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# 4 ratio scale (dmc)

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Scale, Ratio, Graphs from Data

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### 4 ratio scale (dmc)

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