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GCSE · Statistics

S07 Collecting Data

EDEXCEL 1ST0 · Calculator allowed · about 70 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

For each variable below, write down whether it is best described as categorical, discrete or continuous data.

(a)The eye colour of a group of pupils.(1)

(b)The number of pets owned by a family.(1)

(c)The height, in cm, of a sunflower plant.(1)

(d)The number of goals scored by a team in a match.(1)

(Total for Question 1 is 4 marks)

A survey is carried out to find out students' favourite school lunch option, out of Sandwiches, Hot meal, Salad and Packed lunch brought from home.

(a)Design a suitable data collection sheet to record the results of this survey. Your sheet should include columns for the category, tally and frequency.(3)

(b)Give one reason why the categories on a data collection sheet should not overlap.(1)

(Total for Question 2 is 4 marks)

A student wants to find out how pupils in her class travel to school on a normal school day.

(a)Suggest four suitable, non-overlapping categories she could use on a data collection sheet, making sure every pupil's response can be recorded.(2)

(b)Design the data collection sheet, using your four categories from part (a), with columns for tally and frequency.(2)

(Total for Question 3 is 4 marks)

A student is investigating the average monthly rainfall in the UK over the last 10 years. She uses rainfall figures published by the Met Office rather than measuring rainfall herself.

(a)Is this primary data or secondary data? Give a reason for your answer.(2)

(b)Give one advantage, for this investigation, of using secondary data instead of collecting the rainfall figures herself.(1)

(Total for Question 4 is 3 marks)

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

(i)A pilot survey is a small-scale trial run of a survey, carried out before the main survey takes place.(1)

(ii)Data collection sheet class intervals such as '10 - 20' and '20 - 30' are well designed, because they give the respondent more choice.(1)

(iii)Data collected by a researcher carrying out her own experiment is called secondary data.(1)

(Total for Question 5 is 3 marks)

60 pupils were asked which sport they play most often: football, netball or swimming. The two-way table shows the results, split by whether each pupil is a boy or a girl.

	Football	Netball	Swimming	Total
Boys	14	6	10	30
Girls	8	15	7	30
Total	22	21	17	60

(a)Write down the number of girls who play swimming most often.(1)

(b)Work out the number of boys who do not play football most often.(2)

(c)One of these 60 pupils is chosen at random. Find the probability that this pupil is a girl who plays netball most often.(2)

(Total for Question 6 is 5 marks)

A school wants to survey a sample of its 900 pupils about a proposed new canteen menu. The school has a complete, up-to-date list of the names of all 900 pupils, known as the school register.

(a)What name is given to a list, such as the school register, from which a sample is selected?(1)

(b)Give one reason why the school register is a suitable sampling frame for this survey.(1)

(Total for Question 7 is 2 marks)

60 customers at a cafe were asked whether they bought a hot drink and whether they bought a cake. Some of the results are missing from the two-way table.

	Cake	No cake	Total
Hot drink	18	?	42
No hot drink	?	11	?
Total	25	?	60

(a)Work out the number of customers who bought a hot drink but did not buy a cake.(2)

(b)Work out the total number of customers who did not buy a hot drink.(2)

(c)Hence work out the number of customers who did not buy a hot drink but did buy a cake.(2)

(d)Complete the table by working out the total number of customers who did not buy a cake.(2)

(Total for Question 8 is 8 marks)

A gardener measures the height, in cm, of 30 tomato plants. The heights range from 8 cm to 92 cm.

(a)Design a data collection sheet to record this data, using five equal class intervals of width 20 cm, starting at 0 cm. Your sheet should include the class interval, tally and frequency columns.(3)

(b)Give one reason why the class intervals in part (a) should not overlap.(1)

(Total for Question 9 is 4 marks)

A researcher wants to record, for each pupil in a sample, both their year group (Year 9, Year 10 or Year 11) and how they usually travel to school (Walk, Cycle or Bus). Design a two-way data collection sheet that could be used to record this information for a sample of pupils.

(Total for Question 10 is 3 marks)

A student is recording how long, in minutes, 40 people take to travel to work, using the data collection sheet below. Two features of this data collection sheet make it unsuitable.

Time taken (minutes)	Tally	Frequency
0 - 10
10 - 20
20 - 30

(a)Explain two reasons why the class intervals shown are not suitable for recording this data.(2)

(b)Rewrite the class intervals so that the data collection sheet is suitable, using inequality notation.(2)

(Total for Question 11 is 4 marks)

A gardener wants to find out how the temperature inside a greenhouse changes during the day. She records the temperature every hour from 8 am to 6 pm.

(a)Give one advantage of using an electronic data logger, rather than a person taking readings by hand, to record the temperature.(1)

(b)Design a data collection sheet the gardener could use to record the readings by hand if a data logger were not available. Include suitable column headings and enough rows for all the readings described above.(2)

(c)The gardener wants to see how the temperature changes during the day. Suggest a suitable way to display this data once it has been collected, and give a reason for your choice.(1)

(Total for Question 12 is 4 marks)

Before carrying out a full survey of 200 shoppers about their spending habits, a market researcher plans to carry out a pilot survey of 15 shoppers first.

(a)Give one reason why the researcher should carry out a pilot survey before the full survey.(1)

(b)State one thing the researcher should check for during the pilot survey.(1)

(c)One question on the pilot survey reads: 'Don't you agree that you spend too much money on impulse purchases?' Identify one flaw in this question, and rewrite it as a better, unbiased question.(2)

(Total for Question 13 is 4 marks)

A student wants to investigate the hypothesis: 'Pupils in Year 11 spend more time on homework each week than pupils in Year 7.' She plans to sample 20 pupils from each year group.

(a)Plan: State a suitable sampling frame the student could use to select pupils for this investigation, and give one advantage of using it.(2)

(b)Collect: Design a suitable data collection sheet to record, for each pupil sampled, their year group and the number of hours they spend on homework in a week, to the nearest hour.(3)

(c)Process: State one calculation the student could carry out on the results for each year group, so she can compare the average time spent on homework.(1)

(d)Interpret: Give one reason why the student should be cautious about generalising her conclusion to all pupils nationally.(1)

(Total for Question 14 is 7 marks)

A newspaper wants to find out what proportion of adults in a city support a new cycle lane. A reporter plans to stand outside a cycling shop on a Saturday morning and ask the first 50 customers who leave the shop whether they 'Support' or 'Do not support' the cycle lane.

(a)Identify one way in which this data collection method could produce biased results, and explain why.(2)

(b)Suggest one improvement the reporter could make to the data collection method to reduce this bias.(2)

(c)Suggest one additional response category that should be added to the data collection sheet, and explain why it is needed.(2)

(Total for Question 15 is 6 marks)

Mark scheme · S07 Collecting Data

Question 1

(a) B1 categorical cao
(a) Answer: Categorical
(b) B1 discrete cao
(b) Answer: Discrete
(c) B1 continuous cao
(c) Answer: Continuous
(d) B1 discrete cao
(d) Answer: Discrete

Question 2

(a) B1 all four given categories listed once each, with no gaps or overlaps
(a) B1 a tally column included, ready to record responses with tally marks
(a) B1 a frequency column included, clearly headed
(a) Answer: Data collection sheet with columns Lunch option | Tally | Frequency, listing Sandwiches, Hot meal, Salad, Packed lunch as the four categories.
(b) B1 so that each response can be tallied into exactly one category (avoids confusion or double counting)
(b) Answer: So each response only fits into one category, avoiding double counting.

Question 3

(a) B1 three sensible, mutually exclusive methods of travel given (e.g. Walk, Cycle, Car, Bus)
(a) B1 an 'Other' or similar catch-all category included, so every response can be recorded
(a) Answer: e.g. Walk, Cycle, Bus, Other (accept any 3 sensible non-overlapping methods plus a catch-all category).
(b) B1 categories from (a) listed in one column, ft
(b) B1 tally and frequency columns both included and clearly headed
(b) Answer: Table with columns Method of travel | Tally | Frequency, using the four categories from (a).

Question 4

(a) B1 secondary data
(a) B1 reason: because the data was already collected/recorded by someone else (the Met Office), not by the student herself
(a) Answer: Secondary data, because it was collected by the Met Office, not by the student.
(b) B1 e.g. it gives access to 10 years of rainfall records that the student could not have collected herself in the time available (saves time/cost, or covers a longer period than she could measure)
(b) Answer: It provides many years of data that the student could not have collected herself in the time available.

Question 5

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

Question 6

(a) B1 7 cao
(a) Answer: 7
(b) M1 30 - 14, oe
(b) A1 16 cao
(b) Answer: 16
(c) M1 15/60 seen, oe
(c) A1 1/4 oe cao
(c) Answer: 1/4

Question 7

(a) B1 sampling frame cao
(a) Answer: Sampling frame
(b) B1 e.g. it lists every pupil in the population exactly once, and is up to date/complete, so every pupil has a chance of being selected
(b) Answer: It includes every pupil in the population exactly once and is up to date.

Question 8

(a) M1 42 - 18, oe
(a) A1 24 cao
(a) Answer: 24
(b) M1 60 - 42, oe
(b) A1 18 cao
(b) Answer: 18
(c) M1 18 - 11, using the total for 'No hot drink' from part (b), ft
(c) A1 7 cao
(c) Answer: 7
(d) M1 60 - 25, oe (or 24 + 11)
(d) A1 35 cao
(d) Answer: 35

Question 9

(a) B1 five class intervals of width 20, written with correct inequality notation and no gaps (e.g. 0 ≤ h < 20, 20 ≤ h < 40, 40 ≤ h < 60, 60 ≤ h < 80, 80 ≤ h < 100)
(a) B1 tally column included
(a) B1 frequency column included, clearly headed
(a) Answer: Table with class intervals 0 ≤ h < 20, 20 ≤ h < 40, 40 ≤ h < 60, 60 ≤ h < 80, 80 ≤ h < 100, and Tally / Frequency columns (h = height in cm).
(b) B1 so that each plant's height can be tallied in exactly one interval (avoids ambiguity/double counting)
(b) Answer: So each height fits into exactly one interval, with no ambiguity about where to tally it.

Question 10

B1 a two-way grid drawn with year groups as the headings for one set of rows/columns and methods of travel as the headings for the other
B1 cells provided for every combination of year group and method of travel, ready for tally marks
B1 row and column totals included, clearly labelled
Answer: A two-way table with Year 9/10/11 as rows, Walk/Cycle/Bus as columns, a tally/frequency cell for each combination, and a Total row and column.

Question 11

(a) B1 the intervals overlap (e.g. a time of 10 minutes could be tallied in either '0 - 10' or '10 - 20'), so it is not clear where to record some values
(a) B1 there is no interval for times of 30 minutes or more, so some people's travel times could not be recorded at all
(a) Answer: The intervals overlap at their boundaries, and there is no interval to cover times of 30 minutes or more.
(b) B1 non-overlapping intervals using correct inequality notation, e.g. 0 ≤ t < 10, 10 ≤ t < 20, 20 ≤ t < 30
(b) B1 an interval included to cover all remaining times, e.g. t ≥ 30 (or '30 and over')
(b) Answer: e.g. 0 ≤ t < 10, 10 ≤ t < 20, 20 ≤ t < 30, t ≥ 30 (t = time in minutes).

Question 12

(a) B1 e.g. a data logger can take readings automatically at exact times without anyone needing to be present, reducing the risk of missed or inaccurate readings
(a) Answer: It records readings automatically and accurately without needing a person present at every hour.
(b) B1 columns for Time and Temperature clearly headed, with units (deg C) shown
(b) B1 11 rows provided, one for each hour from 8 am to 6 pm inclusive
(b) Answer: Table with columns Time | Temperature (deg C), and 11 rows for 8 am, 9 am, 10 am, 11 am, 12 pm, 1 pm, 2 pm, 3 pm, 4 pm, 5 pm, 6 pm.
(c) B1 a line graph/time series graph, because it shows the trend/change in temperature over time
(c) Answer: A line graph (time series graph), because it clearly shows how temperature changes over time.

Question 13

(a) B1 e.g. to check that the questions are clear and easy to understand, and that the data collection sheet works well, so problems can be corrected before the full survey
(a) Answer: To check the questions and data collection sheet work well, so any problems can be fixed before the full survey.
(b) B1 e.g. whether the questions are easy to understand / whether there are enough response categories / whether the survey takes a sensible amount of time to complete
(b) Answer: Whether the questions are clear and easy for shoppers to understand.
(c) B1 identifies that the question is leading/biased, as it pressures the respondent to agree
(c) B1 gives an improved, neutral question with a clear response format, e.g. 'How much money, if any, do you spend on impulse purchases in a typical week? Please tick a box: £0, £1-£10, £11-£25, more than £25'
(c) Answer: The original question is leading; an improved version asks neutrally, e.g. 'How much do you spend on impulse purchases each week?' with response boxes.

Question 14

(a) B1 a suitable sampling frame named, e.g. the Year 7 and Year 11 class registers
(a) B1 an advantage given, e.g. it lists every pupil in each year group exactly once, so every pupil has a chance of being selected
(a) Answer: The Year 7 and Year 11 registers; using them means every pupil in each year group has a chance of being chosen.
(b) B1 columns for Year group and Hours spent on homework (nearest hour), clearly headed with units
(b) B1 space/rows provided for all 40 pupils in the sample (20 from each year group)
(b) B1 table set out so results can be filled in for each pupil individually (e.g. one row per pupil)
(b) Answer: Table with columns Pupil / Year group / Hours spent on homework (nearest hour), with 40 rows, one per pupil sampled.
(c) B1 e.g. the mean (or median) number of hours for each year group
(c) Answer: Calculate the mean (or median) hours of homework for each year group.
(d) B1 e.g. the sample is small and from a single school, so it may not be representative of pupils nationally
(d) Answer: The sample is small and from only one school, so it may not represent all pupils nationally.

Question 15

(a) B1 identifies that only customers of a cycling shop are surveyed
(a) B1 explains that these customers are more likely to already support cycling infrastructure than adults in the city generally, so the results would not be representative
(a) Answer: Only cycling-shop customers are surveyed, who are more likely to support a cycle lane than adults generally, so results would be biased.
(b) B1 a valid improvement given, e.g. survey people at several different locations and times across the city (not only outside one shop)
(b) B1 brief justification that this would give a more representative range of adults' opinions
(b) Answer: Survey people at several different locations and times across the city, giving a more representative sample of adults.
(c) B1 an 'Undecided/No opinion' (or similar) category suggested
(c) B1 explanation: because not every respondent will have a definite view either way, and forcing a choice would misrepresent their actual opinion
(c) Answer: Add an 'Undecided / No opinion' category, since some people will not have a strong view either way.

Collecting Data - Worksheets, Questions and Revision