Core Skills
Numeracy
Outcome 3
Tables, Graphs and Charts
[INTERMEDIATE 1]

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© Learning and Teaching Scotland 2004
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CONTENTS
Section 1 Constructing tables
1.1 Categories
1.2 Setting up the table
1
2
Section 2 Constructing graphs
3
Section 3 Constructing charts
3.1 Bar charts
3.2 Pie charts
7
11
Section 4 Constructing flow diagrams
16
Outcome 3 SAQ answers
25
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CONSTRUCTING TABLES
SECTION 1
1.1 Categories
A table is a handy way of linking two sets of data. Each set of data is
subdivided into categories.
As we will see, the table actually shows the overl ap between categories.
Before we can construct a table we need to be sure in our minds what our
sets of data are and how each is subdivided.
Example 1.1a
A number of people take part in a survey about their health.
One possible set here is ‘people’, subdivided by age, e.g. 20–29, 30–39,
etc.
Another set might be number of visits to the doctor in the past year,
subdivided into 0, 1, 2, 3, 4, more than 4.
Example 1.1b
Data about cars may show the make of car and the type of engine.
Can you suggest subdivisions for this data?
Make of car may be divided, for example, into Ford, Vauxhall, Toyota, etc.
Type of engine might be petrol or diesel.
Questions 1.1
Suggest possible subdivisions for the following sets of data:
1.
2.
Political parties and voters.
Holiday resorts and time of year for holiday.
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CONSTRUCTING TABLES
1.2 Setting up the table
Once we have decided what our sets of data are and how they are
subdivided we simply put one set along the top row and the other set
down the first column.
If one of the sets of data is subdivided into units of time (e.g. months of
the year) then it is usual to put that set along the top row.
Example 1.2
A primary head teacher submits data to the education authority about the
pupils at each stage in her school. She does so by means of a table.
Here is her categorisation:
Pupils
– Boys and Girls
Stage
– P1, P2, P3, P4, P5, P6 and P7.
This allows her to construct a table, after calculating the necessary totals:
Boys
Girls
P1
28
25
P2
26
26
P3
28
31
P4
23
21
P5
22
19
P6
24
29
P7
26
31
Questions 1.2
Construct a table to show the following information from a political survey:
68
51
23
60
2
people
people
people
people
vote
vote
vote
vote
Labour, of whom 38 are 50 or under
Conservative, of whom 20 are 50 or under
Green, of whom 11 are 50 or under
SNP, of whom 22 are over 50.
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CONSTRUCTING GRAPHS
SECTION 2
As we saw in Outcome 2, Section 2, line graphs display information about
one commodity. A line graph shows changes in that commodity over time.
A graph needs two axes:
2.
Each axis needs a label:
Cost
1.
Number
Points should be plotted carefully:
•
Cost
3.
• •
•
Number
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CONSTRUCTING GRAPHS
4.
Points should be linked by a line:
Cost
•
• •
•
Number
5.
A title should be added:
Cost of Hire
Cost
•
• •
•
Number
Example 2.1
Draw a line graph to show these temperatures:
Day
Temperature
4
Mon
19º
Tue
20º
Wed
20º
Thu
17º
Fri
21º
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Sat
23º
Sun
20º
CONSTRUCTING GRAPHS
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CONSTRUCTING GRAPHS
Questions 2.1
1.
This table shows costs for hiring a car. Draw a line graph of these
costs.
No. of days
Cost (£)
2.
1
50
2
50
4
80
5
95
6
110
7
125
8
130
9
135
Draw a line graph to show the measured temperature of a cup of t ea
as it cools.
Minutes after pouring
Temperature
6
3
65
0
88
2
64
4
52
6
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CONSTRUCTING CHARTS
SECTION 3
3.1 Bar charts
A bar chart is a quick and easy way of displaying a list of data, e.g. the
number of supporters of football teams counted in a survey. Here is a
table which shows the data gathered in the survey:
Football team
Rangers
Celtic
Partick Thistle
Kilmarnock
No preference
Number of people
20
25
5
2
8
On a bar chart, the number of each item is always shown up the side.
When setting up a bar chart, we must choose our scale for up the side
carefully. In this example our numbers range from 2 to 25. We will choose
to go up in twos. (Going up in ones would produce quite a high bar chart.)
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CONSTRUCTING CHARTS
Draw the vertical axis first then add the horizontal axis, allowing enough
width for each of the categories (five in this case):
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CONSTRUCTING CHARTS
Add the bars and, finally, add a title:
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CONSTRUCTING CHARTS
Questions 3.1
Construct bar charts for each of the following sets of survey data:
1.
Houses for sale through local paper:
House type
Detached
Semi-detached
Bungalow
Flat
2.
Holiday destinations last summer. (Take care to choose an
appropriate scale for the vertical axis in this question.)
Destination
Scotland
England
Wales
Europe
North America
Elsewhere
10
Number of houses
16
15
7
22
Number of people
30
20
5
60
50
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CONSTRUCTING CHARTS
3.2 Pie charts
A bar chart is used to show ‘how many of each thing…’.
A pie chart is used to show ‘what share of the total…’.
Before constructing a pie chart we must calculate the total amount of all
the data.
Here is our football team supporter data again:
Football team
Rangers
Celtic
Partick Thistle
Kilmarnock
No preference
Total
Number of people
20
25
5
2
8
60
To construct a pie chart for this data we must share out the 60 football
fans around a whole, circular ‘pie’.
There are 360° in a complete circle.
60 people are to be shown in 360º of ‘space’. First of all, divide
360º ÷ 60 = 6º per person.
Then multiply each figure in turn, e.g. for Rangers 20 x 6º = 120º
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CONSTRUCTING CHARTS
Football team
Rangers
Celtic
Partick Thistle
Kilmarnock
No preference
Totals
Number of people
20
25
5
2
8
60
Degrees
x6º = 120º
x6º = 150º
x6º = 30º
x6º = 12º
x6º = 48°
360º
Check that the total of degrees calculated is 360º.
Now we can construct our pie chart, using compasses and a protract or.
Firstly draw a circle using compasses.
It is best to use a radius of at least 5 cm.
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CONSTRUCTING CHARTS
Next draw a radius line.
Using a protractor, place the first sector onto the pie chart (in this case
Rangers 120º).
Rangers
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CONSTRUCTING CHARTS
Notice that we do not write the size of the angle or the number of people
in the diagram, only the name of the category (in this case the football
team ‘Rangers’).
From the edge of the first sector, measure round 150º for the second
sector (Celtic) and continue round until all are shown.
Survey of football supporters
Rangers
Celtic
No
preference
Partick
Thistle
Total = 60 people
Give the pie chart a title and state the total number of people beside it.
If you construct your pie chart accurately you will find that the last sector
(‘no preference’) doesn’t need to be measured. After ‘Kilmarnock’ a sector
will be left which is exactly 48º in size.
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CONSTRUCTING CHARTS
Questions 3.2
1.
Construct a pie chart for this data (which we met in Questions 3.1)
about houses for sale in the local newspaper.
House type
Detached
Semi-detached
Bungalow
Flat
2.
Construct a pie chart for this data (again from Questions 3.1) about
holiday destinations last summer.
Destination
Scotland
England
Wales
Europe
North America
Elsewhere
3.
Number of houses
16
15
7
22
Number of people
30
20
5
60
50
15
Construct a pie chart to represent this data about the running costs
of a factory.
Item
Wages
New building
Maintenance
Other
Cost
£8,000,000
£7,000,000
£3,000,000
£2,000,000
Take care calculating angles here. The total is £20,000,000, but it is
difficult to calculate 60º ÷ 20,000,000. Better just to ‘think in millions’
and divide 360º ÷ 20 = 18º. That gives 18º per £million.
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CONSTRUCTING FLOW DIAGRAMS
SECTION 4
Flow diagrams can also be called logic diagrams. They are a systematic
way of showing a logical process.
Flow diagrams show all the steps in any process, in the correct order.
To draw a flow diagram we need to list all the steps in a process. This
may involve knowing when decisions must be taken.
Example 4.1 (very simple)
To find the average of a set of numbers we:
1.
2.
add up the numbers
divide the total by how many numbers there are.
Here, there are only two steps and no decisions to be made. The flow
diagram looks like this:
START
Add up all the numbers
Divide by how many numbers
STOP
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CONSTRUCTING FLOW DIAGRAMS
Notice that the two steps are written inside rectangles. These are known
as statement boxes.
Also notice that the flow diagram begins with a START box and ends with
a STOP box.
Example 4.2
Entrance to a tourist attraction is free for children under 5 years of age.
Here is a simple flow diagram for deciding how much to charge for a child:
START
Yes
Is child
under
5?
No
Charge for a
child ticket
Admit for free
STOP
Notice that a decision has to be made here. The decision step is
contained inside a diamond.
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CONSTRUCTING FLOW DIAGRAMS
– shape of a start or stop box
– shape of a statement box
– shape of a decision box
Example 4.3
Here is a set of instructions for calculating the cost of taking a group of
people on a canal boat trip:
If there are more than six people, charge £5 each. Otherwise charge £7
each.
Shows this information in a flow diagram.
Solution
START
Yes
Is number
of people
more
than 6?
Charge £5 each
Charge £7 each
STOP
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No
CONSTRUCTING FLOW DIAGRAMS
Example 4.4
Here are the instructions for trimming a hedge. Make a flow diagram from
them.
Trim the hedge, then gather up the trimmings. Put them in the wheelie bin.
If there are trimmings left over, take them to the tip.
Solution
START
Trim hedge
Gather up trimmings
Fill wheelie bin
Yes
Any
trimmings
left over?
No
Take them to
the tip
STOP
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CONSTRUCTING FLOW DIAGRAMS
Questions 4
Construct flow diagrams for each of the following sets of instructions:
1.
Accepting a cheque at the checkout.
If the value of the cheque is less than £100, accept the cheque.
Otherwise call for the supervisor.
2.
Deciding if a number divides by five.
Does the number end in a 5 or a 0? If so then it divides by 5. If not
then it does not.
3.
Deciding if a number divides by three.
Add up the digits in the number. Divide this total by 3. If there is a
remainder then the number does not divide by 3. If there is no
remainder then it does divide by 3.
4.
Calculating a salesman’s wage.
If his total sales are less than £10,000 then pay him a basic wage of
£700. If his sales are more than £10,000 then give him a bonus of
3% of the value of his sales (remember to include the basic wage).
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SAQ ANSWERS
SAQ ANSWERS
Section 1
Answers 1.1
1.
Political parties can be categorised as Labour, Conservative, SNP,
Greens, Independents, etc.
Voters can be categorised in many ways. The most straightforward
way is male and female. Alternatively they may be categorised by
age, e.g. 18–30, 31–45, 46–60, 61+. The categories begin with 18
because this is the youngest age at which a person may vote in the
UK. For example:
2.
Age
Party
Conservative
18–30
31–45
46–60
61+
28
144
150
173
Labour
66
88
51
54
SNP
91
105
84
29
Green
42
30
28
25
Holiday resorts may be categorised by name of hotel or type of
accommodation. Time of year for holiday may be categorised by
month or week. For example:
Hotel Rosamar
May
£728
June
£840
July
£912
August
£988
Hotel da Vinci
£403
£500
£564
£525
Springhill Hotel
£184
£216
£240
£240
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SAQ ANSWERS
Answers 1.2
Labour
Conservative
Green
SNP
22
Age 18–50
38
20
11
38
Age 50+
30
31
12
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SAQ ANSWERS
Section 2
Answers 2.1
1.
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SAQ ANSWERS
2.
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SAQ ANSWERS
Section 3
Answers 3.1
1.
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SAQ ANSWERS
2.
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SAQ ANSWERS
Answers 3.2
1.
House type
Detached
Semi-detached
Bungalow
Flat
Totals
Number of houses
16
15
7
2
60
Degrees
96°
90°
42°
132°
360°
360° ÷ 60 = 6° per house
Houses for sale
Detached
Semidetached
Bungalow
Flat
Total = 60
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SAQ ANSWERS
2.
Destination
Scotland
England
Wales
Europe
North America
Elsewhere
Totals
Number of people
30
20
5
60
50
15
180
Angle
60°
40°
10°
120°
100°
30°
360°
360° ÷ 180 = 2° per person
Holiday destinations
England
Scotland
Europe
Elsewhere
North
America
Total = 180 people
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SAQ ANSWERS
3.
Item
Wages
New building
Maintenance
Other
Totals
Cost
£8,000,000
£7,000,000
£3,000,000
£2,000,000
£20,000,000
Angle
144°
126°
54°
36°
360°
360° ÷ 20 = 18° per £million
Running costs of a factory
Wages
New
Building
Other
Maintenance
Total = £20,000,000
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SAQ ANSWERS
Section 4
Answers 4
1.
START
Yes
Is the value
of the
cheque
less than
£100?
Accept cheque
No
Call for supervisor
STOP
2.
START
Yes
Does the
number
end in a 5
or a 0?
The number does
not divide by 5
The number
divides by 5
STOP
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No
SAQ ANSWERS
3.
START
Add up the
digits
Divide the total by 3
Yes
Is there a
remainder?
Number does
not divide by 3
No
Number does
divide by 3
STOP
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SAQ ANSWERS
4.
START
Yes
Are sales
less than
£10,000?
No
Calculate 3% of
sales
Pay = £700
Pay = £700 + 3%
of sales
STOP
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