Mayfield High School - investigate the correlation between a certain topics.

So if we substitute the words for the actual numbers that I am working with then we can see how I have worked out my stratified sample. HERE!!!! This will then give me the number of pupils that I will need from each year group in proportion to each other year group. I will then have to take a random sample. I can do this by using the random function on a calculator. This will give me a random number from 0-1. I can then multiply this number by the amount of pupils that I will need to take from each year and this will give me a number, I can then round this number up or down accordingly and I will then take that number person from my sample. After I have got my 35 pupils I will then be able to start to look for correlations in my pupils.

Prediction

I predict that the more siblings that a pupil has the less pets that a pupil will have. The way that I have come to my conclusion is that I believe that in some cases young people are lonely without a sibling to play with or have for company. So I believe that a pet is almost a substitute for the absent sibling.

Method

The first thing that I will have to do is to plot a scatter graph, so that I can see if there is any direct correlation between the two pieces of data that I have chosen. A scatter graph is one of the easiest ways of seeing if there is any direct correlation between two pieces of data at this early stage in the analysis. I will also have to plot several different types of graphs, they could include cumalitative frequency graphs and variable width histograms.

Step by Step

I will first have to plot a scatter graph with all of the data for my sample that I have chosen. I will then plot a scatter graph with all of the data from the individual year groups separately. I will then construct cumulative frequency graphs for then whole data sample and then again for the year groups individually. I will then work out a mean for the amount of pets that a person has for the whole school and then also then the individual year groups.   I will work out the means for both the amount of siblings and then amount of pets this will then give me an instant example of the average amount of siblings and an average amount of pets that that same person has. I will then have to tabulate all of the results into a cumulative frequency table, so that I can then construct a cumulative frequency graph. On the cumulative frequency graph that I will construct I will mark out then median and then upper and lower quartiles. I will then have a different type of average that I can then analyse. I will then have to construct several different types of variable width histograms. I will then be able to pin point what area of the sampled data is the mode or has the most people in it.

Conclusions

I can see from my scatter graph that there is no direct correlation in this area of data that I have selected and as it can be seen there is not a line of best fit, let alone a line of best fit that shows a positive correlation. This leads me to the conclusion that I can not really work with this set of sampled data, as there is not really a correlation between the two different types of data. As it would be very hard to try and construct different types of graph with these sets of data. So I have decided to start again with different sets of data.

Aim

I have chosen to use the same sample of people but instead I will use their height and weight types of data. I will analyse this data in much the same way as I had planned to in the first experiment that I did. So my first task is to construct a scatter graph and then try to plot the line of best fit. I Will then be able to see if this data I a piece of data that I can work with.

Analysis

I can see from my scatter graph that there is a positive correlation between the heights and weights of this set of data. There is not as much correlation as I would have expected but there is however two or three anomalous readings that I have plotted. I have decided that I will go ahead with this line of enquiry.

The next step that I will do is to work out the mean of all of the heights for each of the years individually. This will tell me which year is the tallest or the shortest. I will also work out the mean weights for all of the years so that I can tell which year is the heaviest or the lightest.

I can see from the results that the average height for a year 7 is 156.5 cm and then at the other end of the scale I can see that the average height for a year 11 is 162.6cm but this is not the tallest year in the school on average it is year 10 that has the tallest average height of 172.3cm. but this is closely followed by year 8 with an average height of 171.0cm. from this data I can conclude that Mayfield High School is getting to be a on average a taller school. All of the newer pupils that are coming into the school are taller than the year before them.

I could then suggest that the taller a person is, then the heavier that that person should be. It could also be said that the older that a person is then the heavier that that same person should be in proportion to a younger person as the younger that a person is the less time that they have had to develop their muscles or body fat so a year seven would be lighter that a year 11.. So I will now look at then average weights of each of the year individually. I can see from my results that the year that is the heaviest is a tie between year 9 and year 10. the readings for year 10 back up my theory that a taller person is a heavier person. However year 9 is a relatively short year in terms of height, but it is one of the heaviest years, in terms of body weight. So I can conclude that year 9 is made up of rather short and rather fat pupils and year 10 is made up of rather tall rather fat pupils so their body weight and height is more poportionate than that of the pupils in year 9. Year 7 is made up of rather small and rather thin pupils this would then back up the second part to my theory that the younger that a pupil is then the shorter and thinner that a pupils is.

Cumulative Frequency

I will now construct a cumulative frequency table so that I can graph my results into a cumulative Frequency Graph. Once this is done then I will be able to see what the upper and lower quartiles are, and what the median is.

Analisys

I can see from my table and graph that the median height for the whole school is 163cm and that the upper and lower quartiles are 169.5cm and 157cm. this would then suggest that most of the people in the school should be somewhere in side of these two brakets.

Histograms

I will now construct a variable width Histogram table so that I can graph my results into Variable Width Histogram. I do this by looking at the table that I have already constructed with my Cumulative frequency table and then I dicide which intervals that I will use and then merge the two or three intervals and then I have to work out the standard interval and then also the frequency density. So that a Histogram can be constructed.

Overall Conclusions

I can see from all of my combined graphs that there is infact a correlation between the height and the weight of a person. I think that this is beacause the older that a person is then the more time that a body has had to develop and alos grow. But from the mean of heights and weights that I worked out I can see that Mayfield High School is getting to be a taller school and the year sevens at this school are not a small as the year 11s were when they were in year 7. I can see that most of the people in this school show be 163cm tall and that they should be no taller than 169.5cm and no shorter that 157cm. I saw this from my cumalitive frequency graph.