Mathematical Literacy Level 4 Module 13

Mathematical Literacy NQF 4 Downloaded from hlayiso.com Maths Lit NQF Level 4

Collecting and organising data Module 13 Downloaded from hlayiso.com Maths Lit NQF Level 4

Overview 13.1 Research and collecting data 13.2 Data collection 13.3 Developing questionnaires 13.4 Data collection instruments 13.5 Using tally tables to sort data 13.6 Grouping data using intervals Downloaded from hlayiso.com Maths Lit NQF Level 4

Research and collecting data Unit 13.1 • Data is collected by individuals, organisations and governments usually because they need specific information. • Data collection is used to study and record information, to make decisions about important issues and to pass information on to relevant people or communities. • Whatever the specific reason, data is always collected to provide information. Data is used by: Governments Weather Reports Businesses Economic forecasts, etc Downloaded from hlayiso.com Maths Lit NQF Level 4

How data is used by different groups Unit 13.1 • Everyone – from students to pensioners – uses some form of data at some time during their lives. The data may be used to complete an essay, a major project or simply to satisfy curiosity. • Data about drug abuse by young people can focus on campaigns to prevent drug use. • Data about social media can be used by business to watch the latest trends in marketing. • Provincial and national governments use data to inform their decisions about the needs of the people they serve. Downloaded from hlayiso.com Maths Lit NQF Level 4

How data is used by different groups Unit 13.1 • Data about social development can result in decisions about building new hospitals, schools and clinics. • Data about economic development can measure the impact of investment in the country. • Data about the local economy can be used to inform building of new offices, factories and warehouses. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 13.1 Unit 13.1 Complete Exercise 13.1 on page 251 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Revision of data and concepts Unit 13.1 Range: The range (or spread) of data refers to the difference between the smallest and the largest value in the data sample. Downloaded from hlayiso.com Maths Lit NQF Level 4

Revision of data and concepts Unit 13.1 Research Question: A research question may be simple or complex. You need to determine what question it is that you want answered. Downloaded from hlayiso.com Maths Lit NQF Level 4

Revision of data and concepts Unit 13.1 Population: The population includes all the people or things that you want to collect data about. Downloaded from hlayiso.com Maths Lit NQF Level 4

Revision of data and concepts Unit 13.1 Target Population: A target population is a group that a researcher hopes to understand by collecting and analysing data about that group Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.5 page 253 Unit 13.1 Sebenza TVET college conducts a census in their school about how sexual harassment. They want to know whether any student has experienced sexual harassment from a fellow student or from a lecturer. 1. Who is their target population? 2. Who do they need information from? 3. Write two simple research questions that require a yes/no/maybe answer. 4. Would you recommend that this census should be answered with the students’ names, or anonymously? Explain. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.5 page 253 Unit 13.1 1. All students at the college. 2. They need information from the students, but they may want to include information from lecturers and parents as well. 3. Here are examples of questions that are appropriate: A. Have you experienced sexual harassment on campus? B. Do you know someone who has been sexually harassed? C. Have you heard about someone who has been sexually harassed? D. Do you know anyone on campus who has sexually harassed others? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.5 page 253 Unit 13.1 4. This census should be kept anonymous to avoid embarrassment. However, it should advise anyone who has been sexually harassed where to go for help, and anyone who knows someone who has harassed others to notify campus authorities. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection instruments Unit 13.1 SURVEY A survey is a process of collecting data from a sample of the population that we are interested in. A survey can focus on getting opinions or on getting facts from respondents. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection instruments Unit 13.1 QUESTIONNAIRE A questionnaire uses a set of questions and provides spaces for respondents to write their responses. This instrument is good for getting information from a variety of people. Questionnaires are also appropriate for getting information from people that are spread over a wide area and are not easy to contact face to face. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection instruments Unit 13.1 INTERVIEW An interview involves asking people a set of questions face to face. That is, you talk to the participants directly and they tell you their answers. Interviews are appropriate for a small number of participants and for short and long responses. Interviews are also appropriate when all participants can be contacted easily. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection instruments Unit 13.1 OBSERVATION Observation involves simply observing a trend (also known as a phenomenon). The researcher simply observes, watches and records information. There is no discussion with participants. Observation is appropriate for collecting information where there is no need for any communication. Downloaded from hlayiso.com Maths Lit NQF Level 4

Explaining some important concepts Unit 13.1 Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.14 page 258 Unit 13.1 • Samantha is part of a team of researchers at Muizenberg beach collecting data about why more sharks are venturing closer to shore. However, she has a strong belief that chumming is a big reason for sharks coming closer to shore. Explain why she might not be objective when conducting this survey. • Samantha has her own strong belief on the subject. This makes it difficult for her to be objective. Study the sources of income for the two months of December and January. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.15 page 259 Unit 13.1 • Refer to this questionnaire: Dear Customer, The Squeeza Family Restaurant is dedicated to improving customer satisfaction. This survey will be helpful to enhance our services and meet your needs. Your response will be used only for survey purposes. Attached is a gift voucher that can be used in the next month as a token of our goodwill. In case you have any questions regarding the survey, please call 123-456-7890. Thank you very much for your time and suggestions. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.15 page 259 Unit 13.1 Strongly Strongly Agree Neutral Disagree agree disagree 1. The restaurant is accessibly located. 2. The restaurant hours are convenient for my family needs. 3. The advertised dish was in stock. 4. A good selection of dishes was present. 5. The meals sold are good value for money. 6. The restaurant has the lowest prices in the area. 7. Meals sold are of the highest quality. 8. Restaurant atmosphere and decor are appealing. 9. Do you agree that naughty children should not be allowed in a restaurant? 10. I agree that MSG is harmful and should be avoided. 11. What could we do to make your restaurant dining experience better? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.15 page 259 Unit 13.1 a) Identify anything in the explanation to the customer that would influence their answers. b) For each question, decide if it is biased or subjective. c) If it is biased, change the wording to make an unbiased question. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.15 page 259 Unit 13.1 a) The attached gift voucher will influence customers to say positive things about the restaurant. b) • Questions 1–5 and 8 are positive statements about the restaurant, but respondents can disagree in their choice of answer category. • Question 6 and 7 assume that respondents would know about prices in the area and what makes for highest quality. They are not direct questions about their own experience of the restaurant and will be answered by ‘hearsay’, or a general feeling of like or dislike of the restaurant. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.15 page 259 Unit 13.1 b) • Question 9 is biased. It puts the opinion into the respondent’s head that naughty children should not be allowed in the restaurant. • Question 10 is biased. It tries to influence the respondent to be opposed to MSGs. c) Question 9 can ask if children should be allowed in the restaurant. Customers who want ‘naughty’ children to be kept out of the restaurant can comment on this in Question 11. Question 10 can ask if the restaurant should avoid putting MSGs in the food. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection Unit 13.2 Definition Data collection describes a process of obtaining specific information about a certain trend or phenomenon taking place. ” • The collected data (tallies, lists of answers, lists of measurements) is called raw data. • In order to gain insight into the data, we need to find ways to summarise, organise and represent it before we can analyse it. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection Unit 13.2 The process of data collection needs to be ordered and systematic. To start, check that you: Have a clear objective for your research. Know what data you need, why you need it and how you will use it. Identify specific data procedures that are appropriate to the context within which the data is being collected. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection process Unit 13.2 1. Identify data needs • What kind of data? • How it will be used? • Identify data that is easy to find. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection process Unit 13.2 2. Identify data categories • What data types or categories will you organise data into? • Use simple categories. • These categories will become the framework for your questionnaire. Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection process Unit 13.2 3. Design and test data collection • Choose an appropriate instruments data collection instrument. Examples: questionnaires, interviews, observations, surveys. • Decide what you want the instrument to measure e.g. status, progress, problems, attributes . Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection process Unit 13.2 4. Processing and storage • Store data in records or a database. • Data is ready for processing and analysing. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 13.3 Unit 13.2 Complete Exercise 13.3 on page 261 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Developing questionnaires Unit 13.3 Designing a questionnaire • A questionnaire is a data collection instrument. • It should include specific questions that will enable the collection of each category of data that you wish to collect. • It could also include tables that respondents can complete. Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for designing a questionnaire Unit 13.3 The questions should be clear and unambiguous with simple layout. The questions must be written in clear, simple language, not be too long and be in logical order. Avoid offensive questions. Clear instructions how to complete each section and explain difficult terms. Prompts for additional information, such as ‘Please specify’ or ’Others’, may be added. Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for designing a questionnaire Unit 13.3 Allow anonymity to increase the number of people participating. Avoid sensitive information that would make people not to participate or respond. Explain the purpose the questionnaire to respondents Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 13.4 Unit 13.3 Complete Exercise 13.4 on page 266 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Data collection methods Unit 13.4 Observations Interviews Conducting surveys Use observations and Observe, watch and interviews to gather record information. information. Ask people a set of questions face to face. There is no discussion Distinguish between with participants. descriptive surveys and analytic surveys. Downloaded from hlayiso.com Maths Lit NQF Level 4

Observations Unit 13.4 Definition Observation involves simply watching participants in the situation that you are investigating and then recording the information. It does not involve discussion with participants. ” Downloaded from hlayiso.com Maths Lit NQF Level 4

Observations Unit 13.4 • Direct observation requires the observer to remain anonymous and unnoticed so that the behaviour of participants is not influenced by the presence of the observer (as far as possible). For example, observing young children interacting in the playground. • Participant observation includes the observer in the event, culture or activity taking place. For example, in a health of human service programme, the observer can participate in the activities being observed. • Observation can also be done by conducting tests or using specific observation tools (for example, a checklist of criteria to rate participants). Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.23 page 268 Unit 13.4 At Vuyelwa College in the Northern Cape, Thandeka was conducting a survey about how many students visited the library during the exam times. a) What method of observation should she use? Explain. b) Who is the target population of Thandeka’s research? c) Which considerations should Thandeka bear in mind when setting up and carrying out her observations? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.23 page 268 Unit 13.4 a) Direct observation. Thandeka will be the observer and she will remain anonymous and generally unnoticed. b) The target population are the students at Vuyelwa College visiting the library during exam times. c) Thandeka should consider the student’s behaviour, her own attitudes, the conditions and the effects of some of the behaviour of students and staff at the library. Downloaded from hlayiso.com Maths Lit NQF Level 4

Interviews Unit 13.4 Here are some questions you should ask yourself before conducting interviews: ? Are you targeting the right target population? Is the target population accessible? Are you able to adjust or amend your interview in the time required? Downloaded from hlayiso.com Maths Lit NQF Level 4

Interviews Unit 13.4 A successful interview is preceded by: • Learn as much as possible about the target population that you will be interviewing. • Do some research about the target population that you will be interviewing. Contact the appropriate person(s) and request an interview. • Explain the purpose and intention of the interview as well as use of the results. • Cover all issues of confidentiality and permission of participants. Downloaded from hlayiso.com Maths Lit NQF Level 4

Interviews Unit 13.4 Establishing trust can be the most difficult part of an interview. Here are some steps to help you do this: • Treat everyone with equal respect. • Don’t assume you know more than anyone else. • Share what you do know freely. • Discuss the outcomes you want and how the interview will achieve this. • Follow through on whatever you say you will do. Don’t make promises you cannot keep. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.25 page 269 Unit 13.4 Pumla is given a project to investigate human rights violations in her community or a community close to her. She decides to draw up a set of questions that she will use during her interviews. She also decides that she will visit a mall close to where she lives and interview some people visiting the mall. Look at some of the questions she has written down and state whether you think she would receive proper feedback during her interviews. 1. Do you know what human rights violations are? 2. Human right violations are bad. Do you agree or disagree? 3. Have you ever been a victim of a human rights violation? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.25 page 269 Unit 13.4 Human Rights violations encompass so many aspects and some people may not even be aware that their human rights are violated. The Constitution entrenches the rights of all human beings in South Africa, so she should start out explaining this and highlight the human rights to make people aware of them. The nature of these types of questions could also be very sensitive, so it would not be a good idea to interview people in a mall. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 13.5 Unit 13.4 Complete Exercise 13.5 on page 273 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Using tally tables to sort data Unit 13.5 • We can organise data in many ways: Using a Category combi- nation of Event methods Grouping data using Place intervals Organising Data Using tally Individual tables Time of obser- Group vation Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 13.6 Unit 13.5 Complete Exercise 13.6 on page 275 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Grouping data using intervals Unit 13.6 When working with a large range of data we can group the data. Grouping data makes the data more manageable. How is this done? • Choose equal sized groups within the number range, making class intervals. • Decide how large each class interval should be. • The data range determines the size of the class intervals. • If intervals are too wide, too much data falls into the same class interval. • If intervals too small, there are too many intervals with not enough data to fill them! Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.31 page 276 Unit 13.6 Malik is the HR Manager at Britannica Boating Company. The company runs a training course for company employees who complete a competency test out of 100 at the end. Malik uses a grouped frequency table to record the results. The scores are grouped into the classes 0–9, 10–19, 20–29, etc. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.31 page 276 Unit 13.6 Complete the frequency column to be able to answer these questions. 1. How many employees scored between 30 and 39? 2. What is the score class in which most employees fall? 3. Which score class contains the smallest number of employees? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 13.31 page 276 Unit 13.6 1. 22 2. 50–59 3. 90–99 Downloaded from hlayiso.com Maths Lit NQF Level 4

Continuous and discrete data Unit 13.6 Continuous data Discrete data is not restricted to whole can be counted because it numbers and can be any only takes on whole number value in a continuous values. range. For example: For example: mass, height and time are the number of students in a ongoing and measured in class is discrete because there a continuous way. will not be half a student or quarter of a student in the class! Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 13.7 Unit 13.6 Complete Exercise 13.7 on page 278 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Module assessment Module 13 Complete Module assessment on page 280 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

TERMS AND CONDITIONS This PowerPoint Presentation has been developed by Macmillan Education South Africa (Pty) Ltd. All texts, images, videos, animations, audio and vector simulations contained in the slides are property of Macmillan South Africa. Reproducing, reselling and redistributing this material without the written permission of Macmillan South Africa is prohibited. Lecturers are granted permission to: (i) modify the slides by adding and removing content; (ii) print copies of the presentation; and (iii) download and save the slides to a computer or local server. Nothing in this copyright notice constitutes permission to assert or imply that your use of the materials is sponsored or endorsed by Macmillan South Africa. Downloaded from hlayiso.com Maths Lit NQF Level 4