1. Where will you view the Torch Relay? Getting to the Point in 2012 © Royal Statistical Society Centre for Statistical Education 2011

2. PlanCollectProcessDiscuss Start screen What is the Olympic Torch Relay? Where is the Olympic Torch going? How can you find out?

3. When did the Olympic Games last take place in the UK? The first Olympic Games after the end of the Second World War were held in London in the summer of 1948. There was an Olympic Torch Relay that started in Athens and carried the flame across Europe to the UK. The Olympic Torch landed in Dover and was carried in relay to the Wembley Stadium in London. PlanCollectProcessDiscuss Start screen

4. Why is there an Olympic Torch Relay? When was the Olympic Torch Relay last in the UK? When was the most recent Olympic Torch Relay?

5. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Statistical Problem Solving Approach You can build on the first try by continuing here... Have you got all the evidence you want? First you decide what problem to solve and what data you need Then you collect suitable data.

6. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach

7. PlanCollectProcessDiscuss Start screen Where is the Olympic Torch visiting? Is our school near to the Olympic Torch Relay? Plan Distance by road or as the crow flies? Distance from your home? How do road and flight distances compare? Where will you view the Olympic Torch Relay?

8. CollectProcessDiscussPlan Is there a relationship between the road and crow flight distances between two locations?

9. CollectProcessDiscuss Plan In Cornwall An example using a random sample of schools in Cornwall. For this example the data is provided.

10. Collect ProcessDiscuss PlanCollect How to find the distances Crow flight distance Road distance

11. Collect ProcessDiscussPlan Data for a random sample of Cornwall schools

12. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach You are now here.

13. Process PlanCollectDiscuss Mean? Standard Deviation? Median? Interquartile Range? Graph or statistic?

14. Process PlanCollectDiscuss StatisticKey Crow flight distance between two locations (miles) Road distance between two locations (miles) Minimum ValueMin0.00 Quartile 1Q10.901.13 Median Value (Quartile 2)Med3.204.30 Quartile 3Q36.809.45 Maximum ValueMax26.2035.70 Total distance Road 246.6 miles Crow 191.5 miles What are the distances like? (In Excel)

15. Process PlanCollectDiscuss Variable N Mean Min Q1 Median Q3 Max Road 40 6.17 0.00 1.13 4.30 9.45 35.70 Crow 40 4.788 0.000 0.900 3.200 7.000 26.200 Total distance Road 246.6 miles Crow 191.5 miles What are the distances like? In Minitab

16. Process PlanCollectDiscuss St Pedroc’s School Bude EX23 8NJ Direct distance 26.2 miles Road distance 35.7miles

17. Process PlanCollectDiscuss How much further by road?

18. Process PlanCollectDiscuss How much further by road?

19. Process PlanCollectDiscuss How much further by road? How can we look at the relationship between the crow flight and road distances for this sample of schools?

20. Process PlanCollectDiscuss Is there a relationship between crow flight and road distance? The first school has crow distance = 9.8 and road distance = 13.1 miles. All the schools can be plotted on this graph.

21. Process PlanCollectDiscuss Line of best fit

22. Process PlanCollectDiscuss Use the graph to predict road distance using crow flight distance Crow flight distance 15 miles Road distance about 19 miles

23. Process PlanCollectDiscuss Road distance = 1.31 Crow flight distance – 0.09 Find the equation of the line of best fit using Excel.

24. Process PlanCollectDiscuss Find the equation of the line of best fit from the scatter plot. 25.0 miles 32.5 miles

25. Process PlanCollectDiscuss We can predict road distance from crow flight distance using the equation of the line of best fit. Road distance = 1.31 × Crow flight distance + - 0.09 (Y variable = gradient × X variable + intercept) Using the equation above find the road distance for a crow flight distance of 15 miles. Road distance = 1.31 x Crow flight distance – 0.09 = 1.31 x (15) - 0.09 = 19.65 – 0.09 = 19.6 miles

26. Process PlanCollectDiscuss Interpreting the line of best fit. Road distance = 1.31 × Crow flight distance + - 0.09 Gradient ~ for every mile travelled by crow flight we would expect to travel 1.3 miles by road. Intercept ~ if we travel zero miles by crow flight we would expect to travel -.09 miles by road. Does this make sense in real life?

27. Process PlanCollectDiscuss Based on the analysis in this lesson which one of the following statements is correct? a)It is 31 % longer to travel between two locations by road rather than by crow flight. b)In Cornwall it is 31 % longer to travel between two locations by road rather than by crow flight. c)On average in Cornwall for every mile travelled by crow flight we would expect to travel 1.3 miles by road. d)On average in Cornwall for every mile travelled by crow flight we would expect to travel 1.3 miles by road for distances less than 25 miles.

28. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach You are now here.

29. Discuss PlanCollectProcess Discussion Are there any issues with the graphs created from the distances? Were there any patterns linking crow flight distance and road distance in Cornwall? How do your class results relate to Cornwall data? Would you expect a graph of road distance against crow flight distance to look the same wherever pupils live? Would you expect a graph of road distance against crow flight distance to look the same for Scotland?

30. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach You are now here. You can develop another solution by continuing here...

31. Discuss Process PlanCollectProcessDiscuss Plan Collect End of slideshow