Statistical investigation.

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Mathematics GCSE

Mayfield High School

The total number of students at the school is 1183.

 

I have been given data on all the students covering a range of different things such as hair colour, eye colour, numbers of brothers or sisters and even favourite music and IQ. There are 27 different categories and there for a total of 31941 datum points.

1183 x 27 = 31941

What I first need to do is to decide which line of enquiry I will choose. There are several options but I need to pick I think will show successfully what I can do within the area of statistics. I have decided to compare these four things:

>Year Group

>Sex

>Height

>Weight

I feel that these four sections will enable me to carry out a statistical investigation. I aim to find out whether there is any relationship between them and differences between age and sex.

Collecting Data

The first step I need to take is to take a random sample of the data. Before I do this I will need to decide how many students’ data I want to be analysing. I think 60 would be a good amount allowing me to have 30 boys and 30 girls. Now I need to use stratified sample to find out how many boy and girls I need from each year group.

282/ 1183 x 60 =14.30262

270/ 1183 x 60 =13.694

261/ 1183 x 60 =13.23753

200/ 1183 x 60 =10.1437

170/ 1183 x 60 =8.622147

Total = 60

The reason I have decided to do a stratified sample is because stratified sampling is the best way to represent data in a proportional way. It makes it a much fairer process to randomly select data by giving each one an equal chance of being selected. Because I can’t exactly have 13.694 prices of data I need to simplify each value by rounding it up to the nearest whole number.

 So now I know exactly how many pupils’ data I need to select from each year group.

The table above shows how I got to my sample of 60 students now I need to decide whether or not to do a similar thing but for the sex of the pupil’s instead of the year. This will allow me to see if gender has any affect on the height and weight of teenagers, so I think I will. I have already realised that I should have done a stratified sample of both sex and age together in the beginning instead of doing one after the other this is a mistake which has cost me some time.

It has taken me a while to calculate accurately how many boys and girls I will need form the different years but now I can begin randomly selecting the data which I will be using.

I have put all my data into a spreadsheet and sorted it into two groups of gender. I then separated the data in the each gender according to year group and numbered them from one onwards. When I finished numbering my data in the spreadsheet I made sure that the last number in every section corresponded to the total population of each gender in each year group/. This was to ensure that I had sorted the data successfully with out any errors. I then used the random number formula on the spreadsheet to select the exact amount of data I needed from each section.. I made a table of all the random numbers I collected and used that table to help me pick the exact amount of boys and girls from every year group. Instead of having to compare each number to the gender in order to determine whether or not I could use it, I numbered the males and females separately allowing me pick the first random number hat came up. This was a long process but I had to ensure that I was doing this investigation fairly. If I had not done this and numbered each year group from 1 regardless of gender I would have had to take an even longer method of comparing the random number to the sex as I mentioned before. The table below shows the random numbers and there relative numbers after being multiplied by the population of each gender in each year group.

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