1. PROJECT ON STATISTICS Viju Thomas Sridhar Srikanth A Viju Thomas Sridhar Srikanth A

2. STATISTICS PROJECT REPORT STATISTICS PROJECT REPORT Goal The goal of doing this project is to empower ourselves and to get familiarized with the various statistical techniques used in data analysis. Thereby helping us to do various computations on a given set of data and to reach on various meaningful conclusions. So as to show an understanding in the basic concepts of statistics. In this project we have made an attempt to understand how different cars in the global market produced by various different auto makers vary from each other with respect to their engine capacity, horse power, mileage, transmission etc.

3. Data collection www.automotoportal.com www.carfolio.com www.autocarindia.com The manufacturers we considered were BMW VOLVO GENERAL MOTORS- CHEVEROLET MERCEDES NISSAN HONDA SUZUKI TOYOTA HYUNDAI FORD LEXUS

4. ATTRIBUTES CHOSEN Quantitative Attributes Chosen. Quantitative Attributes Chosen.  Engine Capacity (cc)  Brake Horse power (BHP)  Mileage (kilo meter/liter of fuel)  Top Speed (Kilometer/hour) Qualitative Attributes Chosen. Qualitative Attributes Chosen.  Gear Transmission (Automatic/ Manual/Both)  Segment (Sedan/SUV/MUV)  Fuel Type (Petrol/Diesel/Both )

5. ORGANIZED DATA Company/ Car Name Engine Capacity Horse Power Mileag e Top Speed Transmissio n Segme nt Fuel Type BMW 1. BMW 3 Series 300023010.2236BothSEDANPetrol 2. BMW 5 Series 480036013.1250BothSEDANPetrol 3. BMW 7 Series 600043813.8250AutomaticSEDANpetrol 4. BMW X5 4.8i 480035513.1246AutomaticSUVPetrol Volvo 1. Volvo V50 T5 25002189.2240AutomaticMUVPetrol 2. Volvo XC70 250020811.2230BothSUVBoth 3. Volvo S40 T5 25002189.8240ManualSEDANpetrol 4. Volvo XC90 440031113.8210AutomaticSUVBoth Chevrolet 1. Aveo 14009410170ManualSEDANPetrol 2. Aveo U-VA 12007612140ManualSEDANPetrol 3. Tavera 25008014.3160ManualMUVBoth 4. Optra 16001049165ManualSEDANBoth Mercedes Mercedes Benz E 350026812.4236AutomaticSEDANDiesel Mercedes Benz SL Mercedes Benz SL500030214.7240AutomaticSEDANPetrol Mercedes Benz E 500030214.7240Automatic WAGO N Petrol Mercedes Benz SLK 550035515246AutomaticSEDANPetrol

6. Nissan Nissan Xterra SE 400026114.7230AutomaticSUVPetrol Nissan Sentra 2.0 20001408.4140ManualSUVBoth Nissan Quest 3.5 350023513.1220AutomaticSEDANBoth Nissan Pathfinder 400026614.7230AutomaticMUVBoth Honda Honda Civic Si 200019710.2160ManualSEDANPetrol Honda CR-V 240016610.2180AutomaticSUVPetrol Honda Element LX 240016611.2180ManualSUVDiesel Honda Pilot EX 350024413.8200AutomaticMUVPetrol Suzuki Suzuki SX4 200014310.2160manualSUVPetrol Suzuki XL7 360025213.8220automaticSUVPetrol Suzuki Aerio 23001559.4150manualSEDANPetrol Suzuki Grand Vitara 270018512.4200automaticSEDANPetrol

7. Toyota Toyota Highlander 330021512.4200AutomaticSUVPetrol Toyota Camry 24001589.8160ManualSEDANDiesel Toyota Corolla 18001267.4140ManualSEDANPetrol Toyota Land Cruiser 470027518.1300AutomaticSUVPetrol Hyundai Hyundai Accent 13991107.4177ManualSEDANBoth Hyundai Elantra 15991388.4182ManualSEDANBoth Hyundai Sonata 235923411.8203ManualSEDANBoth Hyundai Sante Fe 199124212.4166ManualSEDANBoth Ford Ford Fiesta 129716010.2160ManualSEDANBoth Ford Mustang 460130013.8230AutomaticSEDANBoth Ford Fusion 226116010.2180ManualSUVBoth Lexus Lexus IS 350 345630611.2229AutomaticSEDANPetrol Lexus LS 430 429328812.4211AutomaticSUVPetrol Lexus ES 330 331421811.2230AutomaticSEDANPetrol Lexus SC 430 429328812.4250AutomaticSEDANPetrol

8. DATA ANALYSIS *Classes in 100's MidpointFrequency Cumulative freq <120060000 1200-1800150044 1800-24002100711 2400-300027001122 3000-36003300224 3600-42003900630 4200-48004500535 4800-54005100641 5400-60005700142 6000-66006300143 43 The above given table represents the frequency distribution of Engine Capacity measured in cubic capacity. Here the classes are chosen with class width of 600 units. With the first class starting from 0 to 1200 and going up to 6600 units The frequency distributions of the cars are done in respect to the above taken classes. Frequency Distribution of engine capacity

9. Measures of Central tendencies Mean3383.721 Median2972.727 Mode2584.615 Standard Deviation 859.2587 Mean = Σfx/Σf, where f is the frequency and x is the midpoint of the class intervals. where: L = lower limit of the interval containing the median I = width of the interval containing the median N = total number of respondents F = cumulative frequency corresponding to the lower limit f = number of cases in the interval containing the median Mode = Lmo +(d1/(d1+d2))*w Where: LmoLower limit of the modal class d1frequency of the modal class minus the frequency of the class directly below it d2frequency of the modal class minus the frequency of the class directly above it wwidth of the modal class interval

10. Histogram From the histogram we can infer that the maximum number of cars in the data collected belong to the 4 th class i.e. with an engine capacity ranging between 2400 cc to 3000cc

11. The frequency polygon constructed helps us to sketch the distribution of the engine capacities of the cars much more clearly.

12. The ogive shown is constructed using the cumulative frequency. Here we are showing a less than ogive curve.If we take a point on the curve and connect it to the x- axis and then to the corresponding point on the y- axis. It helps us to infer the total number of cars that would lie below the corresponding class of engine capacity given in the x-axis.

13. Representation Of Frequency Distribution Of Qualitative Data Qualitative data if it has to be represented graphically, doing it on a pie- chart is the best way to do it. As this kind of representation clearly gives the reader an idea about what percentage of the data under study belongs to which category. Here in our data set we have taken totally three attributes which are qualitative. Out of which we have chosen the Fuel Type to be represented graphically. Fuel Type Frequency Petrol26 Diesel3 Both14

15. Probability Distribution of Transmission with respect to the Horse power Class of Horse power AutomaticManualBothtotal 0 - 50 0000 50 - 100 0303 100 - 150 0606 150 - 200 2608 200 - 250 53210 250 - 300 7007 300 - 350 5005 350 - 400 2013 400 - 450 1001 450 - 500 0000 total2218343

16. Find the probability that the selected car has an automatic gear system? Total number of cars with automatic gear system is =22 Total number of cars =43 Therefore, probability that a selected car has a gear system in it is =0.5116 So there is a 51.16 % chance that the selected car has an automatic gear system in it. Find the probality that a selected car with a manual gear system has a horse power of 175 bhp. Total number of cars with manual gear system = 18 Cars falling in the class with horse power of 175 bhp = 6 Hence probability that a selected car with a manual gear has a horse power Of 175= 0.3333 33.33% chances are there that a selected car would have a manual gear system with 175 bhp.

17. Binomial Distribution Binomial Distribution  Success defined as picking a car which has mileage above 13 km/l. From the data set we can find the values of the following.  Success event: p = 0.348  Failure event: q = 0.651 Probability of picking up 6 cars with mileage more than 13 kmpl in 10 trails from the data set.  No of trials: n = 10  Random variable x = 6  Probability of (X = x) = nCx * p x * q (n-x )  Therefore, P(X=6) = 0.068 We can say that 6.8% of the time the selected random experiment is true.

18. Normal Distribution Normal Distribution Probability that a randomly selected car from the data set will have a top speed less than 220  Mean of Top speed =204.34  Standard Deviation =38.70  x=220  μ =204.34  σ =38.70  P (x <= 220) = 0.6570 65.70 % of the times a randomly selected car from the data will have a top speed less than 220. 65.70 % of the times a randomly selected car from the data will have a top speed less than 220.

19. APPLICATION OF CORRELATION

20.   From the graph it is observable that there is a high degree of positive correlation between the two attributes.   The correlation coefficient was found out to be 0.91526. Which means that as the engine capacity increases the horse power also increases. This conclusion led us to apply the concept of regression in the current aspect.   As a result of which we were able to get the regression equation- Y=13.927X + 16.285   Here Y represents engine capacity and X represents the horse power.   Using this equation we can predict what the engine capacity will be for a given value of horse power.   Eg:- What will the engine capacity be for a car with an horse power of 600 BHP   Y=13.927X+16.285   Here X=600   Therefore Y= 13.927*600+ 16.285   Hence the engine capacity=Y=8372.485 cc   In turn the coefficient of determination was found to be R 2 =0.8377

21. THANK YOU THANK YOU