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Scale, Ratio, Graphs from Data
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Ra
Scales Ratios and Data
The National Certificate in Adult Numeracy
Scale, Ratio, Graphs
What is Scale?
Scale
• Scale is used to reduce the size of a real life object down to a manageable size
The previous slide showed a scaled down model of ‘Big Ben’ next to a photograph of the actual building
Exercise
• The model appears to be about 1m tall
• Checking on the internet, we are told that Big Ben is 96.5m tall (nearly 100m)
• How would we describe the scale of the model?
Maps
Scale 1cm to 4km
Ipswich
ColchesterColchester – Ipswich = 6 cm
Ratio (scale) 1 : 400000
Map exercise
• The map on the previous slide shows a scale of 1cm represents 4km
• If we want to show a scale without the units we must compare the same units with each other
1cm:4km = 1cm:4000m=1cm:400000cm
Now for Some Data
• The following slides relate to data given in tabulated form
• We shall investigate these data using scatter graphs and line graphs
Tallest Buildings
Tallest Buildings
Rank Building City Country Height Floors Built
1 Burj Khalifa Dubai UAE 828 m 2,717 ft 160 2010
2 Taipei 101 Taipei Taiwan 509 m 1,671 ft 101 2004
3 Shanghai World Financial Center
Shanghai China 492 m 1,614 ft 101 2008
4 International Commerce Centre
Hong Kong China (PRC) 483 m 1,584 ft 118 2009
5= Petronas Tower 1 Kuala Lumpur Malaysia 452 m 1,483 ft 88 1998
5= Petronas Tower 2 Kuala Lumpur Malaysia 452 m 1,483 ft 88 1998
7 Nanjing Greenland Financial Center
Nanjing China (PRC) 450 m 1,476 ft 89 2009
8 Willis Tower Chicago United States
442 m 1,451 ft 108 1973
9 Guangzhou West Tower Guangzhou China (PRC) 440 m 1,444 ft 103 2009
10 Trump International Hotel and Tower
Chicago United States
423 m 1,362 ft 96 2009
Exercise
• I want to manufacture a plastic model
of the Petronas Towers. • My model needs to be packed in a
box that is 600mm long
What would be a sensible scale for my model?
Working Out
• 600mm 0.5m (allowing for packaging in the box)
• Petronas Towers are 452m tall 450m
• So we have an approximate ratio of0.5 m : 450m
So scale = 1 : 900
Drawing a Scatter plot
• What scales would you use to plotBuilding height against number of
floors from the data given?
I would be interested in how the number of floors varies as the height increases
So I would plot Floors on the vertical axis and height on the horizontal.
Draw a Scatter-Plot of Building Height v’s Number
of Floors• Step1 - Draw suitable axes (note;
does the vertical axis have to start at zero?)
• Step2 - Label these axes• Step3 – Plot the information from the
table of data• Step4 – observe any relationships
Drawing a Scatter plot
Height
Floors
800700600500400
160
150
140
130
120
110
100
90
80
Scatterplot of Floors vs Height
Conclusions From Scatter Plot
• The scatter plot does not seem to indicate a direct relationship between the height of a building and the number of floors it contains
• The plot only shows obvious things such as; to have more than 100 floors, a building would need to be at least 420m tall.
Another Scatter plot
• Let’s see if we can show a scatter plot that does reveal a relationship
• Try to plot Height in feet against height in metres from the same table as before.
Height in Feet v’s height in metres
height/m height/ft
828 2717
509 1671
492 1614
483 1584
452 1483
452 1483
450 1476
442 1451
440 1444
423 1362
Height in Feet v’s height in metres
height/ m
heig
ht/
ft
800700600500400
2750
2500
2250
2000
1750
1500
Scatterplot of height/ ft vs height/ m
• Now go back to ‘blackboard’ to answer a summary of questions on this PowerPoint