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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