Communicate information with numbers, graphs and tables
Mathematical Literacy 2Future Managers 1
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
Mathematical Literacy 2Future Managers 2
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”
Mathematical Literacy 2Future Managers 3
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
Mathematical Literacy 2Future Managers 4
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
Mathematical Literacy 2Future Managers 5
Collect information to answer questions
• Collection process– Tick or tally lists– Surveys– Questionnaires– Existing databases
Mathematical Literacy 2Future Managers 6
Tick or tally lists
• Draw vertical lines for the first four ticks
• Draw a horizontal line crossing previous four vertical lines for the fifth.
• It is then easier to count the total
Mathematical Literacy 2Mathematical Literacy pg 132
Colour of carsRed: |||| |||| |||| |||| |||| || =27White: |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||=58Green: |||| ||| =8Blue: |||| |||| |||| |||| ||| = 23Yellow: |||=3Silver: |||| |||| |||| |=16Gold: |||| =4Black: |||| |||| |||| |||| |||| |||=28
Total =27+58+8+23+3+16+4+28=167
Future Managers 7
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 2
Mathematical Literacy pg 132
Future Managers 8
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 2
Mathematical Literacy pg 132
Future Managers 9
Sample Questionnaire
Mathematical Literacy 2
Services 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 pg 132
Future Managers 10
Surveys
• Surveys are a longer form of questionnaire
• A survey will be done on a large sample of people called a poll
Mathematical Literacy 2
Mathematical Literacy pg 134
Future Managers 11
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
Mathematical Literacy 2Future Managers 12
Present Information
Presenting information is about organising data into a useable and understandable format
Mathematical Literacy 2Future Managers 13
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
Mathematical Literacy 2Future Managers 14
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
Mathematical Literacy 2Future Managers 15
Essential features of a graph• Graphs should have the following:
– Descriptive title– Title on x-axis– Title on y-axis– Key
Mathematical Literacy 2Future Managers 16
Types of graphs
Mathematical Literacy 2
•Pie Chart•Line Graph•Bar Graph
Mathematical Literacy pg 138
Future Managers 17
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
Mathematical Literacy 2Future Managers 18
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
Mathematical Literacy 2Future Managers 19
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)Mathematical Literacy 2Future Managers 20
Cartesian plane
Mathematical Literacy 2
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
(-5; 5)(3; 3)
(-3; -3) (1; 0)
(6; -4)
Future Managers 21
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
Mathematical Literacy 2Future Managers 22
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
Mathematical Literacy 2Future Managers 23
Bar Graph
Mathematical Literacy 2
Rainfall (mm) from Jan - June
0
5
10
15
20
25
30
35
40
45
Jan Feb Mar Apr May Jun
Month
Rai
nfa
ll (m
m)
Informative title
x–axis label
Y-axis label Equally spaced
Future Managers 24
Analyse and interpret information
Mathematical Literacy 2Future Managers 25
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
Mathematical Literacy 2Future Managers 26
Techniques to analyse data
• Percentages
• Proportions
• Rates
• Mean
• Median
• Mode
Mathematical Literacy 2Future Managers 27
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
Mathematical Literacy 2Future Managers 28
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
Mathematical Literacy 2Future Managers 29
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
Mathematical Literacy 2Future Managers 30
Finding the median
Mathematical Literacy 2
Find the median of the following:
10; 12; 20; 5; 7; 15; 21; 16Answer:5; 7; 10; 12; 15; 16; 20; 21
Arranged in order of
magnitude
Middle two numbers
(12 + 15) / 2 = 13.5
Find the meanFuture Managers 31
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
Mathematical Literacy 2Future Managers 32
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
Mathematical Literacy 2Future Managers 33
Interpreting information
Mathematical Literacy 2
Increasing Graph(Positive Gradient)
Constant Graph(Zero Gradient)
Decreasing Graph(Negative Gradient)
x axis
y axis
Future Managers 34
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
Mathematical Literacy 2Future Managers 35
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