Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com 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. 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.

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. ?

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 □ 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 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? 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 ?

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. Have a large a sample size as before so as to be more representative of the whole population. 2 ?

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. ? Only women were asked/you need to ask men. Only people leaving the cinema were asked/you need to 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: 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.

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 ? How many of each type of animal should I sample? 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 Bro Tip: you can only sample a whole number of things. You will lose a mark if you don’t round. ? 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.

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.

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.”

Exercises (on your sheet) ? Students in school = 591 Proportion sampled = 150/591 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 Tesco: 53 Aldi: 47 Waitrose: 21 M&S: 14 ?