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Maths Driving test data: analysis and manipulation.
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Introduction The objective of this project is to successfully manipulate a large set of data in order to prove/ disprove a set of hypotheses. The data consists of results and statistics from a set of driving instruction and tests. The dependant variable in the data is the number of mistakes made during the test. The hypotheses will have been synthesized by myself and in response to influenced by the data that I have been given. The data will have to be subjected to sampling to reduce the vast amount of information. The data will then be processed so...

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This Database contains information about some...This Database contains information about some used cars, and many different makes of cars are included. I am going to include the following: "¢ Specifying clearly what I plan to do and why I am approaching this investigation in this way. "¢ Collating the data I need and representing it in a way which helps to develop my investigation. "¢ Interpreting my results and drawing a conclusion for them. Introduction In this project I am going to investigate Used Cars. I am going to look at the price of the cars and what kind of shape they are in. E.g. price when new, second hand prices, age, color etc. we will also see how, the younger the car the more expensive it will be because it will be a new car. And if the car is old the less expensive it will. I am going to collect the data I am going to use and try to further develop it to suit the investigation I am going to do. I am going to plot my results onto a scatter diagrams and interpret my results. Hypotheses 1 I am going to be testing Price and Mileage. There is a positive correlation between the old price of the car and the mileage. I.e. the more expensive a car is the less the mileage is. So I think that the higher the mileage the lower the price will be. Hypothesis 2 But it will all depend on the model of the car as well. E.g. if it is a brand new Lexus, the price is bound to be at around £35.000. Plan of Action I am going to use Second hand information. I am going to start with working with the price and mileage. The data is going to show a lot of use because the cheaper the price of the car the more mileage it will have on it meter gauge. And the more expensive the car the less it will have traveled. I am going to collect 40 samples of used cars, which will show a number of information that will be needed to know about the car. E.g. 92. Volkswagen at £8.710.00 that has traveled 50000 miles. In order for my graph too look professional and extremely accurate I have decided to use the computer program AUTOGRAPH. I hope to show that the more expensive the car is the less mileage it has. I plan to draw a cumulative frequency graph, histogram, box plot, whisker diagram along with a tally and pie chart. Data Collection have collected all of the 40 randomly selected samples out of 100. My tables have clear headings of type, model, old price, and mileage. Make Model Price when Price Age Color Engine Fuel MPG Mileage New Second Hand Size Ford Orion 16000 7999 1 black 1.8 unleaded 25-47 7000 Mercedes A140 Classic 14425 10999 1 red 1.4 unleaded 29-50 14000 Vauxhall Vectra 18580 7999 2 white 2.5 unleaded 26-44 20000 Vauxhall Astra 14325 6595 4 black 1.6 unleaded 32-52 30000 Nissan Micra 7995 3999 3 blue 1 unleaded 40-55 37000 Renault Megane 13610 4999 4 blue 1.6 unleaded 30-50 33000 Mitsubishi Carisma GDI 14875 5999 2 black 1.8 unleaded 34-56 24000 Rover 623 Gsi 22980 6999 4 green 2.3 unleaded 25-41 30000 Renault Megane 13175 6999 3 black 1.6 unleaded 30-50 41000 Vauxhall Tigra 13510 7499 4 marine 1.4 unleaded 33-57 27000 Fiat Bravo 10351 3495 5 red 1.4 unleaded 31-53 51000 Vauxhall Vectra 18140 6499 4 blue 2.5 unleaded 26-44 49000 BMW 525i SE 28210 5995 8 white 2.5 unleaded 21-38 55000 Vauxhall Corsa 8900 4995 2 silver 1.6 unleaded 26-46 24000 Fiat Punto 8601 3995 4 gold 1.2 unleaded 38-51 31000 Rover 820 SLi 21586 3795 6 red 2 unleaded 22-38 51000 Mitsubishi Carisma 15800 5999 2 blue 1.8 unleaded 34-56 33000 Fiat Cinquecento 6009 1995 6 white 0.9 unleaded 43-60 20000 Rover 416i 13586 3795 6 silver 1.6 unleaded 30-55 49000 Nissan Micra 6295 1795 8 white 1.2 unleaded 40-58 47000 Daewoo Lanos 11225 5999 3 silver 1.6 unleaded 24-46 42000 Rover 114 Sli 8595 2495 6 red 1.4 unleaded 35-56 33000 Ford Escort 8785 1595 7 blue 1.3 unleaded 39-54 68000 Fiat Uno 6864 1495 8 red 1 unleaded 44-55 51000 Rover Metro 6645 895 7 nightfire 1.1 unleaded 40-58 43000 Vauxhall Nova 5599 1000 10 green 1.4 unleaded 31-50 75000 Toyota Corrolla 13800 7495 2 black 2 diesel 34-53 25000 Vauxhall Cavalier 10150 850 10 red 1.6 unleaded 33-53 73000 Volkswagen Golf 400 15 green 1.4 unleaded 33-49 Volkswagen Golf 9524 3695 7 red 1.4 unleaded 33-49 49000 Seat Ibiza 5995 795 7 silver 0.9 unleaded 32-53 45000 Rover 214i 9565 1700 8 blue 1.4 unleaded 32-50 55000 Ford Fiesta 7310 1050 8 blue 1.1 unleaded 45-62 90000 Fiat Tempra 10423 1295 6 silver 1.6 unleaded 31-50 81000 Ford Fiesta 7875 1495 11 red 1.8 unleaded 32-50 74000 Hyundai Sonnata 11598 1195 9 silver 2 unleaded 28-41 65000 Renault Clio 6795 1995 8 black 1.2 unleaded 41-61 47000 Citroen Debut 5715 1495 7 black 0.95 unleaded 50-62 50000 The scatter diagram of the old price and mileage shows me that there is a positive correlation between the price and mileage depreciation of a cars price. The equation of the equations line of best fit or the "Trend Line" is Y=0.04687x+1.304E+004. This equation shows the gradient and where the line crosses the axis. In order for me to construct my graph accurately I am going to use Autograph from the computer. Scatter Graph Cumulative Frequency Graph Mileage The cumulative frequency graph shows me the median, the range of the mileage and the interquartile ranges. Table of Values of Data Set 1: Class Int. Mid. Int. x Class Width Freq. Cum. Freq. 0 § x < 20000 1E+004 2E+004 6 6 20000 § x < 40000 3E+004 2E+004 8 14 40000 § x < 60000 5E+004 2E+004 20 34 60000 § x < 80000 7E+004 2E+004 3 37 80000 § x < 100000 9E+004 2E+004 2 39 100000 § x < 120000 1.1E+005 2E+004 1 40 120000 § x < 140000 1.3E+005 2E+004 0 40 140000 § x < 160000 1.5E+005 2E+004 0 40 160000 § x < 180000 1.7E+005 2E+004 0 40 180000 § x < 200000 1.9E+005 2E+004 0 40 Öf = 40 Öfx = 1.8E+006 Öfx² = 1.008E+011 Mean = 4.5E+004 Standard Deviation = 2.225E+004 Variance = 4.95E+008 Histogram The histogram of the graph was not as I expected because I found out that the cheaper the car the more mileage it has and the more expensive the car the less mileage it has. Table of Values of Histogram [Data Set 1]: Class Int. Mid. Int. x Class Width Freq. Cum. Freq. 0 § x < 20000 1E+004 2E+004 6 6 20000 § x < 40000 3E+004 2E+004 8 14 40000 § x < 60000 5E+004 2E+004 20 34 60000 § x < 80000 7E+004 2E+004 3 37 80000 § x < 100000 9E+004 2E+004 2 39 100000 § x < 120000 1.1E+005 2E+004 1 40 120000 § x < 140000 1.3E+005 2E+004 0 40 140000 § x < 160000 1.5E+005 2E+004 0 40 160000 § x < 180000 1.7E+005 2E+004 0 40 180000 § x < 200000 1.9E+005 2E+004 0 40 Öf = 40 Öfx = 1.8E+006 Öfx² = 1.008E+011 Mean = 4.5E+004 Standard Deviation = 2.225E+004 Variance = 4.95E+008 Bow and Whisk By the information I found in the Cumulative Frequency graph it has enabled me to draw the Bow and Whisker diagram for the mileage alone. PRICE My cumulative frequency graph of used price gives me information on the median the price range and the lower and upper quartiles. Table of Values of Data Set 1: Class Int. Mid. Int. x Class Width Freq. Cum. Freq. 0 § x < 10000 5000 1E+004 15 15 10000 § x < 20000 1.5E+004 1E+004 20 35 20000 § x < 30000 2.5E+004 1E+004 2 37 30000 § x < 40000 3.5E+004 1E+004 2 39 40000 § x < 50000 4.5E+004 1E+004 0 39 50000 § x < 60000 5.5E+004 1E+004 0 39 60000 § x < 70000 6.5E+004 1E+004 0 39 70000 § x < 80000 7.5E+004 1E+004 0 39 80000 § x < 90000 8.5E+004 1E+004 0 39 90000 § x < 100000 9.5E+004 1E+004 1 40 Öf = 40 Öfx = 5.9E+005 Öfx² = 1.76E+010 Mean = 1.475E+004 Standard Deviation = 1.491E+004 Variance = 2.224E+008 Grouped Data Statistics: Total Frequency, n: 40 Mean, x: 14750 Standard Deviation, x: 14914.3 Modal Class: 10000- Lower Quartile: 6666.67 Median: 12500 Upper Quartile: 17500 Semi I.Q. Range: 5416.67 ______________________________________ Histogram Table of Values of Histogram [Data Set 1]: Class Int. Mid. Int. x Class Width Freq. Cum. Freq. 0 § x < 10000 5000 1E+004 15 15 10000 § x < 20000 1.5E+004 1E+004 20 35 20000 § x < 30000 2.5E+004 1E+004 2 37 30000 § x < 40000 3.5E+004 1E+004 2 39 40000 § x < 50000 4.5E+004 1E+004 0 39 50000 § x < 60000 5.5E+004 1E+004 0 39 60000 § x < 70000 6.5E+004 1E+004 0 39 70000 § x < 80000 7.5E+004 1E+004 0 39 80000 § x < 90000 8.5E+004 1E+004 0 39 90000 § x < 100000 9.5E+004 1E+004 1 40 Öf = 40 Öfx = 5.9E+005 Öfx² = 1.76E+010 Mean = 1.475E+004 Standard Deviation = 1.491E+004 Variance = 2.224E+008 This histogram is very much surprising because it shows that more people who buy second hand cars would rather buy it in between 10000 and 20000 and there were no buyer around 40000 and 90000. Box and Whisker Table of Values of Data Set 1: Class Int. Mid. Int. x Class Width Freq. Cum. Freq. 0 § x < 10000 5000 1E+004 15 15 10000 § x < 20000 1.5E+004 1E+004 20 35 20000 § x < 30000 2.5E+004 1E+004 2 37 30000 § x < 40000 3.5E+004 1E+004 2 39 40000 § x < 50000 4.5E+004 1E+004 0 39 50000 § x < 60000 5.5E+004 1E+004 0 39 60000 § x < 70000 6.5E+004 1E+004 0 39 70000 § x < 80000 7.5E+004 1E+004 0 39 80000 § x < 90000 8.5E+004 1E+004 0 39 90000 § x < 100000 9.5E+004 1E+004 1 40 Öf = 40 Öfx = 5.9E+005 Öfx² = 1.76E+010 Mean = 1.475E+004 Standard Deviation = 1.491E+004 Variance = 2.224E+008 From this box and whisker, I can tell that the used car price is not symmetrical and not in equal distributions. There are more cars on the upper side of the market. Final Conclusion Overall, my investigation of the factors that effect the price of a second hand car as reached the following conclusion: There is evidence of positive correlation between the used price and the mileage. E.g. the higher the mileage the cheaper the car will be. There is also evidence of negative correlation on the histogram diagram. It has come to chow that only cheap cars are bought and not the high and expensive ones. My hypothesis in the introductions states that there should be a cars that have a higher price and a low mileage. And in my investigation it was proven true and not false. In conclusion I was able to prove my hypothesis to be correct in my investigation.   

This Database contains information about some used cars, and many different makes of cars are included. I am going to include the following: • Specifying clearly what I plan to do and why I am approaching this investigation in this way. • Collating the data I need and representing it...

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Minimum Surface Area Investigation Introduction...Minimum Surface Area Investigation Introduction For my maths coursework I have been asked by a tin manufacturing company to minimise the amount of metal required to produce cans. The cans must be cylindrical and come in four different sizes: 1. 300 cm3 2. 400 cm3 3. 600 cm3 4. 750 cm3 I have been asked to come up with a reverse formula to enable them to find the height and radius for any given formula of a cylindrical tin that will ensure that the surface area is a minimum. Method I am going to devise a method using a spreadsheet package called excel. I have decided to use a spreadsheet because it is accurate, easy to use and any adjustments can be easily made. I can see immediate results and I can produce graphs of all kinds. The spreadsheet will use formulae which will calculate the surface areas, heights and radii by just entering key information. These formulae can be easily adjusted or corrected. I will use this spreadsheet to calculate the four given formula's: 1. 300 cm3 2. 400 cm3 3. 600 cm3 4. 750 cm3 I will get a greater degree of accuracy in my results by adjusting the radius from initially an integer then to decimal of 1 decimal place, then 2 decimal places, then 3 decimal places. This will bring all the results to a greater accuracy. The spreadsheet will use formulas to make it more efficient. The formulae in the spread sheet will be The Formulae I Used"¦ Area of side of cylinder = c x h Volume = 2πr3h The total surface area of the cylinder = 2πr r+h Height = _V_ πr2 Table Of Results For Cylinder "“ Volume 300cm3 Radiuscm Heightcm Volumecm3 Surface Areacm3 1 95.4930 300.00 606.283185307 2 23.8732 300.00 325.132741229 3 10.6103 300.00 256.548667765 4 5.9683 300.00 250.530964915 5 3.8197 300.00 277.079632679 6 2.6526 300.00 326.194671058 7 1.9488 300.00 393.590365766 8 1.4921 300.00 477.123859659 9 1.1789 300.00 575.604676548 10 0.9549 300.00 688.318530718 3.0 10.6103 300.00 256.548667765 3.1 9.9368 300.00 253.929797899 3.2 9.3255 300.00 251.839817546 3.3 8.7689 300.00 250.242069813 3.4 8.2606 300.00 249.104210386 3.5 7.7953 300.00 248.397591442 3.6 7.3683 300.00 248.096748248 3.7 6.9754 300.00 248.178969017 3.8 6.6131 300.00 248.623932678 3.9 6.2783 300.00 249.413402368 4.0 5.9683 300.00 250.530964915 3.60 7.3683 300.00 248.096748248 3.61 7.3275 300.00 248.088085391 3.62 7.2871 300.00 248.083229893 3.63 7.2470 300.00 248.082160673 3.64 7.2072 300.00 248.084856881 3.65 7.1678 300.00 248.091297899 3.66 7.1287 300.00 248.101463330 3.67 7.0899 300.00 248.115333003 3.68 7.0514 300.00 248.132886965 3.69 7.0132 300.00 248.154105477 3.70 6.9754 300.00 248.178969017 3.620 7.2871 300.00 248.083229893 3.621 7.2831 300.00 248.082952934 3.622 7.2790 300.00 248.082713817 3.623 7.2750 300.00 248.082512521 3.624 7.2710 300.00 248.082349024 3.625 7.2670 300.00 248.082223306 3.626 7.2630 300.00 248.082135347 3.627 7.2590 300.00 248.082085124 3.628 7.2550 300.00 248.082072618 3.629 7.2510 300.00 248.082097808 3.630 7.2470 300.00 248.082160673 Values For Minimum Surface Area, radius & Height. Table Of Results For Cylinder "“ Volume 400cm3 Radiuscm Heightcm Volumecm3 Surface Areacm3 1 127.3240 400.00 806.283185307 2 31.8310 400.00 425.132741229 3 14.1471 400.00 323.215334431 4 7.9577 400.00 300.530964915 5 5.0930 400.00 317.079632679 6 3.5368 400.00 359.528004392 7 2.5984 400.00 422.161794338 8 1.9894 400.00 502.123859659 9 1.5719 400.00 597.826898770 10 1.2732 400.00 708.318530718 3.5 10.3938 400.00 305.540448584 3.6 9.8244 400.00 303.652303803 3.7 9.3005 400.00 302.233023072 3.8 8.8174 400.00 301.255511625 3.9 8.3711 400.00 300.695453650 4.0 7.9577 400.00 300.530964915 4.1 7.5743 400.00 300.742296233 4.2 7.2179 400.00 301.311579295 4.3 6.8861 400.00 302.222607958 4.4 6.5767 400.00 303.460649365 4.5 6.2876 400.00 305.012280248 3.92 8.2859 400.00 300.631571357 3.93 8.2438 400.00 300.605509718 3.94 8.2020 400.00 300.583340714 3.95 8.1605 400.00 300.565044325 3.96 8.1193 400.00 300.550600733 3.97 8.0785 400.00 300.539990321 3.98 8.0379 400.00 300.533193665 3.99 7.9977 400.00 300.530191542 4.00 7.9577 400.00 300.530964915 4.01 7.9181 400.00 300.535494941 4.02 7.8788 400.00 300.543762963 3.990 7.9977 400.00 300.530191542 3.991 7.9937 400.00 300.530099294 3.992 7.9897 400.00 300.530044782 3.993 7.9857 400.00 300.530027988 3.994 7.9817 400.00 300.530048891 3.995 7.9777 400.00 300.530107473 3.996 7.9737 400.00 300.530203716 3.997 7.9697 400.00 300.530337601 3.998 7.9657 400.00 300.530509108 3.999 7.9617 400.00 300.530718219 Values For Minimum Surface Area, radius and height. Table Of Results For Cylinder "“ Volume 600cm3 Radiuscm Heightcm Volumecm3 Surface Areacm3 1 190.9859 600.00 1206.283185307 2 47.7465 600.00 625.132741229 3 21.2207 600.00 456.548667765 4 11.9366 600.00 400.530964915 5 7.6394 600.00 397.079632679 6 5.3052 600.00 426.194671058 7 3.8977 600.00 479.304651480 8 2.9842 600.00 552.123859659 9 2.3579 600.00 642.271343215 10 1.9099 600.00 748.318530718 4.0 11.9366 600.00 400.530964915 4.1 11.3614 600.00 398.303271843 4.2 10.8269 600.00 396.549674533 4.3 10.3291 600.00 395.245863772 4.4 9.8650 600.00 394.369740274 4.5 9.4314 600.00 393.901169137 4.6 9.0258 600.00 393.821766317 4.7 8.6458 600.00 394.114712372 4.8 8.2893 600.00 394.764589477 4.9 7.9544 600.00 395.757238409 5.0 7.6394 600.00 397.079632679 4.50 9.4314 600.00 393.901169137 4.51 9.3896 600.00 393.876005493 4.52 9.3481 600.00 393.854714764 4.53 9.3069 600.00 393.837279622 4.54 9.2659 600.00 393.823682894 4.55 9.2253 600.00 393.813907558 4.56 9.1848 600.00 393.807936740 4.57 9.1447 600.00 393.805753715 4.58 9.1048 600.00 393.807341902 4.59 9.0652 600.00 393.812684867 4.60 9.0258 600.00 393.821766317 4.563 9.1728 600.00 393.806884872 4.564 9.1687 600.00 393.806609927 4.565 9.1647 600.00 393.806372793 4.566 9.1607 600.00 393.806173454 4.567 9.1567 600.00 393.806011893 4.568 9.1527 600.00 393.805888094 4.569 9.1487 600.00 393.805802040 4.570 9.1447 600.00 393.805753715 4.571 9.1407 600.00 393.805743101 4.572 9.1367 600.00 393.805770183 4.573 9.1327 600.00 393.805834944 Values For Minimum Surface Area, Radius & Height. Table Of Results For Cylinder "“ Volume 750cm3 Radiuscm Heightcm Volumecm3 Surface Areacm3 1 238.7324 750.00 1506.283185307 2 59.6831 750.00 775.132741229 3 26.5258 750.00 556.548667765 4 14.9208 750.00 475.530964915 5 9.5493 750.00 457.079632679 6 6.6315 750.00 476.194671058 7 4.8721 750.00 522.161794338 8 3.7302 750.00 589.623859659 9 2.9473 750.00 675.604676548 10 2.3873 750.00 778.318530718 4.0 14.9208 750.00 475.530964915 4.1 14.2018 750.00 471.474003550 4.2 13.5336 750.00 467.978245962 4.3 12.9114 750.00 465.013305632 4.4 12.3312 750.00 462.551558456 4.5 11.7893 750.00 460.567835804 4.6 11.2823 750.00 459.039157622 4.7 10.8073 750.00 457.944499606 4.8 10.3616 750.00 457.264589477 4.9 9.9430 750.00 456.981728205 5.0 9.5493 750.00 457.079632679 4.85 10.1491 750.00 457.074576904 4.86 10.1074 750.00 457.048298990 4.87 10.0659 750.00 457.025891164 4.88 10.0247 750.00 457.007337360 4.89 9.9837 750.00 456.992621641 4.90 9.9430 750.00 456.981728205 4.91 9.9026 750.00 456.974641374 4.92 9.8624 750.00 456.971345600 4.93 9.8224 750.00 456.971825461 4.94 9.7827 750.00 456.976065659 4.95 9.7432 750.00 456.984051019 4.920 9.8624 750.00 456.971345600 4.921 9.8584 750.00 456.971223936 4.922 9.8544 750.00 456.971140013 4.923 9.8504 750.00 456.971093815 4.924 9.8464 750.00 456.971085328 4.925 9.8424 750.00 456.971114535 4.926 9.8384 750.00 456.971181422 4.927 9.8344 750.00 456.971285974 4.928 9.8304 750.00 456.971428174 4.929 9.8264 750.00 456.971608008 4.930 9.8224 750.00 456.971825461 Values For Minimum Surface Area, Radius & Height. Explanation Of Why The Height Of A Cylinder Is Twice The Radius When The Surface Area Is At A Minimum. The most efficient three dimensional shape to contain a volume is a sphere, so the cylinder tries to imitate a sphere in order to achieve the minimum surface area. So as further investigation for the tin manufacturing company, I will now look at alternate minimum shapes & therefore reduce expenditure. I'll now calculate the minimum surface area of a sphere & a cube with a volume of 900cm3 in addition to the cylinder I have already correctly predicted. This further investigation will tell me whether a cylinder is the best 3D shape to use. Sphere V = 4_ πr3 S.A = 4 πr2 3 900 = 4_ πr3 S.A = 4π x 5.989418137 2 3 2700 = 4 πr3 S.A. = 450.7950419 2700 = r3 4π r = 3√2700 4π r = 5.989418137 Cube Volume = l3 900 = l3 l = 3√900 l = 9.654893846 S.A. = 6l3 = 6 x 9.6548938462 S.A. = 559.3018511 Analysis Of Investigation into which Spreadsheet To Use After Investigating the minimum surface Area for a volume of 900cm3 my results were: "¢ Cylinder "“ 516.0315049 cm3 "¢ Sphere - 450.7950419 cm3 "¢ Cube - 559.3018511 cm3 So from these results I can see that as I previously stated the sphere is the best 3-D shape to store any volume water because it has the smallest surface area. However the manufacturing company has chosen the cylinder because although a sphere has a smaller surface area it would be very difficult to stack on supermarket shelves and store safely, whereas a cylinder can be kept upright.   

Minimum Surface Area Investigation Introduction For my maths coursework I have been asked by a tin manufacturing company to minimise the amount of metal required to produce cans. The cans must be cylindrical and come in four different sizes: 1. 300 cm3 2. 400 cm3 ...

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