Statistics Controlled Assessment

Statistics Controlled AssessmentRoad Transport

Talbot Turner

Talbot Turner Controlled Assessment

Table of Contents

Planning and Hypothesis.........................................................3Question 1...............................................................................................3Question 2...............................................................................................4Question 3...............................................................................................5

Analysis and Conclusion..........................................................6Question 1...............................................................................................6Question 2...............................................................................................7Question 3...............................................................................................8

Results and Calculations.........................................................9Question 1 Results..................................................................................9Question 1 Calculations...........................................................................9Question 2 Results................................................................................10Question 2 Calculations.........................................................................10Question 3 Results.........................................................................11 - 12Question 3 Calculations.........................................................................12

Appendix .............................................................................13Charts Q1.1 and Q1.2............................................................................14Charts Q1.3 and Q1.4............................................................................15Charts Q2.1 and Q2.2............................................................................16Charts Q2.3 and Q2.4............................................................................17Charts Q2.5 and Q3.1............................................................................18Charts Q3.2 and Q3.3............................................................................19Charts Q3.4 and Q3.5............................................................................20Charts Q3.6 and Q3.7............................................................................21Charts Q3.8...........................................................................................22Formula.................................................................................................23

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Question 1

Question: What is the relationship of the number of cars that pass a road and the amount of lanes in different areas such as Al Khabisi, Al Tawia and Al Jamia.

I will be investigating this as it will be both interesting and would have great statistical information showing the proportionality of number of lanes on a road to the amount of cars that pass that road in 20 minutes. I chose this time frame as it is not too long so I can get enough values but long enough for the results to be accurate. I will be collecting the information from several different areas in Al Ain, UAE. I will simply count the numbers of cars that drive past in 20 minutes for several different locations.

I predict that there will be more cars on roads with more lanes in more popular roads. I made this hypothesis as I know that more people will use the more popular roads and more lanes are added to accommodate the larger number.

My source is reliable because I will be collecting the data (primary data collection) therefore it would be primary sources which means that I know exactly if any errors are made or if the data is fabricated or not. I will sample one side of the road each time because it would be too difficult to count the cars on both sides at one time.

I plan to use 4 different charts: A scatter diagram to show the relationship between the values

(amount of lanes and the amount of cars) A bar chart to illustrate the results in a neat presentable manner A pie chart to show what streets have the highest ratios of cars

And a Cumulative frequency diagram to show the progression

I will use 3 different Calculations: A mean to show the average car number A median to show the middle value and to show how far it is from

the mean And standard deviation to show how spread out the data is

Question 2

Question: To investigate the changes in the number of car sales with different C02g/km when prices change by one percent.

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I will be doing this topic because it is interesting and it evolves other aspects and concepts outside statistics. I can expand well on this and produce an interesting hypothesis on this.

My hypothesis is that the more CO2g/km given off the larger the change, as more fuel would be used and they would have a bad reputation for increasing pollution.

I will search for results in an appropriate secondary data source. This is secondary data collection, as I will use results that were collected by others. Although I will be collecting the data from a reliable source, I know this as I will use official documents taken from legitimate statistical agencies the data will not be totally reliable and make contain incorrect values or fabricated values.

I will sample from 100g/km to 200g/km this will be easier to handle and shows the majority of the cars that emit CO2.

I plan to use 5 different charts: A scatter diagram to show the relationship between the values A bar chart to illustrate the results for each group in a neat

presentable manner A pie chart to show what groups have the highest change in car

sales And a Cumulative frequency diagram to show the progression A line graph to show the progression of the sales changes over

the groups

I will use 5 different Calculations: A mean to show the average change in car sales. A median to show the middle value of car sales and to show how

far it is from the mean And standard deviation to show how spread out the data is

in order to see if this factor changes the sales of cars by a lot.

The range to show the range of the data Inter-quartile range to show a more accurate range of the

dataQuestion 3

Question: What is the relationship between car torque and horsepower?

This is a fairly easy topic to research as there are many different websites that have the information I need and I can obtain a large range of data. I will go online and utilize the readily available data from car websites.

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My hypothesis is that the horsepower and the torque of a car are directly proportional, as cars with higher torque tend to have a large amount of horsepower.

There are far too many cars to collect so this would take too long so I will sample a couple of new Sedans from several well-known brands like BMW. I chose sedans because they are very similar and are the most used and purchase car type.

I will include the following charts: Bar charts to show the data in a better way A Scatter graph to show the proportionality of torque and

horsepower Pie charts to show what car manufacturer produced the cars

with the highest torque and horsepower

I will include the following calculations Median to find the middle value Mean to find the average Mode to locate the most common value Standard deviation to determine the spread of data

In Conclusion

The road “Rashid Bin Saeed Al Maktoum Street” was recorded in Abu-Dhabi with the “Abu-Dhabi – Dubai Road” in Abu Dhabi because there are no four lane roads in Al Ain and in order for the results to be more conclusive a wider range of results would be needed. This is why the last result was so high.

With an Inter-quartile range of 179, a Standard deviation of 137 and a mean of 192, the results are widely spread so they are very

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conclusive because the gradient on the scatter diagram would be larger.

In final conclusion the results show that there is clear evidence that the more lanes there are the more cars with drive on those roads as illustrated in chart 1.2 which shoes a strong correlation between the number of cars and the number of lanes, however this is because more lanes are made to accommodate the number of cars not the other way around.

In Conclusion

The range and inter-quartile range show that the data is fairly spread out, but the standard deviation indicates that it’s more compact. The mean and median are quite close so I conclude that the data is well balanced from the median.

The bar chart and the pie chart show that there are 2 groups that have the largest change in car sales. These include the 141 to 150 and the 151 to 160; the median is located inside these groups of data.

Charts 2.3 and 2.4 show that there is a weak positive correlation between the 2005 Sales and the CO2g/km emitted. However it peaks in the middle to groups where the median is located. This

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indicates that these cars are more popular for other reasons and other variables may cause this peak.

Chart 2.5 shows that there is a larger rise from 4 to 6, this therefore confirms my previous statement about there being a peak in the modal values.

In final conclusion the change in sales of cars in 2005 when prices change by 1% is weakly proportional as the is a very weak positive correlation to the amount of CO2 emitted.

Analysis + Conclusion

The results table is far too long to analyze, so by using the mode, median and the mean I am able to work out the average or the middle values and the standard deviation would help me see how far the other values deviate from these middle values.

The first 5 charts (charts 3.1 – 3.5) so the results in a much easier and presentable manner, this would make interpreting the results much easier. These charts show that for each car make the torque and horsepower for each car model is relatively similar to each other. This shows that the cars have similar engines and are built in similar ways.

Chart 3.6 confirms my hypothesis by showing a very strong correlation where a line of best fit was easy to construct. This shows clearly that the amount of horsepower and torque in a car is directly proportional to each other with very few exceptions.

The last 2 charts (Charts 3.7 and 3.8) show car manufacturer can produce the highest torque and horsepower. The data for these

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charts are taken from the highest value from each category. This shows what company produced the sedan with the highest torque and horsepower.

In conclusion the information backs my hypothesis that the horsepower and torque of a car is directly proportional.

Street Lanes Cars Robot Roundabout

11th Street Al Khabisi 1 29 Y N

6th Street 1 39 Y N

2nd Street Al Tawia 1 43 N Y

14th street, Al Harmoozi com, Al Sarooj dist. 1 62 N Y

11th Street 2 94 Y N

6th street Al Tawia 1 97 N Y

Khaled Ibn Al Waleed Street 2 109 N Y

3rd Street 2 145 N Y

Othman Ibn Affan 3 166 Y N

2nd Street 2 173 N Y

Khalid Bin Saltan Street 3 198 Y N

129th Street 2 201 Y N

Al Jamia Street 3 257 N Y

Sultan Bin Zayed Al Awwal Street 3 273 N Y

Khalifa Street (town) 3 303 Y Y

Dubai - Abu Dhabi road 4 328 Y N

Al Baladiya 3 351 N Y

Rashid Bin Saeed Al Maktoum Street 4 582 Y N

Total 3450

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Mean 191.6666667

Standard Deviation 136.8173966

Median 169.5


CO2g/km 2005 Sales Cumulative Frequency

100 to 110 5,719 5,719

111 to 120 25,857 31,576

121 to 130 32,011 63,587

131 to 140 87,324 150,911

141 to 150 161,520 312,431

151 to 160 164,892 477,323

161 to 170 87,145 564,468

171 to 180 124,628 689,096

181 to 190 75,216 764,312

191 to 200 61,911 826,223

Results:

Calculations:

Mean 82,622

Median 81,181

Low Quartile 32,011

Higher Quartile 124,628

Inter Quartile Range 92,617

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Range 159,173

Standard deviation 51,944

Make Year ModelHorse Power Torque

BMW 2010 M5 500 383BMW 2010 7 series 544 553BMW 2010 M3 414 295BMW 2010 5 series 360 360BMW 2010 3 series 300 425

BMW 2011

3 series Active Hybrid 455 515

BMW 2011 7 series 535 550BMW 2011 M3 414 295

BMW 2011 5 series 400 450

BMW 2011 3 series 300 425Volvo 2010 S80 311 325Volvo 2010 S40 227 236

Volvo 2011 S60 300 325

Volvo 2011 S80 300 325

Volvo 2011 S40 227 236Volvo 2011 S60 300 325Audi 2010 S6 435 398Audi 2010 A8 350 325Audi 2010 S4 333 325Audi 2010 A6 350 325Audi 2010 A4 211 258

Audi 2011 A8 372 328

Audi 2011 S6 435 298

Audi 2011 S4 333 325

Audi 2011 A6 350 325

Audi 2011 A4 211 258

Mercedes-Benz 2010 S-class 604 738

Mercedes-Benz 2010 E-class 518 465

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Mercedes-Benz 2010 C-class 451 443

Mercedes-Benz 2011 S-class 624 738

Mercedes-Benz 2011 E-class 518 465

Mercedes-Benz 2011 C-class 451 443

Lexus 2010 LS 600 hL 389 385

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Lexus 2010 LS 600 hL 389 385

Lexus 2010 Ls 460 380 367

Lexus 2010 IS F 416 371

Lexus 2010 GS 450h 292 267

Lexus 2010 GS 342 339

Lexus 2010 ES 350 272 254

Lexus 2010 HS 250h 187 200

Lexus 2010 IS 306 277

Lexus 2011 LS 600 hL 389 385

Lexus 2011 Ls 461 380 367

Lexus 2011 IS F 416 371

Lexus 2011 GS 450h 292 267

Lexus 2011 GS 342 339

Lexus 2011 ES 351 272 254

Lexus 2011 HS 250h 187 200

Lexus 2011 IS 306 277

Calculations

Horse Power


Mean 367

Median 350

Mode 300

Torque


Mean 363

Median 327

Mode 325

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Chart 1.1

Chart 1.2

Chart 1.3

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Chart 1.4

Chart 2.1

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Chart 2.2

Chart 2.3

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Chart 2.4

Chart 2.5

Chart 3.1

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Chart 3.2

Chart 3.3

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Model

Chart 3.5

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Chart 3.6

Chart 3.7

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Chart 3.8

Formula

Mean: Sum of Value / Number of Values

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Mode: Group with the most values

Median: middle value

Interquartile range: Upper Quartile / Lower Quartile

Standard Deviation: meannumber of values

Range: First Value / Last value

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Date post:	28-Mar-2015
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Statistics Controlled Assessment

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