Mathematical Literacy Level 3 Module 16 hlayiso.com

Mathematical Literacy NQF 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Collect and organise data to answer questions in a workplace based context Module 16 Downloaded from hlayiso.com Maths Lit NQF Level 3

Overview 16.1 Key concepts related to data collection and handling 16.2 Identifying possible sources of error, bias or misinterpretation 16.3 Questions and instruments for collecting data 16.4 Classifying and organising data 16.5 Grouping data using intervals Downloaded from hlayiso.com Maths Lit NQF Level 3

Key concepts related to data collection Unit 16.1 and handling Downloaded from hlayiso.com Maths Lit NQF Level 3

Key concepts related to data collection Unit 16.1 and handling • Gathering information is an important way to help people make decisions about topics of interest. • We often see the results of data collection on television, radio or in the newspaper. • In the workplace, surveys can help decide what needs to be changed, where money should be spent, what products to purchase, what problems there might be, and so on. • We use different methods to collect data by using surveys of people (e.g. questionnaires, opinion polls) Downloaded from hlayiso.com Maths Lit NQF Level 3

The process of data collection Unit 16.1 Clarify the research Define the Ask Summarise questions population questions and and the of interest – present 1234 type of data A census or and tally the results the results to be a sample collected Downloaded from hlayiso.com Maths Lit NQF Level 3

1. Clarify the research questions and the type of data to be collected. Unit 16.1 What questions do you want answered? These can be Or they can be more simple questions, complex questions, For example, For example, What is your favourite colour? Which roads have the worst traffic? Downloaded from hlayiso.com Maths Lit NQF Level 3

2. Define the population of interest and choose a census or a sample Unit 16.1 Example 16.1 page 308 In a shopping centre on a Saturday, 250 customers go to a restaurant. You want to know more about them to see what the target market for the restaurant should be. You could interview every person there, which is a census. You could just choose to ask every tenth person who leaves the restaurant. That is a sample. Downloaded from hlayiso.com Maths Lit NQF Level 3

2. Define the population of interest and choose a census or a sample Unit 16.1 Example 16.1 page 308 continued… If you use a sample, you need to choose it randomly to make sure that the data is correct. After completing a sampling survey you can use the information to make a prediction about how the rest of the population would respond. The more people you have asked, the better your result will be. Downloaded from hlayiso.com Maths Lit NQF Level 3

3. Ask questions and tally the results Unit 16.1 Example 16.3 page 308 To collect information about the favourite colours of a group of people at a shopping centre, you could keep a tally of results as you ask people. Every 5th mark crosses the previous 4 marks, so you can see groups of 5 and count up the tallies. Downloaded from hlayiso.com Maths Lit NQF Level 3

4. Summarise and present the results Unit 16.1 Example 16.4 page 309 You have collected information about how long it has taken customers to get to a shopping centre. You could present the information like this: • Shortest journey: 10 minutes • Average journey: 22 minutes • Longest journey: 45 minutes Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 16.1 Unit 16.1 Complete Exercise 16.1 on page 309 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Identifying possible sources of error, Unit 16.2 bias or misinterpretation Two things can go wrong when you collect data: • If questions in the survey are worded poorly or ambiguously, people's answers can be inaccurate. This results in error in your data. • You may introduce bias into the process. Definition Bias is information that is not truly representative of the situation you are investigating • Bias may be a result of: • poorly prepared questions • a sample that is not representative of a population • collecting agents with different ways of collecting the data. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 16.5 page 310 Unit 16.2 • Thandi carried out a survey to find out how much money people living in a town spend on food each week. • She asked 100 people at the shopping centre closest to where she lives on a Tuesday morning. • Explain why Thandi’s survey might be biased and advise her on how to avoid this bias. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 16.5 page 310 continued ... Unit 16.2 Thandi could be introducing bias by: • surveying shoppers at one shopping centre only • only asking shoppers on one week day • only asking shoppers at one time of day. She should rather choose a variety of different places to ask people, and survey people on other days, including weekends, and at different times of the day, including after normal working hours. Downloaded from hlayiso.com Maths Lit NQF Level 3

Choosing your sample Unit 16.2 • The sample chosen from the larger group (population) must represent that group. • There are always some variables that cannot be represented. To make the sample represent the whole population as closely as possible:  choose a random sample containing all the different kinds of people representing the population from which it is drawn  choose a large enough sample to fairly represent the population Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 16.2 Unit 16.2 Complete Exercise 16.2 on page 311 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Questions and instruments for collecting Unit 16.3 data We can differentiate between two types of questions: Closed Open-ended questions questions Questions with a set number Questions that can be of answers to choose from. answered in any way. e.g. Write down your gender: e.g. How do you feel about M (male) or F (female) people that litter? Downloaded from hlayiso.com Maths Lit NQF Level 3

Questions and instruments for collecting Unit 16.3 data • It is a good strategy to have a selection of closed questions, but follow up with some open-ended questions. That way you can be sure that you get the information you need. Points to remember: • The questions must provide the information that we want. • The questions must be short and simple. • The questions must be clear and unambiguous. • The questions must mostly be closed and not open- ended. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 16.6 page 311 Unit 16.3 • Your class wrote a test marked out of 50. • You want to find out how well the class felt that they did in the test. • Develop a question that you can use to find this out. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 16.6 page 311 continued ... Unit 16.3 • The term ‘how well’ is not clear. To make it clear we can use the words poor, average, good and excellent. But these words on their own are still not clear, so we must state the marks that would be considered poor, average, good and excellent. • A suitable question might be: Tick the list. How well did you do in the test? Description Poor Average Good Excellent Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 16.6 page 311 Unit 16.3 • You might also ask the students to add any comment to their answer. For example, they might want to add that in their opinion, the test was unreasonably difficult. • You could leave space for this by inserting an open- ended question such as: ‘Is there any other comment you would like to make about the test?’ • Do not give them an example of a possible response or “lead” their answer in any way. Downloaded from hlayiso.com Maths Lit NQF Level 3

Instruments of data collection Unit 16.3 • Three instruments for collecting data or ways of collecting data are: Observation You simply observe, watch and record the information. Interview Face-to-face questions, appropriate for small numbers and short responses. Questionnaire You write a set of questions and provide spaces for participants to write their responses. This instrument is good for getting information from many people. • The instrument type is determined by: i. info required ii. type of question Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 16.3 Unit 16.3 Complete Exercise 16.3 on page 313 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Classifying and organising data Unit 16.4 • Data can be organised by using:  tallies  frequency tables • Organising data when it is collected makes it easy to find the totals. • The table shows the results of a survey: Number of Tally Frequency vehicles 0 ||| 3 1 |||| ||| 8 2 |||| |||| || 12 3 | 1 4 || 2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Classifying data Unit 16.4 Once data has been collected and organised it needs to be classified. 1. Numerical data is data that is measured in numbers and units.  Discrete data has exact separate values e.g. the number of people in a room  Continuous data is data that can have any value, including fractions e.g. 12,5cm 2. Categorical data is data that is described, not measured in units. e.g. a person’s gender; makes of cars; types of animals. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 16.4 Unit 16.4 Complete Exercise 16.4 on page 315 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Grouping data using intervals Unit 16.5 • When a large amount of data is collected we can group the data into class intervals. • We decide on the size of the class intervals using the range of the data and a useful number of intervals spread through the range. Range = highest – lowest score • We don't want too much data in the intervals, but we also don't want too many intervals to work with. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 16.8 page 316 Unit 16.5 The grouped frequency table represents the ages of 200 people in a shopping centre on a Saturday. Age (years) Tally Frequency 0-9 |||| ||| 8 10-19 |||| |||| || 12 20-29 |||| |||| |||| |||| |||| 24 30-39 |||| |||| |||| |||| |||| |||| 43 |||| |||| ||| 40-49 |||| |||| |||| |||| |||| |||| 41 |||| |||| | 50-59 |||| |||| |||| |||| |||| || 27 60-69 |||| |||| |||| |||| ||| 23 70-79 |||| |||| |||| ||| 18 80-89 ||| 3 90-99 | 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 16.8 page 316 Unit 16.5 Age is continuous data. So there are no gaps between the intervals. Each class interval represents all of the possible ages up to the beginning of the next class interval. So the interval 0–9 years represents all of the ages up to 10 years, including 9 years 6 months etc. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 16.5 Unit 16.5 Complete Exercise 16.5 on page 316 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Module assessment Module 16 Complete Module assessment on page 319 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

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