Maths Coursework Essays

Maths Coursework Essays Maths Coursework Essay Maths Coursework Essay In my investigation I plan to find out whether my theory that year 10 pupils are better at estimating the length of a stick than year 7 pupils. Plan- In my investigation I plan to use secondary data gathered from both year 7 and year 10 pupils, which I will then do a random sample of which will be used to find the mean, median, mode, range as well as standard deviation which I will then put into groups and frequency tables to compare and from this I will hopefully be able to come to a conclusion. Aim- I am hoping to find if the statement that year 10 pupils are better at estimating length than year 7 pupils is true and find different ways of proving this. I am hoping to find a mean for the both groups to compare where I will hope to find that the year 10 mean is closer to the actual value (1.36m) than year 7 pupils and this I hope will help me come to a fair conclusion. I am also hoping to find the standard deviation for both groups and hope to find that year 10 pupils will have a smaller standard deviation than the year 7 pupils because I believe it is more reliable because it shows less range which means all of the pupils have answered fairly similarly because a wide range means people where miles away with their guessing. Sampling- I will number each piece of raw data and then I will use the random search on my calculator. I will have to use a sampling because there is too much data to work with and it will be random to make it fair. Because I will use a random sample I will need to find a certain number of the population that I will randomly choose. So I need to find what proportion of year 7 and 10 pupils I will need. I have chosen to use 20%, which is 36 pupils so it is in the same proportion as the population, i have chosen 20% because i believe this number represents a fair selection of the population. To do this I will need to figure out how many boys and girls I will need to randomly select, first I will use the data of year 7 pupils, Year 7 Boys Girls Because I am working with this certain type of data which is given to me in people it means I cannot use decimal points so I will need to round the figures up and down. Boys Girls To select my 15 boys and 21 girls from year 7 I will use the random button on my calculator. To do this I have numbered all of my data values so they maybe selected fairly. I have done this because it is random and not biased towards anyone so it is completely random. Example- I used the random button on my calculator and the number 0.145 acme up so I looked through my data and looked for which record was given this number and then I recorded its gender which was female and then its estimate which was 1.50 then I repeated this process again using my calculator and the number 0.234 came up so I looked through my records and saw it was outside my range so I ignored it and when I came to the end and had found the number of females I wanted but not males I would simply continue until another male record came up ignoring the rest of the females. Year 7 Sample- Year 10 In year 10 there are 93 girls and 87 boys, because they are different values I will have to do a calculation to figure out the proportion of the population who will be included in my 20% (36 people). I will use the same method to do the year 10 pupils as I did with the year 7 pupils to make the investigation fair. Year 10 Girls Boys Again because I am working with data that in this case cannot be used with decimal places, so I will need to round them up and down. Boys Girls Year 10 Sample Because I have now randomly chosen a fair amount of both year 7 and year 10 pupils, I have now decided to find the mean, median, mode, range and standard deviation for the groups of year 7 boys and girls and year 10 boys and girls. Analysis of results To find out the standard deviation and the mean ( ) I will use my calculator, to find out the mode and range I can simply read off the answers and to find the median I will write down the values the find the answer. Year 7 Boys Girls Mean ( ) Median- Mode- Range- Standard Deviation (2d.p)- Year 10 Boys Girls Mean ( )- Median- Mode- Range- Standard Deviation (2d.p)- Because I am trying to find that year 10 pupils are better at estimating length than year 7 pupils I will need to find an overall mean, median, mode, range and standard deviation for year 7 and Year 10 pupils. Year 7 Mean ( )- Median- Mode- Range- Standard Deviation (2d.p)- Year 10 Mean ( )- Median- Mode- Range- Standard Deviation (2d.p)- Now I have decided to put my results in to graphs and frequency tables because I believe these will help me come to a fair conclusion. I have chosen to use standard deviation because it shows the average distance each data value is from the mean, which i believe will help me with my investigation and the mean will help me see what the average data value from the selected data is and i believe these will help me come to a fair conclusion. Conclusion- From my results I have proved my hypothesis correct because the mean of the year 10 pupils estimations is closer to the correct length of the stick, which is 1.36m. With the mean of the year 7 estimations being 1.43m the overall year 10 mean is 1.38m meaning that the year 10 pupils are better at estimating length than year 7 pupils. But the standard deviation of year 10 pupils is 0.22 with the standard deviation of the year 7 pupils being 0.13 this shows that the year 7 results are more reliable because the results are closer together showing a similarity in the answers and also showing that pupils in year 10 have estimated a wider range which is also shown in the range because the year 10 pupils have a much wider range meaning it is less reliable. This tells me that not all year 10 pupils are better at estimating length than year 7 pupils. So overall I believe the results of my investigation where inconclusive because although the mean of the year 10 pupils was closer to the actual length which does in a way prove that year 10 pupils are better at estimating length than year 7 pupils but the standard deviation shows how the year 10 pupils results are also less reliable than year 7 pupils results. So I believe that both of my results can cancel each other out leaving me no choice but to say the results of my investigation where inconclusive. Evaluation- I believe that the random sampling method that I used in my investigation worked very well as well as the way I chose the percentage of the population, which I planned to use. I believe there was nothing wrong with this method and if I was made to re-do this investigation I would have used the same method. The main point that forced me to come to the conclusion that my investigation turned out inconclusive was the results themselves because I am trying to prove that a certain group of people (year 10) is better at estimating length than another group of people (year 7) and with these results I found that some year 7 pupils where actually better at estimating length than some year 10 pupils even though the majority in year 10 where better at estimating length it meant that I could not say that all year 10 pupils where better at estimating length and shows how difficult it was to come to the conclusion with the results of the standard deviation to consider as well. Another thing I believe is that the mean is hard to come to a conclusion with because out of the whole of year 10 the mean was 1.38m which not 1 person in the year had as their estimate. If I done this investigation again I would choose a lower percentage of people to choose from like 10% which would have been 18 pupils and any pupils whos estimates where way out I would discard them or make sure they do not guess stupidly and this would make it easier to come to a conclusion.