Estimates of a straight line and a curved line

The subject I have decided to carry out is an assignment on estimates of a straight line and a curved line. I am going to find out if there is any relationship between the estimates of a straight line and a curved line.Aims:My aims are as follows1. If you estimate a curved line accurately do you also estimate a straight line correctly?2. Are half of all estimates within 10% of the actual measurement?3. Do Y10 students have a greater number of pupils within 20% of the median than Y7 pupils?4. To find out who is better at estimating straight lines, girls or boys?I am going to answer these questions in my investigation by using the information I gather and the diagrams I formulate, when the aims are found I will then analyse the results.Planning:I am going to look at the recordings taken from Y7 and Y10, boys and girls. The two factors I am going to investigate are age and gender and their ability to estimate a straight line and a curved line. I will take a sample size of 50. I am going to base my hypothesis on how age and gender affect a child’s ability to observe and estimate a straight line and a curved line.Evidence:Before I write my hypothesis I am going to write a small number of my ideas on what affects an individuals ability to estimate a straight line and a curved line.1. I think the older the person is the better they estimate.2. I also think that if the person estimates within a 10% error of the actual length for one of the lines they will be within 10% of the other line.3. I think that boys will have a greater spread of data than girls.4. I think the majority of the girls will b within 10% of the median.The sentences above may not be true and this is not all I am basing my hypothesis on, but they are a few things that are influencing what my hypotheses are going to be.2 Hypothesis:1. If you estimate a curved line accurately you also estimate a straight line accurately.2. Y10 students have a greater number of pupils within 20% of the median than Y7 students.3. 50% of all estimates will be within 10% of the actual measurement.4. To take all the Quantitative data from Y7 girls and Interpolate the mean.Collecting data:For my investigation I will make my sample size 50. I will select my 50 by a simple stratified sampling method so everyone has a fair chance of being selected. I will choose these numbers via calculations. I will then do a systematic sample with this data to get the rest of the sample I need.There’s 102 pupils in Y7 and there’s 111 pupils in Y10so you would do the following calculations.Y7: 102 x 50 = 24 (2sf)214Y10: 111 x 50 = 26 (2sf)214Then with this data you have to divide the number of pupils needed from the group with the number of pupils in the other group.Y7: 102 = 4 (1sf)24Y10: 111 = 4 (1sf)26This shows me that I will pick every 4th person from the list of quantitative data from the circus.Here are the results of the data I collected.GenderCurved line estimateStraight line estimateM3713M3613F3711F4010F2410F3215M3112F4414F3520M6025F3410M4417F3213F2811M3813M5016F3516M3914M3515F3410F10012.5M3013M4013M3614F3010F2118F2812.5M3010M2410F2411M2110M35.512F3514M4411M3414F5010.5M4014M5613M3515F4013M3010F3612M5015M3512M4915F6016M4316F4015F3515F3810Q1 If you estimate a curved line accurately do you furthermore estimate a straight line accurately? That is what I’m going to investigate into. To do this I will have to construct %error table to decipher whether there is a positive correlation. (error/actual measurement x100). Then I will have to use Spearmen’s Coefficient of rank correlation. 1 6 d /n(n -1)Boys errorCurved line=38Straight line=13Curved line estimate% errorStraight line estimate373133651331181260-582530211340-5133651430211024371021451035.571244-161144-16173801350-321639-3143581534111440-51455-45133581530211050-32153581260-5016% errorRank of curved lineRank of straight linedd02.53.51105.53.52481510525-9224.5250.50.250173.513.5182.2505.53.524-85.5104.520.25231720.53.512.25232120.50.50.252322.520.5248810241513.515.524-3113.52410.5110.25013.52.56.25-2319.520.511-82.5107.556.25-151015.55.530.25-812102361-85.5104.530.25022.53.51912.25-151015.55.516231720.53.50-1519.515.5416810100-2324.520.549.25Spearman’s Rank = 1-6 d /n(n -1) = 1-6*925/25 (25 -1) = 1-5550/15600=1-0.35576923=0.644230769Girls errorCurved line=38Straight line=13Curved line estimate% errorStraight line estimate% error373111540-51023243715-15321614-844-1620-5435812.54100-1631023302118-38214412.5428261115243714-83581023341113032161115282616-233581023341110.51950-3213040-512836515-1549-2916-2343-1316-2340-515-1535815-153801023Rank of curved lineRank of straight linedd211-9814.519.5-1522522.51111.5132.251569811525-101008.53.55252519.55.530.251724-749243.520.5420.2518.5117.556.2522.5616.5272.258.519.5-1112111.51.510100151141618.519.5-118.519.5-1112111.515-3.512.25211.519.5380.254.56-1.52.254.511-6.542.252019.50.50.251319.5-6.542.254.511-6.542.258.511-2.56.25119.5-18.5342.25total=2701.5Spearman’s rank = 1-6 d /n(n -1)=1-6*2701.5/25(25 -1)=1-16209/15600=1-1.039038461From these two pieces of information I can see that there is a strong positive correlation in boys estimates and no correlation in girls estimates. This tells me that boys, when they estimate either curved or straight line accurately, they also estimate the other accurately aswell. With girls this doesn’t happen. When girls estimate one line accurately, they usually estimate the other line badly.Q2When the pupils estimate the curved line, do boys and girls in y10 have a greater number of pupils with 20% of the median than Y7’s. I will have to work the % error for both Y10 and Y7’s.Curved line estimate% errorY7 B+GCurved line estimate% error4416337338003655032531183930605835873021341104054053365564513021358124373021321455032235.573580441660580373341104053216024372826032163582441634110358503201001634050321365021544929028264313324374050358358223563805417I will then have to group the pieces of data to make a cumulative frequency diagram.GroupY10 FreqY7 FreqY10 Cumulative frequencyY7 Cumulative Frequency0–432325–99612810–144016815–1924181220–2413191525–2921211630–3430241635–3903241940–4410251945–4901252150–5401252255–5911262360–6400262365–6900262370–7400262375–8900262390–9400262395–99002623100–104002623105–109002623110–114002623115–169002624

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