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

1. Communicate information with
numbers, graphs and tables
Future Managers Mathematical Literacy 2 1

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. 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. 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. 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. Collect information to answer
questions
• Collection process
– Tick or tally lists
– Surveys
– Questionnaires
– Existing databases
Future Managers Mathematical Literacy 2 6

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. 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. 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. 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. 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. 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 Managers Mathematical Literacy 2 14

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. 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. Types of graphs
•Pie Chart
•Line Graph
•Bar Graph
Mathematical Literacy pg 138
Future 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 formula
Angle of Sector = (Frequency)/(Total Number) x 360
Future Managers Mathematical 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 Managers Mathematical 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)
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. 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. 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. 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. Analyse and interpret
information
Future Managers Mathematical Literacy 2 25

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. Techniques to analyse data
• Percentages
• Proportions
• Rates
• Mean
• Median
• Mode
Future Managers Mathematical 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 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. 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. 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. Interpreting information
Increasing Graph
y axis (Positive Gradient)
Constant Graph
(Zero Gradient)
Decreasing Graph
(Negative Gradient)
xaxis
Future Managers Mathematical Literacy 2 34

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