GCSE: Data Collection
Dr J Frost (jfrost@tiffin.kingston.sch.uk)
www.drfrostmaths.com
Last modified: 30th August 2015
Questionnaires
In GCSE papers, you tend to have to do two things to do with questionnaires.
1. What’s wrong with a given question.
2. How you would rewrite it.
Q
Ben wants to find out what food
people like to eat in restaurants, so
asks his family:
“Do you agree that pizza is better
than pasta?”
What’s wrong with his survey? (2)
2 of the following:
a. Biased question.
b. Restricted sample of
people.
c. Doesn’t specify a range of
foods.
d. Nothing to do with eating
habits.
?
Q
Naomi wants to find out how often
people go to the cinema. She uses
this question on a questionnaire.
“How many times do you go to the
cinema?”
□ Not very often □ Sometimes
□ A lot
a) Write down two things wrong
with this question. (2)
2 of the following:
a. No time-scale.
b. Non-exhaustive response
boxes.
c. Labels too vague.
?
Criticising Questions
Q
“What is your age in years?
Q “How many texts have you sent on
your mobile phone?
□ Under 20
□ 20-30
□ 30-40
□ 40-50
□ over 50
□ 0-10
□ 10-20
□ 20-30
□ 30 or more”
What is wrong with this question? (1)
List two things wrong with this
question. (2)
?
Overlapping regions.
•
•
Overlapping regions.
No time frame.
?
Improving/Designing Questions
Q
Naomi wants to find out how often people go to the cinema. She uses this
question on a questionnaire.
“How many times do you go to the cinema?”
□ Not very often
□ Sometimes
□ A lot
a) Write down two things wrong with this question. (2)
b) Design a better question for her questionnaire to find out how often adults
go to the cinema. You should include some response boxes. (2)
How many times did you go to the cinema last month?
□0
□ 1-2
□ 3-5
□ >5
______________________________________________________
What do you think the mark scheme?
is looking for?
• Time period must be included. (1 mark)
• At least 3 non-overlapping response
? boxes. (1 mark)
Improving/Designing Questions
Q
Valerie is the manager of a supermarket.
She wants to find out how often people shop at her supermarket.
She will use a questionnaire.
Design a suitable question for Valerie to use on her questionnaire.
You must include some response boxes. (2 marks)
e.g. How many times each week do you shop at this supermarket?
0, 1, 2, 3, 4 or more
•
•
B1 for an appropriate question with a reference to a time period
OR a question with time period implied by responses.
B1 for at least 3 non-overlapping boxes (ignore if not exhaustive)
Do not accept frequency tables or data collection sheets.
?
Question Bias
How much does the wording of a question change the results?
15.7%
- No religion
?
50.5%
- No religion
?
Tally Charts
Phillip is going to carry out a survey of the football teams supported by each of his
friends. In the space below, draw a suitable data collection sheet that Phillip could use.
(3 marks)
Team
Tally
Frequency
?
1 mark for each column heading.
Sampling
Sampling is the idea of using a few people/things in a population to represent the whole
population.
Suppose we were trying to assess the favourite football teams in England.
To make our sample as good as possible, we should:
1
Ensure the people in our sample are chosen as randomly as
?
possible, i.e. no bias towards particular
types of people.
2
Have a large a sample size as before so as to be more
?
representative of the whole population.
Bias
Melanie wants to find out how often people go to the cinema.
She gives a questionnaire to all the women leaving a cinema.
Her sample is biased.
Give two possible reasons why.
1. Only women were asked/you need to ask men.
? asked/you need to
2. Only people leaving the cinema were
ask people in different places.
Random Sampling
A random sample is:
a sample where each thing in the population
is equally likely to be chosen.
?
Bro Tip: If you are asked in an exam what a
random sample is, the key phrase they’re
looking for is “equal chance”.
You want to take a random sample a student’s favourite TV
programmes at school. Describe how you could achieve a random
sample.
Since it is a random sample, you need to ensure each thing is equally
likely to be chosen. Mark schemes would expect an approach such as:
1. Put all student names into a hat and pick them out to decide who to
?
sample.
2. Use a random number generator where each number represents a
student.
Stratified Sampling
A second type of sampling is stratified sampling.
Whereas random sampling chooses randomly from the whole population, in stratified
sampling, we ensure that each group in the population (e.g. classes in a school, ethnic
groups within a country, etc.) is fairly represented.
 In stratified sampling, the population is divided into groups, and random samples
are taken from each stratum.
(Stratum means group, and literally means ‘layer’)
Stratified Sampling
In a zoo of 36
animals, we wish
to sample 9 of
them to determine
how many are
afflicted with the
disease ‘Redditus’.
How many of
each type of
animal should I
sample?
We’re sampling
9/36 = 25% of the
animals, so:
?
4 pandas.
2 elephants.
2 dolphins.
1 lion.
Test your understanding
50/258 of students sampled.
26 x (50/258) =?5.039
So 5 students.
25 + 48 + 62 = 135 females.
135 x (50/258)?= 26.16
So 26 students.
Bro Tip: you can only
sample a whole number of
things. You will lose a mark
if you don’t round.
Quickfire Questions
Do these in your head...
Q
Out of a herd of 200 big cats, I want to sample 50 of them. There
are 60 lions. How many lions should I sample?
15 lions.
?
Q
Class A has 20 people, Class B 10 and Class C 30. I want to sample
10 people. How many people do I sample from Class C?
5 people
?
Q
In the land of Frostonia there are 1 million people. I want to
sample 50,000 to determine their TV watching habits. If there are
6,000 Indians in Frostonia, how many of them should I sample?
300 Indians.
?
TV Ratings
What method of sampling does it sound like the UK uses?
“These panel homes are drawn from a
household sample that is designed by
RSMB to remain representative of all
television households across the UK.
This means it always encompasses the
full range of demographic and TV
reception variations, amongst other
variables, that are found across the
country and in different ITV and BBC
regions.”
Exercises (on your sheet)
Students in school = 591
Proportion sampled = 150/591
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Year 7: 100 x (150/591) = 25
Year 8: 30 Year 9: 29 Year 10: 33 Year 11: 32
(Notice that due to rounding, we in fact only sample 149 people)
Proportion sampled = 60/564
a) 24 x (60/564) = 3
b) 9
c) 28
?
Proportion sampled = 100/340
18 x (100/340) = 5
?
Total people = 19350
Proportion sampled = 200/19350
Sainsbury’s: 66
Aldi: 47
M&S: 14
?
Tesco: 53
Waitrose: 21