I will first table the data in a frequency table and a cumulative frequency table, to list and sort the data.

This table shows the BMI, grouped into groups of 5. The frequency is the number of people in that category, and the cumulative frequency is the total (which adds up to the population, 240). As we can see, the frequency of people with certain BMI goes up until a point, and then decreases afterwards. The mean BMI is 20.11621, the median is 19.84 and there are 2 modes: 18.52 and 19.81. Now the results have been tabulated, I can find the standard dispersion. From then I will plot the data into graphs.

To find the dispersion, I will first find the dispersion from the mean of all the data. I will then divide it by the mean, but this gives us 0. This isn’t useful, so we must square the deviation from the mean. Since all squares are positive, we will not get zero. This gives us our deviations. To find the mean of the squared deviations, we divide the sum of the squared deviations over the number of results. I worked this out for each group:

I then made a graph to illustrate these results:

Year groups are: 1=Y7, 2=Y8, 3=Y9, 4=Y10, Y=11. This graph shows that as the year groups go higher, deviation increases for males until year 11, when in drops greatly. For females, their deviation drops in the first year, then slowly increases, then drops again in the final year. This suggests as males get older, their BMI increases greatly, then hardly increases at all; for females, their BMI increases very slowly over the years, then averages out.

I then made the BMI results into a bar chart and scatter graph to see if there was a pattern:

As we can see, the graph appears to show no correlation. There are exceptional results, but when looked at closely there is a small positive correlation between peoples BMI and number of hours of TV watched.

I next constructed a pie chart from the frequency table to see if I could extract any useful data:

As we can see, there is a large amount of people in the same group of BMI (just under half). There appears to be no correlation in peoples BMI on its own (i.e. there is no correlation between year group BMI or gender BMI).

From this we can tell that although there is no correlation between BMI in year groups and/or gender alone, when hours of TV watched is introduced, a correlation becomes apparent. To do a more thorough study, I created a cumulative frequency graph for hours of TV watched. I then created one for BMI and compared the two. They are included after this paper.

Looking at the two graphs, we can see a trend. Both graphs start with a steep jump, then level out almost completely, then at the end they rise up sharply in the last few people. The similarities of the graphs definitely show a trend; a small positive correlation between BMI and hours of TV watched per week.

Next, I drew box and whisker diagrams of the two graphs:

These two show different results. Both show a small gap at the start and an extreme gap on the right of the box, the BMI shows a negative skew, and the hours of TV watched shows a positive skew. If anything, this could indicate that there are less people with a higher BMI, but they watch more TV, resulting in the skewness of the diagrams. These along with the other diagrams strengthen my theory of BMI and hours of TV watched. Overall, these diagrams show a trend in BMI and hours of TV watched, albeit a small one.

I decided not to do a histogram as there were very few people with the same BMI, so the bar widths would be the same for almost all of them, and you wouldn’t be able to see a correlation. I still wasn’t convinced my results were reliable, so I decided to use Spearman’s Rank Correlation formula to check if my hypothesis was right. I got the following results:

Since the result is between 0 and 0.5, it shows there is a weak positive correlation. This shows there is a link between people’s BMI and their hours spent watching TV: the more they watch TV, the higher the BMI. This is a very weak correlation, but it proves my theory fully.

Overall these results do show a trend. It is a trend that supports my initial theory, but this evidence could be far more reliable. From the frequency table we can see that a large group of people make up most of the BMI, the group of 16-20 in the BMI make most of the results. The dispersions of each year and gender show that in Year 9 males appear to peak at TV watching, and then drop again in years 10 to 11 and females watch the most TV in year 7 then drop nearer the average in later years, raising a small amount in Year 11. The bar graph and scatter graph shows us there is a small positive correlation between BMI and hours of TV watched, but only a small one. The cumulative frequency graph shows a trend in the data sets of a slump in the middle years, a large rise at the end and a small jump at the start. These graphs and charts show that there is a link between BMI and hours of TV watched, but only very small, and only for a few years, proving my hypothesis half right. The Spearman’s Correlation result shows my theory was right and proved it. My hypothesis was that as there was an increase in BMI there was an increase in hours of TV watched (which there is), but it is negligible, leaving my results open to counter-arguments. Also, it is only right for the middle years (8, 9 and 10 mostly), showing as people get older their TV habits change. Overall however there is a small increase in BMI according to the more TV hours watched. Teenagers are also experiencing growth spurts during their teenage years, increasing their BMI quickly, and rounding off around 15 or 16. The sampling I took (stratified) was a good sampling, but it was only just over 5%, and more could be taken for better results and less chance of bias. Also, the topic could have been better. For example, instead of exploring hours of TV and BMI (which there is unlikely to be a link between in thousands of people), I could have investigated method of travel, distance from school, and BMI, which could have proved more conclusive. My results aren’t conclusive as they do not show a correlation either way in great size, and could be left open to interpretation. There are however a large amount of results and they do show a small correlation, which is better than none at all.