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# NCV 2 Mathematical Literacy Hands-On Training Module 4

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Accompanying slide show - NCV 2 Mathematical Literacy Hands-On Training published by Future Managers (www.futuremanagers.net)

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### NCV 2 Mathematical Literacy Hands-On Training Module 4

1. 1. Communicate information with numbers, graphs and tables Future Managers Mathematical Literacy 2 1
2. 2. Communicate information with numbers, graphs and tables • Collect information to answer questions • Organise information in a presentable format • Present information in various formats • Interpret information to answer questions Future Managers Mathematical Literacy 2 2
3. 3. Collect information to answer questions • At the end of this outcome, you will be able to: – Critically collect information to address a problem – Compile and use: tick and tally lists; surveys; questionnaires – Look critically at the importance and the effect of “phrasing” of a question – Differentiate between “sample of the population” and “the population” Future Managers Mathematical Literacy 2 3
4. 4. Collect information to answer questions • Asking the questions – Ensure there is a specific reason to the question – Ask the correct questions – Formulate the questions accurately – Use well defined terminology Future Managers Mathematical Literacy 2 4
5. 5. Collect information to answer questions • Terminology and Accuracy – Questions should be unambiguous – Questions should be phrased to clearly answer a specific question – Where possible, questions should ask for objective rather than subjective answers – Think carefully about what you want to find out Future Managers Mathematical Literacy 2 5
6. 6. Collect information to answer questions • Collection process – Tick or tally lists – Surveys – Questionnaires – Existing databases Future Managers Mathematical Literacy 2 6
7. 7. Tick or tally lists • Draw vertical lines for Colour of cars the first four ticks Red: |||| |||| |||| |||| |||| || =27 White: |||| |||| |||| |||| |||| |||| |||| |||| • Draw a horizontal line |||| |||| |||| ||| =58 crossing previous four Green: |||| ||| =8 Blue: |||| |||| |||| |||| ||| = 23 vertical lines for the Yellow: ||| =3 Silver: |||| |||| |||| | fifth. =16 Gold: |||| =4 • It is then easier to Black: |||| |||| |||| |||| |||| ||| =28 count the total Total =27+58+8+23+3+16+4+28=167 Future Managers Mathematical Literacy pg 132 Mathematical Literacy 2 7
8. 8. Questionnaires • Questionnaires are used as a tool to collect information for a specific research topic. • Useful guidelines: – Keep the survey short – Keep it straight-forward – Keep it simple Mathematical Literacy pg 132 Future Managers Mathematical Literacy 2 8
9. 9. Questionnaires • Four types of questions to ask: – Yes/no questions – Multiple choice questions – Rating scales from 1-5 – Asking for an opinion (open ended questions) Mathematical Literacy pg 132 Future Managers Mathematical Literacy 2 9
10. 10. Sample Questionnaire Services Rating Sales Consultants 1. How long did you have to wait? 5 min / 10 min /15 min/longer 2. Was the consultant friendly? Yes / No 3. Were all your questions answered? Yes / No 4. Was the product / procedure explained sufficiently? Yes / No 5. Was the time taken to handle your transaction reasonable? Yes / No 6. Will you use our services again? Any other comments: ……………………………………………………………………. Mathematical Literacy 2 Mathematical Literacy pg 132 Future Managers 10
11. 11. Surveys • Surveys are a longer form of questionnaire • A survey will be done on a large sample of people called a poll Mathematical Literacy pg 134 Future Managers Mathematical Literacy 2 11
12. 12. Sampling • A sample is a small group of people that have the same characteristics of a larger group of people • Sampling must be random and not biased Future Managers Mathematical Literacy 2 12
13. 13. Present Information Presenting information is about organising data into a useable and understandable format Future Managers Mathematical Literacy 2 13
14. 14. Organising data into tables • Tables are used in all forms of presenting data • Tabulating the data is an excellent method of organising it • Tables can represent the final presentation of data • Tables can be an intermediate step to a graph Future Managers Mathematical Literacy 2 14
15. 15. Presenting the data using graphs • Graphs are a “picture” of the data • Graphs are used to: – Summarise data to help draw conclusions – Present information in one go Future Managers Mathematical Literacy 2 15
16. 16. Essential features of a graph • Graphs should have the following: – Descriptive title – Title on x-axis – Title on y-axis – Key Future Managers Mathematical Literacy 2 16
17. 17. Types of graphs •Pie Chart •Line Graph •Bar Graph Mathematical Literacy pg 138 Future Managers Mathematical Literacy 2 17
18. 18. Pie Chart • Pie charts are used to represent slices or sectors of a circle • The angles of the slices are in proportion to the percentages of the data • Note: – The information in the pie chart must add up to a whole – The sizes of the pie are calculated according to the formula Angle of Sector = (Frequency)/(Total Number) x 360 Future Managers Mathematical Literacy 2 18
19. 19. Line Graphs • A straight line graph is used when characters on the horizontal axis are continuous • Examples: – Age against pulse rate – Distance of truck vs. cost – Share prices over time Future Managers Mathematical Literacy 2 19
20. 20. Cartesian plane • The Cartesian coordinate system consists of a grid system with a vertical axis called the y-axis and horizontal axis called the x-axis • x and y values are coordinated on the grid • Each axis represents a number line with a negative side • The intersection of the x and y axes is called the origin • The position on the plane is given by an ordered pair of numbers called x and y coordinates (x; y) Future Managers Mathematical Literacy 2 20
21. 21. Cartesian plane (-5; 5) (3; 3) 6 5 4 3 2 1 0 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 (6; -4) -2 -3 -4 -5 (1; 0) Future Managers (-3; -3) Mathematical Literacy 2 21
22. 22. Bar Graphs • Bar graphs are used when the data on the horizontal axis is grouped together for a specific reason • Examples: – Months of the year vs. rainfall figures – Different companies vs. expenditure – Shoe sizes vs. number of people Future Managers Mathematical Literacy 2 22
23. 23. Features of a Bar graph • The width of the bars must be exactly the same • Distance between the bars must be exactly the same • The vertical and horizontal axes must be labelled • The graph has to be informatively titled • A component bar chart should have no more than 5 or 6 sections Future Managers Mathematical Literacy 2 23
24. 24. Bar Graph Informative title Rainfall (mm) from Jan - June 45 40 35 Y-axis label Equally Rainfall (mm) 30 25 spaced 20 15 10 5 0 Jan Feb Mar Apr May Jun Month x–axis label Future Managers Mathematical Literacy 2 24
25. 25. Analyse and interpret information Future Managers Mathematical Literacy 2 25
26. 26. Analyse and interpret information • At the end of this outcome, you will be able to: – Read and interpret information represented through graphs – Analyse information presented though graphs tables and statistics Future Managers Mathematical Literacy 2 26
27. 27. Techniques to analyse data • Percentages • Proportions • Rates • Mean • Median • Mode Future Managers Mathematical Literacy 2 27
28. 28. Mean • This is the most frequently used measure of centre and is usually called the average • The mean is calculated by adding all values and dividing by the number of values • The mean is sensitive to extreme values Future Managers Mathematical Literacy 2 28
29. 29. Calculating the mean • Calculate the mean of the following: 10; 12; 20; 5; 7; 15; 21; 16 Answer: 10 + 12 + 20 + 5 + 7 + 15 + 21 + 16 = 106 Number of entries = 8 Mean = Sum of values / No of entries = 106 / 8 = 13.25 Future Managers Mathematical Literacy 2 29
30. 30. Median • The median is the value that falls in the middle of the set when the values are arranged in order of magnitude • If the number of values is odd, then the median is the middle number • If the number of values is even, then the median is the average of the two centre values Future Managers Mathematical Literacy 2 30
31. 31. Finding the median Find the median of the following: 10; 12; 20; 5; 7; 15; 21; 16 Answer: Arranged in 5; 7; 10; 12; 15; 16; 20; 21 order of magnitude (12 + 15) / 2 = 13.5 Middle two numbers Find the mean Future Managers Mathematical Literacy 2 31
32. 32. Mode • The mode represents the most frequently occurring quantity in a sample • Useful only in a large data set, where the number of occurrences is important Future Managers Mathematical Literacy 2 32
33. 33. Interpreting information • If as graph rises from left to right, we state that an increase occurs • If the graph descents from left to right, we can say that a decrease occurs • If the graph is horizontal, we can say that there is no change • The steepness of the line is called the rate of change or gradient. • Increasing graphs have positive gradients • Decreasing graphs have negative gradients Future Managers Mathematical Literacy 2 33
34. 34. Interpreting information Increasing Graph y axis (Positive Gradient) Constant Graph (Zero Gradient) Decreasing Graph (Negative Gradient) xaxis Future Managers Mathematical Literacy 2 34
35. 35. Misleading graphs • Make sure that the scale of the x and y axes are correct • Start the scale at zero, or otherwise clearly indicate what number you are starting from • The scale must be uniform Future Managers Mathematical Literacy 2 35