Where will you view the Torch Relay? Getting to the Point in 2012 © Royal Statistical Society...

Where will you view the Torch Relay?

Getting to the Point in 2012

© Royal Statistical Society Centre for Statistical Education 2011

Plan Collect Process Discuss

Start screen

What is the Olympic Torch Relay?

Where is the Olympic Torch going?

How can you find out?

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.


Start screen

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?

Discuss

Process


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.

Discuss

Process


Plan

Collect

DHCycleThe Problem Solving Approach


Start screen

Where is the Olympic Torch visiting?

Is our school

near to th

e

Olympic Torch

Relay?

PlanDistance 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?

Collect Process DiscussPlan

Plan

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

Collect Process Discuss

Plan

In Cornwall

An example using a random sample of schools in Cornwall.

For this example the data is provided.

CollectCollect Process Discuss

Plan Collect

How to find the distances

Crow flight distanceRoad

distance

CollectProcess DiscussPlan

Data for a random sample of Cornwall schools

Discuss

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Collect

DHCycle The Problem Solving Approach

You arenow here.

ProcessPlan Collect Discuss

Mean?Standard

Deviation?

Median?Interquartile

Range?

Graph or statistic?


Statistic KeyCrow flight distance between two

locations (miles)Road distance between two

locations (miles)

Minimum Value Min 0.00 0.00Quartile 1 Q1 0.90 1.13Median Value (Quartile 2) Med 3.20 4.30Quartile 3 Q3 6.80 9.45Maximum Value Max 26.20 35.70

Total distanceRoad 246.6 milesCrow 191.5 miles

What are the distances like?(In Excel)


Variable N Mean Min Q1 Median Q3 MaxRoad 40 6.17 0.00 1.13 4.30 9.45 35.70Crow 40 4.788 0.000 0.900 3.200 7.000 26.200

Total distanceRoad 246.6 milesCrow 191.5 miles

What are the distances like?In Minitab

Road Distance (miles)Crow Flight Distance (miles)

40

30

20

10

0

Crow Flight Distances (miles) and Road Distance (miles) in Cornwall


St Pedroc’s SchoolBudeEX23 8NJ

Direct distance 26.2 milesRoad distance 35.7miles


How much further by road?





How can we look at the relationship between the crow flight and road distances for this sample of schools?


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.


Line of best fit


Use the graph to predict road distance using crow flight distance

Crow flight distance15 miles

Road distanceabout 19 miles


Road distance = 1.31 Crow flight distance – 0.09

Find the equation of the line of best fit using Excel.


Find the equation of the line of best fit from the scatter plot.

25.0 miles

32.5 miles


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


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?


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.

Discuss

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Collect


You arenow here.

DiscussPlan Collect Process

DiscussionAre there any issues with the graphs created fromthe 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?

Discuss

Process


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Collect


You arenowhere.

You can develop another solution by continuing here...

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Process


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CollectEnd ofslideshow

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Where will you view the Torch Relay? Getting to the Point in 2012 © Royal Statistical Society...

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