Maths Handling Data Coursework: Mayfield High School
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Jonathan Nisner Maths Handling Data Coursework: Mayfield High School For this handling statistical data coursework I will be investigating the heights and weights of students of years 7 to 11 in Mayfield High School. I will look for a trend in the heights and weights of the students to see if the taller they are, the more they weigh. My hypothesis is that there is no correlation between height and weight, and my Alternative hypothesis is that there is strong, positive correlation between them. I will then investigate the heights of boys in years 7 and compare them to the girls, and then do the same in year 11. I will then be able to compare these two sets of results. These hypotheses. I am carrying this investigation out because from my hypothesis I want to know whether students in the older years should be separated from the younger students. In order to carry out this investigation, I will need to collect the heights and weights of all the students in Mayfield High School between and including years 7 to 11. Instead of collecting the data, I can find the information on an exam board website. This data is reliable because it is provided by the exam board and is based on real students, however, it may be unreliable because it is secondary data, not primary since I am not physically collecting it myself, and the students may not have measured or weighed themselves on the day, and had guessed the measurements instead. Height and weight is continuous data so only some graphs and calculations can be done. I have decided to select a sample size of 100 students because 1183 students are too many. I won't be able to compare the data well since I will have such a wide range of results. I also won't be able to fit all the information on one graph or one box-plot making the comparison even more difficult.
Also, from the box plots I can see that the boys' heights are very slightly positively skewed since the median is a little closer to the lower quartile than to the upper quartile but the girls' heights are a little negatively skewed; the median is a little closer to the upper quartile. The box plots are almost symmetrical meaning that there is almost an equal distribution of students on either side of the median. This is another difference between the girls' and boys' heights in year 7. I will now look to see if there are any outliers in my data. If there are any they may have distorted my data. To do this I must multiply the interquartile ranges each by 1.5. For the boys this is: 10.5 x 1.5 = 15.75. For the girls this is: 12.5 x 1.5 = 18.75. Any boys that are 15.75cm below the lower quartile or above the upper quartile are outliers. Any girls that are 18.75cm below or above the lower and upper quartiles are outliers. Here are the heights of the boys and girls in year 7: Year Group Gender Height (m) Year Group Gender Height (m) 7 Female 1.25 7 Male 1.36 7 Female 1.41 7 Male 1.4 7 Female 1.43 7 Male 1.41 7 Female 1.45 7 Male 1.42 7 Female 1.48 7 Male 1.46 7 Female 1.51 7 Male 1.47 7 Female 1.52 7 Male 1.48 7 Female 1.52 7 Male 1.48 7 Female 1.52 7 Male 1.5 7 Female 1.53 7 Male 1.51 7 Female 1.55 7 Male 1.51 7 Female 1.56 7 Male 1.52 7 Female 1.56 7 Male 1.52 7 Female 1.58 7 Male 1.53 7 Female 1.59 7 Male 1.54 7 Female 1.6 7 Male 1.54 7 Female 1.6 7 Male 1.54 7 Female 1.6 7 Male 1.54 7 Female 1.6 7 Male 1.55 7 Female 1.61 7 Male 1.57 7 Female 1.61 7 Male 1.58 7 Female 1.62 7 Male 1.58 7 Female 1.62 7 Male 1.59
This means that the range of heights isn't that wide as is the case with the year 7 boys' interquartile range whereas the year 11 boys' heights are very spread out and have a wide range. I have proved my three hypothesise correct. They were: 1. The taller you are, the heavier you are. 2. Girls in year 7 are taller than the boys in year 7. 3. Boys in year 11 are taller than the girls in year 11. I accept my three hypothesise since my data supports them but when I furthered my second and third hypothesise I found part of it to be incorrect. There are certain limitations put to my investigation. One of these is that my sample size may have been too small. I could have made this bigger but it would have been time consuming and too much data to put on appropriate graphs. I wouldn't have been able to compare the information sufficiently. The information provided may be inaccurate or incorrect since the pupils at Mayfield High School may not have known their heights and weights accurately and may have given incorrect guesses. They also provided a lot of inappropriate data such as their names which is inappropriate since isn't worth investigating. The data could be biased because it was only collected from one school and not from other areas in the country. The data may be biased because there may have been a lot of snack shops or fast food restaurants near the school, which may have affected the students' weights. I could have investigated further by using more than one school's data and compared them and I could have had more hypothesise. This would have given more precise results due to a larger range and a larger sample. I could have drawn more graphs and made more calculations to get more accurate results. For example I could have calculated the standard deviation for my three hypothesise to get a more accurate spread of data than the interquartile range. ?? ?? ?? ??
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