How to use tables and graphs l Presenting data graphically l Drawing a pie graph
Drawing a pie graph
The Student Guild at Hadrian College conducted a survey on how students travel to
and from college each day. They have asked Pasha to present the data as part of their
report to the University Council.
Follow Pasha as he turns the data in the frequency table below into a pie graph.
How students travel to and from college
Frequency
Type of transport
Walk
70
Bicycle
7
Car
301
Bus
154
Train
168
Total
700
Step 1
The pieces of a pie graph must equal 100% so Pasha begins by working out the
percentage for each category.
He does this by dividing the frequency for each type of transport by the total then
multiplying the answer by 100. For example:
Walk = 70 ÷ 700 x 100 = 10%
He then added in a ‘Percentage frequency’ column to the table. He knows his
percentage frequency is correct as the total for the column equals 100%.
Type of transport
Frequency
Walk
70
10%
Bicycle
7
1%
Car
301
43%
Bus
154
22%
Train
168
24%
700
100%
Total
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Percentage
frequency
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How to use tables and graphs l Presenting data graphically l Drawing a pie graph
Step 2
As a pie graph is a circle, Pasha must work out how many degrees in a circle represent
1% so he can accurately draw the pieces of the pie graph.
Remembering that a complete circle is equal to 360°, Pasha knows that in terms of
percentages, a complete circle is equal to 100%.
360° = 100%
With this knowledge, Pasha works out the value of 1% of the pie by dividing 360°
by 100%.
1% = 360° ÷ 100 = 3.6°
So, 1% of the pie is equal to 3.6° of a circle.
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How to use tables and graphs l Presenting data graphically l Drawing a pie graph
Step 3
Now Pasha converts each percentage into an angle so that he can accurately complete
his pie graph. To do this he multiplies each percentage by 3.6°. For example:
Walk = 10 x 3.6 = 36°
So the angle for the ‘Walk’ piece is 36°.
Pasha adds this information to his table and continues converting the remaining results.
He knows he is correct as his total equals 360°.
Type of transport
Frequency
Percentage
frequency
Angle
Walk
70
10%
36.0°
Bicycle
7
1%
3.6°
Car
301
43%
154.8°
Bus
154
22%
79.2°
Train
168
24%
86.4°
700
100%
Total
360°
Step 4
Using his compass and pencil, Pasha draws a circle on his paper.
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How to use tables and graphs l Presenting data graphically l Drawing a pie graph
Step 4
To divide the pie graph into accurate pieces, Pasha uses his ruler and pencil to faintly
draw the circle’s diameter (a horizontal line through the centre of the circle splitting it
into two equal halves).
He then uses his protractor to work out the first angle of 36°.
Pasha lined up the centre point of the protractor with the middle of the diameter and,
looking at the outer edge of the protractor, found the ‘36°’ on the right side. He marked
the angle with a dot on the paper.
90 100
70 80
110
60
120
90 80
130
50
100
70
110
60
120
40
140
50
130
40
140
30
150
20
© WestOne Services 2010
30
20
150
160
160
10
170
10
170
0
180
0
180
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How to use tables and graphs l Presenting data graphically l Drawing a pie graph
Putting his protractor away, Pasha drew in the angle by drawing a line with his ruler
from the centre of the circle to the 36° mark on the paper. The other side of the angle
is the right half of the diameter.
50 60 7
0 8
0
13 12
0 0 11
01
00
90
90
80
10
70
0
11
0
12
0
13
50
0
14
40
0
30
15
0
20
16
10
0
1
70
0
18
0
60
Where his new line crosses the circle is the ‘Walk’ piece which he labelled and
shaded in.
50 60 7
0
13 12
0 0 11
0 10
80
0
90
90
80
Walk 10%
10
70
0
11
0
12
0
13
50
0
1
40
40
30
15
0
20
16
10
0
17
0
0
18
0
60
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How to use tables and graphs l Presenting data graphically l Drawing a pie graph
Step 6
With one piece completed, Pasha continued to work out the angles for the other pieces
labelling and shading them as he went along.
Each time he began a new piece, he moved his protractor to the newest line of the
previous angle so that he was always accurate.
60
50
0
10 120 13 140 0
1
0
15 60
10
0
1
9
0 0 0
0
70 6 5 4 30
17
80
80
0
2
0
90
10
18
0
70
10
40
30
20
0
0
11
20
1
0
13
0
14
0
15
0
16
0
17
10
0
Walk 10%
0
18
Step 7
After Pasha completed his pie graph he retitled it, ‘Student transportation’ and
continued to help the Guild with their report.
Student transportation
Bicycle 1%
Car 43%
Walk 10%
Bus 22%
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Train 24%
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