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

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Collect information to answer questions

• Collection process– Tick or tally lists– Surveys– Questionnaires– Existing databases

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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

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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

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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

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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

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Essential features of a graph• Graphs should have the following:

– Descriptive title– Title on x-axis– Title on y-axis– Key

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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

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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

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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)

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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

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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

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Bar Graph

Mathematical Literacy 2

Rainfall (mm) from Jan - June

0

5

10

15

20

25

30

35

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45

Jan Feb Mar Apr May Jun

Month

Rai

nfa

ll (m

m)

Informative title

x–axis label

Y-axis label Equally spaced

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Analyse and interpret information

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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

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Techniques to analyse data

• Percentages

• Proportions

• Rates

• Mean

• Median

• Mode

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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

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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

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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

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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

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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

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Interpreting information

Mathematical Literacy 2

Increasing Graph(Positive Gradient)

Constant Graph(Zero Gradient)

Decreasing Graph(Negative Gradient)

x axis

y axis

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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

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