Maths coursework 2001 Oliver Goddard Essays

Maths coursework 2001 Oliver Goddard Essays Maths coursework 2001 Oliver Goddard Essay Maths coursework 2001 Oliver Goddard Essay My hypothesis is to see if there is a difference between two ages estimating angle and length is different. I also think that people are better at estimating lengths than angles.Also to see if males are better than females at estimating the length and angle.And if playing sport helps at estimating lengths and angles.I think that the older people are better at estimating angles and the length because they have more experience at doing so from further education and more experience.I also think that the male sex will be better at estimating this better than the female sex because they play more sport and have to judge lengths and angles more of the time e.g. football, basketball, rugby.I have done a pre test to make sure that my main experiment will work by cheeking the method and data collection sheetFor all three of my experiments the length of the line and the degrees of the angle will be the same the length will be 4.5 centimetres and the degrees of the angle will be 36 degreesPlanI will collect data from year 7 and year 11 boys and girlsTo make sure it will be a fair test by making sure the subjects have the same amount of time to estimate the length of the line and the degrees of the angle. Making sure the angle and the line are all the same place on the paper and are the same colour and that the distance from it is not varied.The experiment will be consisting of an overall sample of 120 people divided into 30 male, 30 female, and 30 students in year 7 and 30 male and 30 female students in year 10 all these people will be extracted at break times during the school day and chosen at random. A scientific calculator does this.If I had a sample of 30 people 15 female and 15 male and I wanted to choose 8 of them 4 male 4 female I would use my calculator Ran# button on my calculator, this is how I did it I got hold of a sample of 30 people.Sample of 30 people:1F11M21F2M12F22M3M13F23F4F14M24M5M15M25M6M16F26F7F17M27F8M18F28M9F19F29M10F20M30FI then did this equation on my calculator:(The equation may vary form calculators)2ndF RAN X 30 =I pressed = symbol and my calculator came up with a random number between 1 and 30I rounded that number to the nearest 10 and underlined that number on my sample the first 8 went like this:1. 2ndF RAN X 30 =16.86 = 17 M2. 2ndF RAN X 30 =28.44 = 28 M the first 4 males Rad# chosen3. 2ndF RAN X 30 =24.12 = 24 M will be the ones that will be in the4. 2ndF RAN X 30 =14.91 = 15 M pre test.5. 2ndF RAN X 30 =13.56 = 14 M6. 2ndF RAN X 30 =12.39 = 12 F7. 2ndF RAN X 30 =15.33 = 15 M this one has been used once so we ignore it.8. 2ndF RAN X 30 =22.86 = 23 FI then underlined the ones that had been randomly chosen:1F11M21F2M12F22M3M13F23F4F14M24M5M15M25M6M16F26F7F17M27F8M18F28M9F19F29M10F20M30FI had to do this 5 more times to get 2 more F for the pre test1. 2ndF RAN X 30 =16.23 = 16 F2. 2ndF RAN X 30 =13.74 = 17 M3. 2ndF RAN X 30 =16.32 = 16 F this one has been used once so we ignore it.4. 2ndF RAN X 30 =15.75 = 16 F this one has been used once so we ignore it.5. 2ndF RAN X 30 =4.2 = 4 FThe first 4 females are the ones that will be put in to the pre test.You cannot have the same number twice because you would be asking the same sample twice so you would get the same result.The samples will be chosen out of the registration of each class. By using the random technique on the calculator. I will avoid bias by using somebody else to gather my result that does not know about my hypothesis or theory. This will get rid of subject bias and experimental bias.I could improve my sample by making it bigger and extending the variety.A small pre-testThe time chosen for the subjects was 10 seconds to look at both length and angleThis pre-test will consist of 8 people 4 male 4 femaleSexLengthAngleSportM3.530YesM530NoM4.840YesM530YesF530NoF420NoF540NoF535Yes-Mean = total of items / number of itemsMedian = middle valueMode =most commonRange =how far from the smallest to the biggestStem and leaf diagramsThese diagrams mak e it easier to find the mean median mode and range as you can arrange the numbers in order of size then you count to the middle number to find the median the mode is the most common median is all the numbers added together and divided by the amount of the numbers and the range is the space between the smallest number and the biggest number.Length354085000003.5+ 4+ 4.8+5+5+5+5+5=37.3Mean: 37.3 / 8 =4.6625Median: 5.5Mode: 5 over all most people are close to the lengthRange: 1.5Angle20030000054000Close to the angle over all20+30+30+30+30+35+40+40=225Mean: 225 % 8 = 28.125Median: 35Mode: 30 most people are close to the chosen angleRange: 20From these two stem and leaf diagramsCumulative frequency and Box and whisker graphsThis is how you compare the two difference using the graph you can place them on top of each other and compare the difference to the samples and see if one is different from the otherBox and whisker graphsThese graphs are the main comparing graphs from these you can te ll how big the range from the other opposing graph and also if the median results are closer to the real results.AngleFrequencycum.freq20 to 291130 to 395640 to 4928LengthFrequencycum.freq3 to 3.9114 to 4.9235 to 5.958Small conclusionThis test was to see if my methods would work I realise there is nothing to compare the grids to but it works on the graph and gives me the cumulative frequency. no I know that all of my theories work I can use them in the real tests and compare graphs and also I can see the base plan of what I have to do for each test. This pre test is the base for all my tests. Using this I can work my way around my coursework. In all the tests I have used Microsoft excel to do some of my calculations. To make this pre test better I could add something to compare my graphs to and also have more samples to work from.How I will evaluate if females are better than males are by the graphs that my results give and the stem and leaf, mean median and mode. The final conclusi ons will give a valid explanation why females/males are better at estimating length and angles and will also mark any mistakes I have made.End of pre-testTest 1Now I have 149 year 7 females and males and for my sample I am going to choose 30 females and 30 malesThe reason for doing this experiment is to determine if males are better than females at estimating length and angles. To get these samples I will use the Ran# technique until I get 30 females and 30 males in year 72ndF RAN X 149 =I could improve my sample by having a wider range of subjects to chose from and also have a bigger sample the calculator technique is proven in the pre-testThese are the 149 children who were used to get 30 random males and 30 random females:THE ONES UNDERLINED WERE THE ONES CHOSEN FOR THE SAMPLE OF 60 BELOW:I did this calculation many times. And ended up with30 random males and 30 random females.If 1 or more of the 60 chosen were absent I chose the nearest female or male to my assistant (who asked the questions and made each of the 60 year 7 review the angle and the line for 10 seconds and collect the data). any one who is not present will be taken out of the test and replaced by the nearest male if the subject is a male or female if the subject is a female, taking the absent bodys place.The resultsSexAngleLengthSportSexAngleLengthSportF405Y1M605YF426N2M158NF635.4Y3M208YF205N4M2710YF295N5M325YF308N6M413YF345N7M818YF316Y8M284NF195N9M304NF284Y10M354NF405N11M394NF373N12M215YF284Y13M288NF645N14M327YF387N15M266YF156N16M348.4YF6110N17M635.5NF609N18M724YF308N19M3012YF307N20M429NF325Y21M384NF306Y22M196YF488N23M373NF564Y24M604NF724N25M612YF316N26M4016YF348Y27M488NF303Y28M379NF389N29M415NF424N30M305NTOTAL1152175.4TOTAL1167189.9I choose 30 males and 30 females for my sample because I think it is a right size sample to work from, as it will get me varied results.I could improve my sample by having a wider range of subjects to chose from and also have a bigger sample from these results I can see from observing my chart that males play more sport than females.Stem and leafFemaleFemaleAngle10592008893000000112447884000228506600134702FemaleAngleMean 1152 / 30 = 38.4Median 34 the median is close to the original angle of 36Mode 30 this means that most females are closer to the original angleRange 57The median is close to the actual angleFemaleLength300400000500000000560000070080000900100LengthMean 175.4 / 30 = 5.846666667Median 5 close to 4.5 cmMode 5Range 70Most females are closer than the males to 4.5 cm plus one female estimated the angle to be 4.5 which was correctCumulative frequency and Box and whisker graphsAngleFrequencyCum.Freq10 to 192220 to 294630 to 39131940 to 4952450 to 5912560 to 6942970 to 79130LengthFrequencycum.freq3 to 3.9224 to 4.9575 to 5.99166 to 6.95217 to 7.92238 to 8.94279 to 9.922910 to 10.9130MaleStem and leafMaleAngle105920016788300022457789400112850600013702801This stem and leaf counts to 29 this is a mistake but dose not affect my resultsAng leMean 1167 / 30 = 38.9 (1167 / 29 = 40.24137931)Median 37Mode 37 the male majority are closer than the females on anglesRange 66The mode and the median are the same meaning that the 15th male was also in the medianMaleLength2030040000000500000560070800000490010011120131415160Huge range no males got the angle rightLengthMean 189.9 /30 = 6.33Median 5 very close to the original angle of 4.5 cmMode 4 the median is also the same as the females medianRange 14The range for the males is bigger than the females because there are a couple of males that estimated a lot higher than I would expectedCumulative frequency and Box and whisker graphsAngleFrequencyCum.freq10 to 192220 to 296830 to 39101840 to 4952350 to 5902360 to 6942770 to 7912880 to 89129LengthFrequencycum.freq2 to 2.9113 to 3.9234 to 4.97105 to 5.96166 to 6.92187 to 7.91198 to 8.96259 to 9.922710 to 10.912811 to 11.902812 to 12.912913 to 13.902914 to 14.902915 to 15.902916 to 16.9130ConclusionMales are better at estimating lent a s the box and whisker graphs prove though the males have a very big range most of the males have been close to the 4.5 cm chosenAn experiment to see if playing sport helps at estimating lengths and anglesThis is a test including only 10 people that play sport and 10 people that dontIn this test sex is not important as it is only comparing non-players against playersThe players and non-players have been chosen at random from a group of 60 people.Here are the results:AngleLengthAngleLength208Y1645N2710Y2387N325Y3156N413Y46110N508Y5609N352Y6308N405Y7304N327Y8354N266Y9394N348.4Y10305N33762.440262I could improve my sample by having a wider range of subjects to chose from and also have a bigger sample.Non-playersLength400050060708090100Mean 62 / 10 =6.2Median 5Mode 4Range 6You can see that the non-players haveAngle1052000058930405060014Mean 402 / 10 =40.2Median 25Mode 20Range 49Most of the non players have there angle marked betweenCumulative frequency and Box and whisker graphLengthFrequ encycum.freq4 to 4.9335 to 5.9256 to 6.9167 to 7.9178 to 8.9189 to 9.91910 to 10.9110AngleFrequencyCum.Freq10 to 191120 to 296730 to 390740 to 490750 to 590760 to 69310PlayersStem and leafLength20304500607080049100Mean 62.4 / 10 =6.24Median 6Mode 8Range 8The players are more spread out than the non-playersAngle10200673022454001500Mean 337 / 10 = 33.7Median 32Mode 32Range 30The angle seems to be .Cumulative frequency and Box and whisker graphsLengthFrequencycum.freq2 to 2.9113 to 3.9124 to 4.9025 to 5.9246 to 6.9157 to 7.9168 to 8.9399 to 9.90910 to 10.9110AngleFrequencyCum.Freq10 to 190020 to 293330 to 394740 to 492950 to 59110ConclusionI used Microsoft excel for some of my calculations as humans can make errors and that it is more accurate.Also I used this program to save time as it would have had taken longer for me to write the tables up. I can see from my graphsAn experiment to see if age makes a difference:Plan = an abbreviation of the main plan on page 11) I will work out the mean median mode and range of the results of the year 7 samples and the year 10 samples2) I will make stem and leaf diagrams3) I will make box and whisker diagrams4) I will make a conclusionMETHOD the same sort of method used on the first two experiments.I got a sample of 60 year 7 and a sample of 60 year 10s and used the random technique on the calculator to select 30 year 7 at random and 30 year 10s at random. I will avoid bias by using somebody else to gather my result that does not know about my hypothesis or theory. This will get rid of subject bias and experimental bias.I think that the older people are better at estimating angles and the length because they have more experience at doing so from further education and more experience.For this experiment I am using excel again as it its a time saving device and also Is a excellent calculator at fast speed if you know the formula to put in for this experiment and all of these experiments I have used the =SUM formula the most. Yea r 10s chosen underlined in red:Year 7Year 10AngleLengthAngleLength6051303.515823052083404.8271043053255404.541363058187204284840530493553541058539411454.5215124552881350432714455266152541561630461101745560918405308193063072030632521404.530622452.548823203564244537242545331626453.5348274543032845438929454424304041124186TOTAL1153130.8I could of hade made my sample bigger but that would had of taken more time and also a sample of 30 is easier to work with.Year 7Stem and leaf diagramsAnglesAngleYear 71055200167883000000122245894012850660001702801Mean 1124 / 30 = 37.5Median 32Mode 30Range 70The year 7s are closer to the angleLengthLength300400000005000060000700800000009001000Mean 186 / 30 = 6.2Median 6Mode 4/8 there are two even modes for this graph as four and eightRange 7 have the same amount on the graph so I put both of them downCumulative frequency and Box and whisker graphsYear 7AngleFrequencycum.freq10 to 192220 to 296830 to 39132140 to 4932450 to 5912560 to 6932870 to 7912980 to 89130LengthFrequencycum.freq3 to 3.9224 to 4.9795 to 5.94136 to 6.94177 to 7.92198 to 8.97269 to 9.922810 to 10.9230Year 10Stem and leaf diagramsAnglesAngleYear 1020005300000000540000000555555555555008Mean 1153 / 30 =38.4Median 40Mode 45Range 38LengthLength25300055400000000555850000000000600Mean 130.8 / 30 = 4.3Median 4.5Mode 5Range 3.5Cumulative frequency and Box and whisker graphsYear 10AngleFrequencycum.freq20 to 293330 to 3981140 to 49172850 to 59230LengthFrequencycum.freq2 to 2.9113 to 3.9564 to 4.912185 to 5.910286 to 6.9230Conclusion