1.1 Introduction to data

Transcription

1 1 Introduction to data Objectives Understand what is meant by a variable Identify qualitative and quantitative data Identify discrete and continuous data Key words Variable Qualitative Quantitative Discrete Continuous Starter Imagine you are old enough to drive. What sort of car would you like to buy? Ask several students to describe their requirements for a car. Main teaching Tell students that the things they described are called variables. Display PowerPoint 1, slide 1 and discuss these points: They are all variables to do with cars. You can describe colour but cannot measure it. You can measure engine size and represent it as a number. (Most cars have an engine size between 800 cc and 6000 cc.) You can count the number of doors and represent it as a number. (Most cars have 2, 4 or 5 doors.) Practise classifying variables into two types on slide Variables described in words, such as colour, are qualitative variables. Variables with numeric values, such as engine size and number of doors, are quantitative variables. Quantitative variables can then be divided into two types as shown on slide Those that can take on any value on a numeric scale (engine size). These are continuous variables. Those that can only take certain values on a numeric scale (number of doors). These are discrete variables. The types of data can be summed up in a single diagram (see slide 4). Display slide Classify the variables to do with cars. Links Choose a car: co.uk/hotlinks (code 4554T) ActiveTeach resources MS PowerPoint presentation: 1 Types of data Chapter 1 game Follow up sections 1 to 5 and Exercise 1A Extra practice Worksheet 1 (answers on page 177) Sections

2 Worksheet 1 sections 1 5 Types of data The table gives some observations of variables. Variable Which of these variables are a) quantitative b) qualitative? Observations A Eye colour blue, brown, green, grey B Height 172 cm, 163 cm, 185 cm C Breed corgi, collie, pug, spaniel D Number of pets 1, 0, 3, 2, 4 Which of the following is a qualitative variable, which is a quantitative variable and which is neither? jumper size taste going waist measurement The table gives some observations of variables. Variable A Number of siblings 0, 3, 2, 5 Observations B Height 172 cm, 163 cm, 185 cm C Amount of milk 5 litres, 25 litres, 1 litre D Time 1 hour, 5 hours Which of these variables are a) continuous b) discrete c) quantitative? State whether each of these quantitative variables is continuous or discrete. a) shoe size b) hand span c) lifetime of a light bulb d) number of people in a cinema. What is an hypothesis? Explain why a) the weight of a cow is a continuous quantitative variable b) the number of conkers on a tree is a discrete quantitative variable. Which of these are categorical data and which are ranked data? a) Positions in class b) Cars grouped by colour c) Computers grouped by manufacturer. a) What are bivariate data? b) Write down which of the following are bivariate data. i) Arm length and serve speed ii) TV price and washing machine price. Ann s height to the nearest half centimetre is 165 cm. Write down a) her maximum height b) her minimum height c) the maximum possible error. 23

3 6 Populations and sampling Objectives Understand what is meant by a population Understand what is meant by a census Understand what is meant by a sample Understand the terms random, random sample Key words Population Census Sample Random Simple random sample Stratified sample Starter What industry would you like to work in? What job would you like in that industry? Main teaching Tell students that they are going to investigate careers. Reveal the careers on slide 1 of PowerPoint 6A. Which of the careers shown do you think would be most popular with students in our school? How would you find out? You need to know about every student in the school. This is known as the population you are studying. To get an accurate answer you could use a census. This means asking every student their opinion. It takes a long time. How could you save time? You could use a sample. This means just asking a few students. It is less accurate, but quicker. Display screen 2 to show the differences between a population, census and sample. If you take the class as a sample you can find which is most popular by filling in each person s choice. Complete the list on screen 3 with a tally. Discuss whether this sample is representative of the whole school. Suggest that to get a really accurate picture everyone in the school must have an equal chance of being selected for the sample. This is known as random selection. Discuss simple random sampling and stratified sampling. Use PowerPoint 6B (see screenshots on page 25) to demonstrate the methods. Links Choose a career: co.uk/hotlinks (code 4554T) ActiveTeach resources MS PowerPoint presentations: 6A Population and sampling, and 6B Random sampling Chapter 1 game Follow up sections 6 and 7 Discuss section 8 Non-random sampling (Higher) Exercise 1B Extra practice Worksheet 6A (answers on page 177) Worksheet 6B Higher (answers on page 177) Sections

4 PowerPoint 6B Sampling methods Higher This PowerPoint presentation is on the ActiveTeach CD-ROM 25

5 Worksheet 6A sections 6 8 Populations and sampling a) What is meant by a census? b) Write down two advantages of using a census. c) Write down two disadvantages of using a census. A hospital manager wishes to find out whether the nurses are happy with the work shifts. a) Describe the population she needs to use. She decides to question a sample of nurses. b) Write down two advantages of using a sample. c) Write down two disadvantages of using a sample. The hospital manager uses all the nurses on one ward as the sample. d) What is wrong with this sample? 7. a) What is meant by a random sample? John uses the first twenty people arriving at work as a sample for the research he is doing. b) Is this a random sample? Give a reason for your answer. Write down four ways of getting numbers for a random sample. The table shows the number of people on each of the four working shifts at a factory. Shift number Number of people The manager decides to ask a sample of 90 workers what they think about the quality of food in the factory canteen. He uses stratified sampling to choose his sample. Describe exactly how he could do this. Below is an extract from a random number table Use this table of random numbers to choose 12 different random numbers each less than 50. Jasmine decides to select a sample of students to ask about college library facilities. a) What sampling frame will she use? She asks 10 people from each year group. b) Discuss whether or not this is likely to be a stratified sample. 26

6 Worksheet 6B Higher Populations and sampling sections 6 8 Describe how a random sampling method differs from a non-random sampling method. A supermarket manager is going to do a survey to find out people s views on a number of different aspects of the supermarket. a) Give the name of a suitable sampling method he should use. b) Describe how this sampling method works. A large nuclear power company needs information about how the staff feel about the facilities they offer. The company workers are spread out over 20 sites. The company manager decides to ask all workers from in a random selection of 5 sites. What is the name given to this type of sample? The head teacher of a large academy wants to get the students views on a new uniform. She decides to use a stratified sample of students. a) Write down the reason why he does not use a census. The table shows the numbers of students in each year group. Year 7 Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Girls Boys b) The head teacher wants to ask a sample of 100 students. Describe how she will do this A gardener decides to give extra fertiliser to a simple random sample of her greenhouse plants. Describe the sampling frame she should use. a) Describe how cluster sampling is used. b) Write down one disadvantage of cluster sampling. A hotel manager wants to find out whether the members of the health club attached to the hotel are happy with its facilities. He decides to use a questionnaire. He will give it to a sample of the members. a) What is the sampling frame he should use? He decides that his sample will consist of 10 members from each age group. b) What is the name given to this method of sampling? An office has 75 office staff. It is decided that a questionnaire will be given to 15 of the office staff. a) The management decide to use systematic sampling to do this. Describe how this will be done. b) Why is systematic sampling not true random sampling? 27

7 9 Collecting data Objectives Know how to collect data using questionnaires interviews observation Key words Questionnaire Interview Observation Open question Closed question Starter What meals are healthy dinner options? The internet link could be used to revise healthy and unhealthy foods. Main teaching Tell students that they will investigate what proportion of students who have school dinners at their school choose a healthy meal. Why might a random sample be used? (It enables information to be deduced about the population.) How could you collect this information from a sample? (Questionnaire, interview or observation.) What questions would you ask? Show the sample questionnaire on slide 1 of PowerPoint 9A. What is wrong with it? (Names are required. The question about eating school dinners is an open question. The healthy dinner question is a leading one that would make students feel they should answer yes.) How could it be improved? (Don t ask for a name and use closed questions with answer boxes.) Slide 2 shows an improved version of the questionnaire. Discuss how you could obtain the information by observation (e.g. stand at dinner time and, for each person having a school dinner, record if it is a healthy meal or not). Display the tally chart on slide 3 as an example of possible results. How can we find out what proportion of students at our school who stay to school dinners eat a healthy dinner? Use the class as a sample. Each student should record their responses on slide Links Healthy eating activities: co.uk/hotlinks (code 4554T) ActiveTeach resources MS PowerPoint presentation: 9A Healthy foods Chapter 1 game Follow up section 9 (with MS PowerPoint presentation: 9B Capture recapture method) and Exercise 1C Extra practice Worksheet 9 (answers on page 178) Section 9 28

8 PowerPoint 9B Capture recapture method This PowerPoint presentation is on the ActiveTeach CD-ROM 29

9 Worksheet 9 section 9 Collecting data State whether the following are primary or secondary data. a) Data used from farm records. b) Data from a car magazine. c) Data you collect yourself. A questionnaire on waste disposal is to be given out to a sample of people on a housing estate. Here are three questions suggested for the questionnaire. A What do you think about the facilities for waste disposal on this estate? B Do you agree that the facilities for waste disposal on this estate are good? C Yes No How often do you use the waste disposal facilities on this estate? Weekly Monthly None of these questions are satisfactory. Explain why. A manager decides to collect data from a sample of his workers. He is going to give them a questionnaire. He decides to do a pilot study first. a) Write down one advantage of doing a pilot study. One question on the questionnaire is: How old are you? Under to to 60 b) c) What is wrong with this question? Write down a better form for this question. A supermarket manager is going to do a survey by using face-to-face interviews. a) Write down one advantage of a face-to-face interview. b) Write down one disadvantage of a face-to-face interview. Write down one disadvantage of doing a) a postal survey b) a telephone survey. A trout fishery wants to find out how many fish are in one of their ponds. They take out 30 fish and tag them. The fish are returned to the pond. A few weeks later they take out 30 more fish and find that 6 of them are tagged. a) b) Work out an estimate for the number of fish in the pond. Write down any assumptions you have made. 30

10 Quick Test 1A Define a) primary data b) secondary data. qualitative quantitative discrete continuous Which of the above words go with a) b) c) weight hair colour number of pets? Write down which of the following ages fall into the categories 0 5, 6 10, and Ages: 2, 7, 3, 9, 13, 17, 20, 1, 3, 6, 17, Write down one advantage and one disadvantage of a) a postal survey b) a personal interview. What is a population? What is a sampling frame? What is meant by taking a census? What is meant by taking a sample? Write down two advantages and two disadvantages of taking a) a census b) a sample. 10. Write down three ways to generate random numbers so you can take a simple random sample. 1 Write down two advantages of using a pilot study/survey. 31

11 Quick Test 1B Higher A sample of 20 mugs is to be chosen from a box of 160 mugs. Describe how to do this using systematic sampling. Write down a brief description of cluster sampling. A supermarket did a survey. They asked questions of 40 people. There were five people from each gender in each of these age groups: 20 to 29, 30 to 39, 40 to 49, and 50 to 59. What is the name given to this type of sampling? Write down three rules you should follow when constructing a questionnaire A nursery school has three classes. There are 18 children in class 1 24 children in class 2 15 children in class Write down how you would select a stratified sample of 19 children from this nursery school. Twenty-eight fish are caught from a pond. They are marked and returned to the pond. Later 50 fish are caught from the pond and 7 are found to be marked. a) Estimate the total number of fish in the pond. b) Why may this estimate be incorrect? Write down why a control group is often used in medical research. What is meant by data logging? The height of a tree is measured to the nearest metre. It is found to be 12 metres tall. Write down the upper and lower boundary heights for this tree. 10. Jenny decides to give a questionnaire to the first 20 people entering the factory gates. What is wrong with using the first 20 people as a sample? 32

12 Chapter 1 Test The Chapter Test is available in two formats: as it appears here and exam-style write-on format on the CD-ROM in the back of this Teacher Guide. An undergraduate collects data for her research on plants. She collects information from three sites. She notes down the following variables: the colour of the flowers, the height of the plants and the number of plants she collects from each site. a) b) c) d) e) Are these data primary data or secondary data? Give a reason for your answer. Which of these data are qualitative data? Which of these data are quantitative data? Which of these data are continuous data? Which of these data are discrete data? (6) a) What is meant by a random sample? b) A student wants to choose a random sample of 10 books from a set of 100 books. He uses a random number table. This is the section from the table that he uses Describe how he will take his sample. (3) 7. A firm making carrier bags decides to do some research into the strength of their carrier bags. a) Why will they not use a census? b) What is the population they will use? (2) A shop wants to know what their members of staff think about the adequacy of car parking provision. They decide to use a census. Write down the advantage of using a census in this case. (1) A large chain of hairdressers wants to find out whether their staff like the products they use. Write down the disadvantages of using a census in this case. (3) a) Which of these are closed questions and which are open questions. A What do you think about the idea of building a new supermarket? B Do you go to the cinema? Yes/No C What do you think of the colour of the wall? b) What is the important difference between a closed question and an open question? (4) A pharmaceutical company needs to research the effectiveness of a certain drug on arthritis. The research organiser decides to use the 100 members of an arthritis society. a) What is the sampling frame they will use? They need to use a control group. b) What is a control group? c) How many people would it be sensible to use in this control group? (3) 33

13 8. Town councillors decide to do a survey to see if the people of the town would like money to be spent on upgrading the sports centre. They decide to give a questionnaire to a sample of people. a) Write down two advantages of using a sample. They will use a questionnaire. b) Write down a reason why it would not be a good idea to give the questionnaire just to people attending the sports centre on one particular day. They decide to give the questionnaire to a random sample of the population of the town. One question on the questionnaire is: Would you like the sports centre to be upgraded? What is wrong with this question? c) Another question is: How old are you? d) Under 20 Over 20 What is wrong with this question? (6) 9. A factory owner wants to find out whether the workers would like to be able to work flexi-time. He divides the workers into groups as shown in the table. Type of worker Office Shift Day Number of workers He decides to ask a stratified sample of 80 workers. Describe exactly how he would do this. (6) 10. A bird reserve warden decides to try to work out an estimate of the number of black-headed gulls there are on the reserve. He captures and rings 45 black-headed gulls. The gulls are returned to the reserve. Several weeks later he captures 100 birds and counts how many are ringed. He finds that 12 are ringed. a) b) Work out an estimate of the number of black-headed gulls that are on the reserve. Write down three assumptions that you made when working out the number. (5) 1 University staff decide to find out what students think about the campus. They decide to use a questionnaire. a) What is the sampling frame they will use? They decide to use a pilot study. b) What are the advantages of using a pilot study? (3) 1 A company decides to send out a questionnaire to a sample of the workers to find out their views on working conditions. a) Describe the population they will use. b) Describe the sampling frame they could use. c) Describe a sampling unit. (3) Total 45 34