Terms: hypothesis, population, sample, data collection method

Definitions:
1. A statement that can be tested and shown to be true or false using data.
2. The whole group that a statistical enquiry is interested in.
3. A smaller part of the population, chosen to represent the whole group.
4. The way in which data will be gathered, such as a questionnaire, observation or experiment.

(a)Which term matches definition 1?(1)

(b)Which term matches definition 2?(1)

(c)Which term matches definition 3?(1)

(d)Which term matches definition 4?(1)

(Total for Question 4 is 4 marks)

A school council is investigating whether a new fundraising raffle was successful. For each activity below, write down which stage of the statistical enquiry cycle (plan, collect, process, interpret) it belongs to.

(a)Deciding how many raffle tickets to sell and writing a hypothesis about how much money will be raised.(1)

(b)Selling the raffle tickets and recording how many are sold each day.(1)

(c)Adding up the total money raised and drawing a bar chart of ticket sales by day.(1)

(d)Comparing the total raised to the original hypothesis and deciding whether the raffle was a success.(1)

(Total for Question 5 is 4 marks)

A student wants to investigate whether adults spend longer using their mobile phones each day than teenagers do.

Write a suitable hypothesis for this investigation.

(Total for Question 6 is 2 marks)

A student is investigating the fuel efficiency of cars. She writes the following as her hypothesis:

"Do bigger cars use more fuel than smaller cars?"

(a)Give a reason why this is not a suitable hypothesis.(1)

(b)Rewrite this as a suitable hypothesis.(2)

(Total for Question 7 is 3 marks)

Before collecting any data, a researcher must plan her statistical enquiry carefully.

(a)State one issue relating to time that the researcher should consider when planning her enquiry.(1)

(b)State one issue relating to cost or resources.(1)

(c)State one ethical issue the researcher should consider.(1)

(Total for Question 8 is 3 marks)

A researcher is planning to send a postal questionnaire to a sample of 350 households. Printing and posting each questionnaire costs 90p. The researcher has a budget of £300 for this stage of her enquiry.

(a)Work out the total cost of printing and posting all 350 questionnaires.(2)

(b)State, giving a reason, one planning decision the researcher could make as a result of your answer to part (a).(1)

(Total for Question 9 is 3 marks)

A student is planning to investigate how much time Year 11 students spend on homework each week.

(a)State the stage of the statistical enquiry cycle at which the student should decide whether to use a questionnaire, an observation, or an experiment to collect her data.(1)

(b)Give one factor, other than cost, that should influence which data collection method the student chooses.(2)

(Total for Question 10 is 3 marks)

A researcher wants to find out whether people in her town prefer tea or coffee. She stands outside a coffee shop and asks the first 20 people she sees which drink they prefer. 15 of the 20 people say they prefer coffee, so she concludes that most people in the town prefer coffee.

(a)Give one reason why the researcher's conclusion might not be reliable.(2)

(b)Suggest one improvement the researcher could make at the plan stage to get a more reliable conclusion.(1)

(Total for Question 11 is 3 marks)

A researcher completes a statistical enquiry into average commute times in her city, and finds that morning commutes take longer, on average, than evening commutes.

(a)Explain why the statistical enquiry cycle is described as a cycle, rather than a one-off process.(2)

(b)Suggest a new question, arising from the researcher's result, that could start a new statistical enquiry cycle.(1)

(Total for Question 12 is 3 marks)

A school wants to find out whether a new revision app improves students' test scores.

(a)Write a suitable hypothesis for this investigation.(2)

(b)State one practical planning issue, other than an ethical issue, the school should consider before starting.(1)

(c)State one ethical issue the school should consider.(1)

(Total for Question 13 is 4 marks)

A student wants to investigate how much time primary school children (aged 5 to 11) spend using screens each day, by interviewing children directly at their school.

(a)Identify one ethical issue with this plan.(1)

(b)Suggest how this ethical issue could be resolved without abandoning the investigation.(2)

(Total for Question 14 is 3 marks)

A national newspaper carries out an online poll on its website, asking readers: "Should the speed limit on motorways be raised?" Only people who visit the website and choose to respond take part. 2000 people respond, and 65% say yes. The newspaper concludes that most people in the country want the speed limit raised.

(Total for Question 15 is 3 marks)

A council wants to investigate how satisfied residents are with a new recycling scheme. It considers two methods:

Method 1: a postal questionnaire sent to a random sample of 500 households across the town.
Method 2: interviewing 50 people at the local recycling centre.

(a)Give one advantage of Method 1 over Method 2.(1)

(b)Give one advantage of Method 2 over Method 1.(1)

(c)The council wants a conclusion that applies fairly to all residents of the town. State which method is more suitable, and explain why, referring to the plan and collect stages of the enquiry cycle.(2)

(Total for Question 16 is 4 marks)

A student investigating "Do students who eat breakfast get better exam grades than those who do not?" carries out the following statistical enquiry:

Plan: she decides to compare the grades of 10 friends who eat breakfast with 10 friends who do not.
Collect: she asks her 20 friends what their grades are and whether they eat breakfast.
Process: she calculates the mean grade for each group of friends.
Interpret: she concludes that eating breakfast always improves exam grades for all students.

(a)Identify one weakness in the plan stage of this enquiry.(1)

(b)Identify one weakness in the collect stage of this enquiry.(1)

(c)Identify two weaknesses in the interpret stage of this enquiry.(2)

(Total for Question 17 is 4 marks)

Suggest how the student in Question 17 could improve her investigation if she repeated the statistical enquiry cycle.

(Total for Question 18 is 3 marks)

A student says: "Once you have completed the interpret stage of the statistical enquiry cycle, the investigation is finished and cannot be improved further."

Evaluate this statement.

(Total for Question 19 is 2 marks)

A gym chain wants to know whether offering a free fitness app to members increases how often they visit the gym. It gives the app to 30 members at one branch for a month, and finds their average number of visits rises from 4 to 7 per month. The gym manager concludes: "Giving every member the app will increase gym visits nationwide, and no further research is needed."

(Total for Question 20 is 3 marks)

Mark scheme · S02 The Statistical Enquiry Cycle

Question 1

(a) B1 Plan cao
(a) Answer: Plan
(b) B1 Collect cao
(b) Answer: Collect
(c) B1 Process cao
(c) Answer: Process
(d) B1 Interpret cao
(d) Answer: Interpret

Question 2

(i) B1 False cao
(i) Answer: False
(ii) B1 True cao
(ii) Answer: True

Question 3

B1 identifies B (Plan) as the first stage
B1 B, D, C, A cao (fully correct order)
Answer: B, D, C, A

Question 4

(a) B1 hypothesis cao
(a) Answer: Hypothesis
(b) B1 population cao
(b) Answer: Population
(c) B1 sample cao
(c) Answer: Sample
(d) B1 data collection method cao
(d) Answer: Data collection method

Question 5

(a) B1 Plan cao
(a) Answer: Plan
(b) B1 Collect cao
(b) Answer: Collect
(c) B1 Process cao
(c) Answer: Process
(d) B1 Interpret cao
(d) Answer: Interpret

Question 6

B1 a statement (not a question) that can be tested using data, oe
B1 clearly compares the two named groups (adults and teenagers) in terms of mobile phone use, oe
Answer: Adults spend longer using their mobile phones each day than teenagers do.

Question 7

(a) B1 it is phrased as a question rather than a statement that can be tested, oe
(a) Answer: It is written as a question, not as a statement that can be tested using data.
(b) B1 phrased as a testable statement, not a question
(b) B1 clearly compares fuel use between bigger and smaller cars, oe
(b) Answer: Bigger cars use more fuel than smaller cars.

Question 8

(a) B1 how long collecting and processing the data will take, and whether this fits any deadline, oe
(a) Answer: Whether there is enough time to collect and process all the data before the deadline.
(b) B1 whether she has enough money, equipment or people to collect and process the data, oe
(b) Answer: Whether she can afford the equipment, printing or staff needed to collect the data.
(c) B1 whether participants' consent, privacy or confidentiality will be protected, oe
(c) Answer: Whether participants need to give their consent, and whether their data will be kept confidential.

Question 9

(a) M1 350 x 0.90, oe
(a) A1 £315 cao
(a) Answer: £315
(b) B1 a valid decision linked correctly to the cost exceeding the £300 budget, e.g. reduce the sample size, or find a cheaper method, oe
(b) Answer: She could reduce her sample size, since £315 is more than her £300 budget.

Question 10

(a) B1 Plan cao
(a) Answer: The plan stage.
(b) B1 identifies a valid factor, e.g. the type of data needed (self-reported time vs directly measured time), or how many students need to be reached, oe
(b) B1 links the factor to how it affects the choice of method, e.g. a questionnaire is quicker to distribute to many students than direct observation of each student's homework time
(b) Answer: How accurately the time needs to be measured: a questionnaire relies on students estimating their own time, whereas observing and timing students directly would give more accurate data but would take far longer to carry out for a large group.

Question 11

(a) B1 identifies that the sample is biased, e.g. people outside a coffee shop are more likely to be coffee drinkers than people in the town generally
(a) B1 identifies that the sample of 20 is small compared with the whole town, so may not be representative
(a) Answer: People standing outside a coffee shop are more likely to prefer coffee than people in the town as a whole, so the sample is biased. It is also a very small sample compared with the whole town.
(b) B1 a valid improvement, e.g. take a larger, random sample from a range of locations across the town, not just outside a coffee shop, oe
(b) Answer: Take a larger sample, chosen randomly from several different locations across the town, rather than only outside a coffee shop.

Question 12

(a) B1 after the interpret stage, the results can lead back into a new plan stage, oe
(a) B1 new questions or hypotheses often arise from the results of an enquiry, starting the cycle again, oe
(a) Answer: The interpret stage often raises new questions from the results, which leads back into a new plan stage, so the four stages can repeat as a new investigation.
(b) B1 a sensible new question linked to the given result, e.g. investigating why morning commutes are longer, oe, or whether this is true on every day of the week
(b) Answer: Why are morning commutes longer than evening commutes, for example, is it caused by heavier traffic at that time of day?

Question 13

(a) B1 phrased as a testable statement, not a question
(a) B1 clearly compares test scores of students who use the app with those who do not, oe
(a) Answer: Students who use the revision app get higher test scores than students who do not use it.
(b) B1 a valid practical issue, e.g. whether all students have a suitable device to access the app, or how long the trial needs to run before test scores can be compared, oe
(b) Answer: Whether every student in the trial has access to a suitable device to use the app on.
(c) B1 a valid ethical issue, e.g. whether it is fair to deny some students access to the app, or whether consent is needed from students/parents, oe
(c) Answer: Whether it is fair to prevent some students from using the app, if it might improve their results.

Question 14

(a) B1 identifies that the children are minors, so consent must be obtained from a parent/guardian (and/or the school) before interviewing them, oe
(a) Answer: The children are under 16, so consent from a parent or guardian, and likely the school, would be needed before interviewing them.
(b) B1 obtains informed consent from parents/guardians and the school before data collection begins
(b) B1 keeps responses anonymous/confidential so individual children cannot be identified, oe
(b) Answer: The student should get permission from parents or guardians and the school before interviewing any children, and should keep all answers anonymous so no individual child can be identified.

Question 15

B1 the conclusion is judged not to be valid, oe
B1 identifies that the sample is self-selecting (only website visitors who choose to respond), so is unlikely to represent the whole country
B1 identifies that people with strong opinions on the topic are more likely to respond, which could bias the 65% figure, oe
Answer: The conclusion is not valid. Only people who visit the newspaper's website and choose to respond are included, so the sample is self-selecting and unlikely to represent the whole country; people with strong views on the issue are also more likely to respond, which could bias the 65% figure.

Question 16

(a) B1 a random sample of households is more representative of all residents than only people who already visit the recycling centre, oe
(a) Answer: A random sample of households is more likely to represent all residents, since people at the recycling centre are more likely to already support recycling.
(b) B1 a valid advantage of interviews, e.g. face-to-face interviews usually get a higher response rate, or answers can be collected/clarified immediately, oe
(b) Answer: Interviewing people face to face usually gets a higher response rate than a postal questionnaire, and any unclear questions can be explained immediately.
(c) B1 identifies Method 1 (the postal questionnaire to a random sample) as more suitable
(c) B1 explains that choosing a random sample of households at the plan stage means the data collected represents all residents, whereas Method 2 only collects data from residents who already visit the recycling centre
(c) Answer: Method 1 is more suitable. Because the plan stage chooses a random sample of households across the whole town, the data collected at the collect stage represents all residents fairly, whereas Method 2 would only reach residents who already use the recycling centre.

Question 17

(a) B1 the sample of 10 friends in each group is small and not chosen randomly, so may not be representative of students in general, oe
(a) Answer: Only 10 friends are chosen for each group, and they are not a random sample, so they may not represent students in general.
(b) B1 grades and breakfast habits are self-reported by friends, so may be inaccurate or not checked, oe
(b) Answer: The grades and breakfast habits are simply reported by her friends, and are not checked against any official record, so may not be accurate.
(c) B1 the conclusion overgeneralises to 'all students' from a small, unrepresentative sample of 20 friends
(c) B1 a link between breakfast and grades does not prove breakfast causes better grades, oe other factors could be involved
(c) Answer: The conclusion wrongly applies to 'all students' when only 20 friends were studied, and even if breakfast and higher grades are linked, this does not prove breakfast causes the better grades, since other factors could be involved.

Question 18

B1 suggests using a larger, randomly chosen sample of students, rather than only her friends, oe
B1 suggests collecting grades from an objective source, e.g. school records, rather than relying on self-reported grades, oe
B1 links the suggested changes to a more valid/reliable conclusion this time, e.g. a random sample of many students with verified grades would better support a conclusion about students in general
Answer: She could repeat the plan and collect stages using a large, randomly chosen sample of students from across the school, and collect their grades from school records rather than by asking friends. This would make her conclusion far more reliable and better able to apply to students in general.

Question 19

B1 the statement is judged to be false/not correct
B1 a valid justification, e.g. the enquiry cycle is repeating: the interpret stage often reveals limitations or raises new questions that lead back into a new plan stage, so the investigation can be improved and continued, oe
Answer: The statement is false. The statistical enquiry cycle is repeating, not a one-off process: the interpret stage often reveals limitations in the original enquiry, or raises new questions, which lead back into a new plan stage so the investigation can be refined and continued.

Question 20

B1 identifies that the manager's conclusion is not fully justified, e.g. one branch's 30 members is a small, potentially unrepresentative sample of all members nationwide
B1 recommends returning to the plan stage to design a larger-scale/randomised trial across multiple branches before rolling the app out nationwide, oe
B1 recognises the enquiry cycle should continue/repeat rather than stop, e.g. results should be interpreted again after a wider trial to check the increase holds nationally, oe
Answer: The manager's conclusion goes too far: 30 members at one branch is a small sample and may not represent all members nationwide. The gym should return to the plan stage and trial the app across a larger, more representative sample of branches, then collect, process and interpret those results again before deciding whether to roll it out to everyone, rather than stopping the enquiry cycle after just one trial.

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The Statistical Enquiry Cycle - Worksheets, Questions and Revision

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S02 The Statistical Enquiry Cycle

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