Mathematical Literacy Level 2 Module 15

Mathematical Literacy NQF 2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Collect and organise data Module 15 Downloaded from hlayiso.com Maths Lit NQF Level 2

Overview 15.1 Key concepts in data handling 15.2 Data collection tools 15.3 Organising data Downloaded from hlayiso.com Maths Lit NQF Level 2

Key concepts in data handling Unit 15.1 Definition Planning, collecting, organising, analysing and presenting data is a process known as data handling. • Understanding the key concepts and terms used in this process is important. ” Research Populations Reliable questions and samples data Downloaded from hlayiso.com Maths Lit NQF Level 2

Research questions Unit 15.1 Description The research question is clear, focused and specific. The primary purpose is to gather information that is precise, accurate and reliable. • Some questions that can help you to write a research question are: • What do I want to find out? ” • How will I find the information that I need? • What will I do with the information that I collect? • Who will find this information useful? • Is the question interesting and relevant? • Is the research question researchable? Consider the available time and • resources. • Is the research question measureable? • Is the research question too broad or too narrow? Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.1 page 282 Unit 15.1 Write a clear research question. • Check what the main idea or fact is that you want to find out. Will it be possible to collect the information you need? Will the answer to the question be useful to someone? • Can you collect measureable data, and can you present it in a table or graph? • Is there a link between how much time students take to get to college and the distance from their home? Downloaded from hlayiso.com Maths Lit NQF Level 2

Population and samples Unit 15.1 Population A population is the group of individuals or units that will be studied. Downloaded from hlayiso.com ” Maths Lit NQF Level 2

Population and samples continued ... Unit 15.1 Sample A sample is a section of the population that is selected. The sample selected must be a fair representation of the population ” from which it is drawn. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.2 page 284 Unit 15.1 Class Activity • A college has 1 500 students. The population is all 1 500 students. • To find information about the population, you could interview or observe only some of the 1 500 students. This group we choose is a sample. • The sample could be all Level 2 students, or only the Level 2 Marketing students, or the 15 rugby team members or a random selection of 30 students from the college. • Decide which of these samples is appropriate. Downloaded from hlayiso.com Maths Lit NQF Level 2

Reliable data Unit 15.1 • A researcher needs data from a sample that is identified reliably and free from bias. • A reliable sample can be used to reach conclusions about the whole population. Bias / subjectivity Prejudice towards the method or result of research. ” • Not all statistical information is accurate or true. Always check if the information is factual or if it is opinion. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.3 page 285 Unit 15.1 Susan drew this graph. Use the graph to answer the questions. a) Make a list of the problems with this graph. b) Between which two intervals do you find the biggest jump? c) Redraw the line graph using even steps on the y-axis. d) How does your new scale affect your answer in Question b)? Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.3 page 285 continued ... Unit 15.1 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.4 page 285 Unit 15.1 a) Comment on this statement: ‘Out of a random sample of 10 women, nine preferred Smoothie Hand Lotion.’ b) Comment on this statement: ‘Out of a random sample of 10 women, nine preferred Smoothie Hand Lotion to their regular brand.’ c) Comment on this statement: ‘Nine out of 10 women prefer Smoothie Hand Lotion.’ Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.4 page 285 continued ... Unit 15.1 a) The statement does not stipulate who the 10 women are; they could be employees of the Smoothie Hand Lotion company. b) The statement does not stipulate what the women prefer Smoothie Hand Lotion to. The comparison could be to something that is not in the same category, such as petroleum jelly. c) According to this statement, only 10 women were sampled. Only sampling 10 women is not representative of all the women in the country. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 15.1 Unit 15.1 Complete Exercise 15.1 on page 286 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Data collection tools Unit 15.2 • There are different ways to collect data. Observations Data Collection Tools Questionnaires Interviews Downloaded from hlayiso.com Maths Lit NQF Level 2

Observations Unit 15.2 • Observation does not require any contact with participants. The method simply entails observing, studying and recording information and data that is needed for the research. Advantage Disadvantage This method is best suited for research where no contact is required with participants. Observation can be influenced by any bias or shortcomings of the observer. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.5 page 288 Unit 15.2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Interviews Unit 15.2 • Interviews can be conducted by observation or by using a questionnaire. • Interviews are suitable where there is a small number of participants and responses are expected to be short. • Interviews are useful when participants agree to face-to-face questions. Disadvantage Observation can be influenced by any bias or shortcomings of the observer. Downloaded from hlayiso.com Maths Lit NQF Level 2

Questionnaires Unit 15.2 • A questionnaire consists of a series of questions designed to gather information and then completed by participants. • The information can be gathered from an oral interview or a written questionnaire. • A questionnaire is the most popular research instrument. Advantage Disadvantage They can be completed online and submitted immediately. Participants are sometimes not truthful. Downloaded from hlayiso.com Maths Lit NQF Level 2

Types of questions Unit 15.2 Closed questions Open-ended questions These are questions that Questions that can be a participant must answered by the choose from a list of participant in their own options. words. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.6 page 288 Unit 15.2 You would like to find information about the heights of the 300 Level 2 students at your college. Develop an instrument that you can use to collect the information. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.6 page 288 continued ... Unit 15.2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.7 page 289 Unit 15.2 a) Which instrument would be appropriate for collecting data for each of the following cases? Give a reason for your choice. i. The weight of all the 300 Level 2 students at a college ii. The colours of cars that are parked in the college parking area iii. The opinions of all the students in your group about a proposed building development in a local area. b) Develop an interview question that you could use to collect data for a) iii) above. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.7 page 289 continued ... Unit 15.2 i. Questionnaire. The number of Level 2 students is large. ii. Observation. There is no need to talk to anyone. You just count the cars for each colour. iii. Interview or questionnaire. There are probably fewer than 25 in the group of students, so the answers can be called out and written down immediately. The students could also be given a questionnaire to answer. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.7 page 289 continued ... Unit 15.2 b) Here is an example of a questionnaire: 1. Are you aware of the proposed development on Smith Street opposite the college?  Yes  No 2. If your answer is yes, what is your opinion on the proposed building development?  I do not have an opinion on the development.  I think it is a good development.  I am opposed to the development. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 15.2 Unit 15.2 Complete Exercise 15.2 on page 290 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Organising data Unit 15.3 • Once data has been collected, the next step is to classify it. • Identify if the data is: • numerical data that is discrete • numerical data that is continuous • categorical data • The next step is to organise the data. Downloaded from hlayiso.com Maths Lit NQF Level 2

Organising data continued ... Unit 15.3 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.8 page 291 Unit 15.3 a) A Mathematical Literacy test out of 10 was written by 30 students. The results of the test are as follows: 8 9 6 10 4 8 7 7 10 9 5 6 7 8 6 7 7 4 5 8 7 6 5 6 7 4 8 9 6 7 i. Classify the data as numerical or categorical. ii. Organise the data into: • a tally table for the marks • a frequency table for the marks Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.8 page 291 continued ... Unit 15.3 i. Numerical data ii. Discrete data iii. Tally table for marks: Tally table for marks: Mark Tally marks Total 4 ||| 3 5 ||| 3 6 |||| | 6 7 |||| ||| 8 8 |||| 5 9 ||| 3 10 || 2 Frequency table for marks: Mark 4 5 6 7 8 9 10 Frequency 3 3 6 8 5 3 2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.8 page 291 continued ... Unit 15.3 b) The weights (to the nearest kg) of 22 students in a class are: 59 61 57 59 62 71 78 81 83 67 58 81 56 60 69 85 69 61 54 48 61 i. Tally the data using the intervals 40 – 49; 50 – 59; 60 – 69; 70 – 79; and 80 – 89. ii. Draw up a frequency table for the data. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 15.8 page 291 continued ... Unit 15.3 a) i. Tally table: Tally table: Mark Tally marks 40 – 49 || 50 – 59 |||| | 60 – 69 |||| ||| 70 – 79 || 80 – 89 |||| ii. Frequency table: Frequency table: Weight (kg) 40 – 49 50 – 59 60 – 69 70 – 79 80 - 89 Frequency 2 6 8 2 4 Downloaded from hlayiso.com Maths Lit NQF Level 2

Module assessment Module 15 Complete Module assessment on page 294 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

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