# NCV 2 Mathematical Literacy Hands-On Training Module 4

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18-May-2015Category

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

- 1. Communicate information withnumbers, graphs and tables Future Managers Mathematical Literacy 2 1

2. Communicate information withnumbers, 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 ManagersMathematical Literacy 2 2 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 phrasingof a question Differentiate between sample of the population and thepopulation Future ManagersMathematical Literacy 2 3 4. Collect information to answer questions Asking the questionsEnsure there is a specific reason to the questionAsk the correct questionsFormulate the questions accuratelyUse well defined terminology Future Managers Mathematical Literacy 2 4 5. Collect information to answer questions Terminology and Accuracy Questions should be unambiguous Questions should be phrased to clearly answer aspecific question Where possible, questions should ask for objectiverather than subjective answers Think carefully about what you want to find out Future Managers Mathematical Literacy 2 5 6. Collect information to answer questions Collection processTick or tally listsSurveysQuestionnairesExisting databases Future Managers Mathematical Literacy 2 6 7. Tick or tally lists Draw vertical lines for Colour of cars the first four ticks Red: |||| |||| |||| |||| |||| || =27White: |||| |||| |||| |||| |||| |||| |||| |||| Draw a horizontal line |||| |||| |||| |||=58 crossing previous four Green: |||| ||| =8Blue: |||| |||| |||| |||| ||| = 23 vertical lines for the Yellow: ||| =3Silver: |||| |||| |||| | fifth. =16Gold: ||||=4 It is then easier to Black: |||| |||| |||| |||| |||| |||=28 count the totalTotal =27+58+8+23+3+16+4+28=167 Future Managers Mathematical Literacy pg 132 Mathematical Literacy 27 8. Questionnaires Questionnaires are used as a tool to collectinformation for a specific research topic. Useful guidelines: Keep the survey short Keep it straight-forward Keep it simple Mathematical Literacy pg 132Future ManagersMathematical Literacy 2 8 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 132Future ManagersMathematical Literacy 2 9 10. Sample QuestionnaireServices RatingSales 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 2Mathematical Literacy pg 132 Future Managers10 11. Surveys Surveys are a longer form of questionnaire A survey will be done on a large sample ofpeople called a poll Mathematical Literacy pg 134Future Managers Mathematical Literacy 2 11 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. Present Information Presenting information is about organising data into a useable and understandable format Future Managers Mathematical Literacy 2 13 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 ManagersMathematical Literacy 2 14 15. Presenting the data usinggraphs Graphs are a picture of the data Graphs are used to: Summarise data to help draw conclusions Present information in one go Future ManagersMathematical Literacy 2 15 16. Essential features of a graph Graphs should have the following:Descriptive titleTitle on x-axisTitle on y-axisKey Future Managers Mathematical Literacy 2 16 17. Types of graphsPie ChartLine GraphBar Graph Mathematical Literacy pg 138Future Managers Mathematical Literacy 2 17 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 formulaAngle of Sector = (Frequency)/(Total Number) x 360Future ManagersMathematical Literacy 2 18 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 ManagersMathematical Literacy 2 19 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. Cartesian plane (-5; 5)(3; 3) 6543210 -6-5 -4 -3 -2 -10 1 23 45 67-1 (6; -4)-2 -3 -4 -5(1; 0) Future Managers (-3; -3)Mathematical Literacy 221 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 ManagersMathematical Literacy 2 22 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 6sections Future Managers Mathematical Literacy 2 23 24. Bar GraphInformativetitleRainfall (mm) from Jan - June 45 40 35Y-axis labelEqually Rainfall (mm) 30 25 spaced 20 15 1050Jan Feb Mar Apr May Jun Month xaxis label Future ManagersMathematical Literacy 2 24 25. Analyse and interpret information Future ManagersMathematical Literacy 2 25 26. Analyse and interpret information At the end of this outcome, you will be able to: Read and interpret information represented throughgraphs Analyse information presented though graphs tablesand statistics Future ManagersMathematical Literacy 2 26 27. Techniques to analyse data Percentages Proportions Rates Mean Median Mode Future ManagersMathematical Literacy 2 27 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. 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. 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. Finding the medianFind the median of the following: 10; 12; 20; 5; 7; 15; 21; 16 Answer:Arranged in 5; 7; 10; 12; 15; 16; 20; 21order ofmagnitude(12 + 15) / 2 = 13.5Middle two numbersFind the mean Future ManagersMathematical Literacy 2 31 32. Mode The mode represents the most frequentlyoccurring quantity in a sample Useful only in a large data set, where thenumber of occurrences is important Future Managers Mathematical Literacy 2 32 33. Interpreting information If as graph rises from left to right, we state that anincrease occurs If the graph descents from left to right, we can saythat a decrease occurs If the graph is horizontal, we can say that there isno change The steepness of the line is called the rate ofchange or gradient. Increasing graphs have positive gradients Decreasing graphs have negative gradients Future Managers Mathematical Literacy 2 33 34. Interpreting information Increasing Graph y axis (Positive Gradient)Constant Graph(Zero Gradient) Decreasing Graph (Negative Gradient)xaxis Future ManagersMathematical Literacy 2 34 35. Misleading graphs Make sure that the scale of the x and y axesare correct Start the scale at zero, or otherwise clearlyindicate what number you are starting from The scale must be uniform Future ManagersMathematical Literacy 2 35