Is a relationship between the height and weight of a selected sample of Year 7 students

Mohammed Patel, 10G1

GCSE STATISTICS COURSEWORK

PLAN

The aim of this coursework is to find if there is a relationship between the height and weight of a selected sample of Year 7 students, and to see if taller, or older, or students who watch too much T.V are generally heavier or lighter. I am doing this investigation because I have a sister in Year 7 who is fat, short, heavy and watches too much T.V and I am intrigued by this to see if all students are like that or whether they are heavier or lighter if they are shorter, or watch too much T.V. Because of my interest in this area of maths, I will measure the height and weight of Year 7 students and see whether they have anything in common in between them. If I wasn’t doing this investigation, I would probably have been doing something else for example to see if students who watch too much T.V have a higher I.Q, but due to the shortage of time and the way the school timetables are set out, I figured that I would not have the time needed in order to complete this task in the appropriate way.

Some factors which may have caused me a problem if I did choose these hypothesis are, that firstly some students may have presented me with unreliable data and I would have had no way of proving how many hours of T.V they really watched. Also, by looking at the time allotted to me for completing the investigation I thought that the best investigation to do was to go for my second option which was to measure the height and weight of some students in different years starting with Year 7. In my chosen investigation there still were difficulties but the ones I have planned for are:

Firstly, I would need a lot of time to measure the heights and weights of all the students in all the years. A way of overcoming this problem could have been to go to the school office and collect my data from there. However I am not doing this because firstly, I want to work with primary data and secondly, data about the students of their heights and weights may not exist or, if it does, it may be out of date so it will not be as accurate as if I collect the data myself. Also, if everyone in my class had done this the secretary will not be too pleased to se thirty students all coming at once for data on approximately 1500 students! So what I have decided to do is to firstly collect a small amount of data from the Year 7s and then compare it with the data given to me by my teacher, which is in the data book from the students of Mayfield School. If there is a similarity between the two pieces of data then I could continue to prove my other hypotheses with the data from the data book. I could have collected the data from the other year groups myself during my maths lessons, but because of the way the school timetables were arranged I could not get access to any other year groups besides Year 7 because they were the only ones who had maths lessons when we had them and going to other classes would disturb the education of other students as well as disturbing teachers.

These are my hypotheses:-

Tall students are heavier than short students.
Older students are heavier than younger students.
Students who watch more T.V is heavier then students who watch less.
Heavier students have a higher I.Q than lighter students.
Students who walk to school are lighter than students who use other forms of transport.
Left handed students are taller than right handed students.

The hypotheses I have chosen to support are:

Tall students are heavier than short students.
Older students are heavier than younger students.
Girls are lighter than boys.
Left handed students are lighter ...

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These are my hypotheses:-

Tall students are heavier than short students.
Older students are heavier than younger students.
Students who watch more T.V is heavier then students who watch less.
Heavier students have a higher I.Q than lighter students.
Students who walk to school are lighter than students who use other forms of transport.
Left handed students are taller than right handed students.

The hypotheses I have chosen to support are:

Tall students are heavier than short students.
Older students are heavier than younger students.
Girls are lighter than boys.
Left handed students are lighter then right handed students.
Students who watch more T.V are heavier than students who watch less.
Heavy students have a higher I.Q than light students.

The reasons why I have not chosen to support the last two are because firstly, I will not have enough time to support all of them and secondly, it will be very difficult for me to find information out primarily about things like I.Q. Even if I did find data like that out it may have been out- of –date and therefore deceiving.

To prove my first hypothesis I will use a sample. There are approximately 1500 students in Smithills. A 10% sample would be 150 students which is simply too large for me and will consume a lot of time. A 5% sample is about 75 students which is also too large a sample for me. A sample of about 60 will be right so that is what I will use. 60 students is like two classes so what I will do for my first hypothesis is that I will look at the Smithills school Year 7 pupils which I can get access to. Well there are only four Year 7 classes which have Maths at the same time we do. So visiting two of them should not be much of a problem for me. To select my sample of 60 students I could use a convenience sample but the problem with that will be that I will not know the difference between Year 7, Year 8 and Year 9 students as they wear the same colour of jumper. (It will be very difficult for me to collect the data.) I could use a systematic sample but the problem with that could be, for example if I was to weigh and measure every fifth student, that I came across in a certain corridor, then I would be confused as to which students belong to which year (this is because years 7, 8 and 9 wear red jumpers in our school and years 10 and 11 wear black.). I could use a quota sample but that wouldn’t be very much of a random sample because it would be I who would choose the students asked and this may bias or skew my results. I could also use a cluster sample but this may also be biased because I may end up with only a certain type of people in a group. Although this is very unlikely, it is not a risk worth taking because my results would end up skewed.

So, in my opinion the best sampling methods to use are the stratified sample for hypotheses 2 and 3 and a random sample for hypothesis 1. This way my results will be more reliable as they won’t be biased or skewed. To use a random sample I will use the random number button on my calculator and then round up the decimal number that is given. For example I would round 37.323 down to 37 and round 37.545 up to 38. I may face a problem in this because if I want, for example, to pick a random sample from a total of 112 it will not be very likely for me to get 112 as all the other numbers as it is the maximum number. So what I will do to solve this problem is if I get a number under 0.5 or over 111.5 I will call it 112.

So, back to my method of supporting my first hypothesis; I will use my primary sample 60 students and then plot them onto a graph. I will use them as a control group. Then I will get another sample of 60 Year 7 students from the secondary source provided, that is, the Mayfield school database. I will then plot that data onto a new graph. Then I will find the line of best fit after finding the mean point and then find the equation for that line of best fit and then use it to predict data which will be both interpolated and extrapolated. Then I will calculate the Spearmans Rank Correlation Coefficient to find out how strong the correlation is between the height and weight. If the two correlations are similar then I will continue supporting my other hypotheses using the Mayfield data.

For my second hypothesis, (i.e. older students are heavier than younger students) I will firstly take a stratified sample of students from each year and then select them using the Mayfield data book provided. As the students from all years and of all sexes are already jumbled up, there would be no point in me trying to find a random sample. Instead I could just go down the list and pick, say, the first 15 year 7 students I come across. After doing this I would put all of the data together and find out the mean and standard deviation from each year group. That way, it will tell me if older students are lighter and how far away from the mean the data is spread out. I have chosen to do standard deviation in this because it is a very accurate way of finding out how far away data is from the mean.

For my third hypothesis (i.e. girls are lighter than boys) I will take another stratified sample from each year group of girls and boys and go down the Mayfield data book and again pick out for example, the first 7 girls I come across. This way my data is unlikely to be biased. After doing this I will manipulate the data to create a two-way table, categorising the weights of the girls and boys, into class widths. After this I will find out the frequency- density of the data and create a histogram for both my male and female pieces of data. From this I will draw a distribution curve and see which way more of the data lies. Also from my frequency- density table, I will also work out the cumulative frequency and draw a cumulative frequency graph for that. From the cumulative frequency graph I will find out the upper- quartile, the lower quartile and the interquartile range. Also from the cumulative frequency graph I will draw a box and whisker diagram and compare the weights of boys and girls.