1. GCSE: Data Collection & Sampling
Dr J Frost
Last modified: 31st October 2016

2. Questionnaires
In GCSE papers, you tend to have to do two things to do with questionnaires.
What’s wrong with a given question.
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) 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:
Biased question.
Restricted sample of people.
Doesn’t specify a range of foods.
Nothing to do with eating habits. ?
2 of the following:
No time-scale.
Non-exhaustive response boxes.
Labels too vague.

3. Criticising Questions
“What is your age in years?
□ Under 20
□ 20-30
□ 30-40
□ 40-50
□ over 50
What is wrong with this question? (1) Q
“How many texts have you sent on your mobile phone?
□ 0-10
□ 10-20
□ 20-30
□ 30 or more”
List two things wrong with this question. (2) ?
Overlapping regions.
Overlapping regions.
No time frame. ?

4. Improving/Designing Questions
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
Write down two things wrong with this question. (2)
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 □ □ 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) ?

5. Improving/Designing Questions
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.

6. Question Bias
How much does the wording of a question change the results?
British Social Attitudes Survey (2002):
“Do you regard yourself as belonging to any particular religion?”
English/Welsh National Census (2001):
“What is your religion?” ?
15.7% - No religion
50.5% - No religion ?

7. 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.

8. Sampling Motivation
I wish to find out the proportion of animals in my zoo that have contracted the deadly disease ‘Chilcotius’.

9. Sampling Motivation
I could test the entire population of animals at the zoo.
(Looking at the entire population is known as a census)
But this would be time consuming. ?
We therefore instead want to just test some of the animals, and hope that the percentage of these animals with the disease accurately reflects the whole population of animals, e.g. if 20% have the disease within our selected group, we assume roughly 20% of all animals have the disease.

10. Sampling Motivation
I could select just some of the animals to test. This selection is known as a sample. ?
We hope that the proportion of animals with the disease in the sample accurately reflects the whole population.
We therefore instead want to just test some of the animals, and hope that the percentage of these animals with the disease within the sample accurately reflects the whole population of animals, e.g. if 20% have the disease within our selected group, we assume roughly 20% of all animals have the disease.

11. Random Sample ? But how do we get our sample?
We could just animals randomly.
Disadvantage of random sampling:
It’s possible not all the different types of animals are represented. In the sample on the left, no dolphins were included. ?

12. Exam Questions on Random Sampling
“Describe a random sample”
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:
Put all student names into a hat and pick them out to decide who to sample.
Use a random number generator where each number represents a student.
“Dave wants to determine the spending habits of the UK population.
He stands outside HSBC bank’s headquarters and asks the first 10 people he sees. Suggest two reasons why his sample will likely be poor.” ?
Sample not random: People working for a bank likely to earn more money.
Sample size too small.

13. Sample Bias Question on your Sheet
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. ?
Only women were asked/you need to ask men.
Only people leaving the cinema were asked/you need to ask people in different places.

14. Stratified Sampling
Instead of sampling animals completely randomly, we might want to ensure that we sample the same proportion/percentage from each group, so that each type of animal is fairly represented. (With random sampling, it’s possible to avoid having any lions!) This is known as a stratified sample.
If we want to do a stratified sample where we sample 25% of all animals, how many do we sample from each group?
Pandas 4
Lions 1
Dolphins 2
Elephants ? ? ? ?

15. Stratified Sampling Example Questions
! “Describe a stratified sample”
In stratified sampling, the population is divided into groups, and random samples are taken from each stratum.
(Stratum means group, and literally means ‘layer’) ?
Typical Question:
In a school, I wish to sample 40 people from Year 8 to Year 10 for their favourite chemical compound.
I wish to do a stratified sample by year group.
How many students should I sample in Year 10?
Bro Tip 1: You can only sample a whole number of things, so you MUST round your final answer.
Year Group
Total Students 8
184 9
154 10
238
Bro Tip 2: Check the your answer looks sensible. Here it does, as slightly under half the students are in Year 10. ? ?
Proportion Sampled: 𝟒𝟎 𝟓𝟕𝟔
Num to sample: 𝟒𝟎 𝟓𝟕𝟔 ×𝟐𝟑𝟖=𝟏𝟔.𝟓𝟐𝟕 → 𝟏𝟕 people

16. Test your understanding?
50/258 of students sampled.
26 x (50/258) = 5.039
So 5 students. ?
= 135 females.
135 x (50/258) = 26.16
So 26 students.

17. Exercises (on your sheet)
Question 1 ?
𝟏𝟓𝟎 𝟓𝟗𝟏 ×𝟏𝟐𝟔=𝟑𝟏.𝟗𝟕 → 𝟑𝟐 students
Question 2
𝟐𝟎𝟎 𝟏𝟗𝟑𝟓𝟎 ×𝟓𝟏𝟎𝟎=𝟓𝟐.𝟕→ 𝟓𝟑 students ?

18. Exercises (on your sheet)
Question 3
a) 𝟔𝟎 𝟓𝟔𝟒 ×𝟐𝟒 →𝟑
b) 9
c) 28 ?
Question 4 ?
𝟏𝟎𝟎 𝟑𝟒𝟎 ×𝟏𝟖 → 𝟓

19. Exercises (on your sheet)
Question 5 ?
×50→6
×30→3
×60→7
×40→5
×76→9
×54→6
×13→1
×24→3 ? ? ? ? ? ? ?

20. What method of sampling does it sound like the UK uses?
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.”

21. Quickfire Questions ? ? ? Do these in your head...
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.