Study an excel spreadsheet which has various details about students and use this information in order to come up with a suitable hypothesis which will provide interesting results.

How:

I am going to show my comparisons using a number of graphs showing the correlation between weight and height of year 7 boys/girls and year 11 boys/girls. I will use scatter graphs in order to display my results for analysis. I am going to do a graph for each sex in each year and then compare them with each other.

I will use these graphs because I believe that they will be the best way to show the correlation most clearly. I will use best fit lines to show a positive/negative correlation. I will also look at the average ratio of weight to height between the boys and girls, and estimate the year's average and compare it with year 11.

The samples I took were as follows:

I got my sample by using Excel's randomising routines to pick a random sample of 35 members from each group (year 7 boys, year 7 girls, year 11 boys, year 11 girls)I have decided to compare each set of results with each other because if I just compared the year 7 boys with the year 7 girls I predict that there would be a huge difference between them . I think that girls seem to generally mature more quickly than boys, which shows that they must grow earlier, so the sample of boys in year 7 would not have reached their full height and weight. I am going to compare my results using scatter graphs and then commenting on the correlation.

I think the chosen samples are good because they seem quite varied and weren't biased because I used the random sampling technique mentioned above. There weren't any obvious other factors which would affect height and weight provided in the data sheet. If there had been I would have ensured that each sample contained a certain percentage of pupils who were affected by these factors people with those factors. For example if 40% were smokers I would make sure that 40% of my sample were also smokers

I will compare my graphs by firstly looking at the comparison between the different correlations of the graphs and then by working out the average (mean) of each sex/year and then comparing them.

Graphs:

Findings:

In year 7 I have found that there is a definite difference between the weight and height of the girls and the boys. I have shown this by working out the average weight to height ratio for each sex in year 7. My findings were that the boys' average weight to height ratio was 27.93(2dp) and the girls' was 28.33(2dp). As you can see the average girl in year 7 is larger than the average boy in year 7 so this backs up my hypothesis.

In year 11 I have found that there is an obvious difference between the weight and height of the girls and the boys. I have shown this by again working out the average weight to height ratio for each sex in year 11. My findings in this year were that the boys' average weight to height ratio was 33.74(2dp) and the girls' was 26.78(2dp). As you can see the average boy in year 7 is significantly larger than the average girl in year 11 unlike in year 7. This again backs up my prediction that the boys would have caught up with the girls and even overtaken them.

There is a significant increase in the weight and height of the boys between year 7 and year 11.

There is actually a minor decrease in the weight and height of the girls between year 7 and year 11.

I then went on to compare year 7 as a whole group with year 11 by using the combined average of girls and boys in the two years.

Year 7 girls have an average height of 1.55 m(2dp)

Year 7 girls have an average weight of 45.26 kg(2dp)

Year 7 girls have an average weight to height ratio of 28.33 kg per m(2dp)

Year 7 boys have an average height of 1.55 m(2dp)

Year 7 boys have an average weight of 44.51 kg(2dp)

Year 7 boys have an average weight to height ratio of 27.93 kg per m(2dp)

Year 7 have an average height of 1.55 + 1.55 ÷ 2 = 1.55 m(2dp)

Year 7 have an average weight of 44.51 + 45.26 ÷ 2 = 44.89 kg(2dp)

Year 7 have an average weight to height ratio of 27.93 + 28.33 ÷ 2 = 28.13 kg per m(2dp)

Year 11 girls have an average height of 1.59 m(2dp)

Year 11 girls have an average weight of 43.31 kg(2dp)

Year 11 girls have an average weight to height ratio of 26.78 kg per m(2dp)

Year 11 boys have an average height of 1.72 m(2dp)

Year 11 boys have an average weight of 60.49 kg(2dp)

Year 11 boys have an average weight to height ratio of 33.74 kg per m(2dp)

Year 11 have an average height of 1.72 + 1.59 ÷ 2 = 1.66 m(2dp)

Year 11 have an average weight of 43.31 + 60.49 ÷ 2 = 51.90 kg(2dp)

Year 11 have an average weight to height ratio of 33.74 + 26.78 ÷ 2 = 30.26 kg per m(2dp)

From these results my findings are that in year 7 the average height of the girls and the boys is exactly the same- 1.55m. This shows me that girls' and boys' heights both develop at the same rate up to this age. When I looked at the weights I found that the girls average weight was heavier than the boys by 0.75kgs heavier. This shows me that although their heights are similar, the girls body mass is greater than the boys so therefore the girls average weight to height ratio will be larger than the boys. I think this is because the girls are developing earlier than the boys, which is reflected in their heavier body mass.

My findings in year 11 are that the average height of the boys is more than the girls, they're taller by 0.13m. When I looked at the average weights I found a very large difference between them, the boys are in fact now 17.18kg heavier than the girls. I think this is my most significant finding and is probably because the boys have matured physically and their body mass has bulked up and the girls on the other hand have not changed much at all because they have already matured physically in year 7 and are now perhaps under even more social pressure to be slim. This is once again obvious when I looked at the average weight to height ratio which tells me that a boy who was 1 metre tall would have a weight of 33.74kg whereas a girl of 1 metre would only have a weight of 26.78kg, which is in fact lower than the ratio of the girls in year 7. When I looked at the average height difference between the girls in year 7 and year 11 they had in fact grown very little just 0.04m, so their weight to height ratio must have also dropped significantly and it had by 1.55kg per m which shows again the drop in body mass of the girls between years 7 and 11. When comparing the average height of the boys there was an increase of 0.17m from year 7 to year 11. This shows that by year 11 they have matured physically and the girls results seem to back up my hypothesis that they had already matured. Since the boys average height has increased you'd expect the average weight to increase too which it did by 15.98kg. I believe this was once again due to their bodies maturing and their body mass bulking up in relation to their height growth. This is also reflected in their average weight to height ratio which has increased by 5.81 kg per m which means that a boy of 1 metre in height in year 7 weighed 27.93kg and a boy in year 11 who was 1 metre high weighed 33.74kg.

When I looked at the comparison between year 7 and 11, I found that the average height had only increased by 0.11m by year 11. I'd expected to have a minimal increase between year 7 to 11 because lots of the girls wouldn't have increased in height because they've already physically matured and this also counteracted the increases in the boys height. The average weight difference between the two years was 7.01kg this was affected by the same factors as the height and therefore the average height to weight ratio would be affected as well. The increase in average weight to height ratio between the two years was 2.13kg per m which was higher than the average girl results but lower than the boys.

Year 7 average ratio = 27.92797337(boys) + 28.33053809(girls) = 56.25851146 ÷ 2 = 28.12925573 = 28.13(2dp)

Year 11 average ratio = 33.73745412(boys) + 26.7814197(girls) = 60.51887382 ÷ 2 = 30.25943691 = 30.26(2dp)

These average combined ratios show that there is a minor increase between the two years but it isn't as significant as I'd expected.

As I wanted to get a more accurate average ratio of year 7 I decided to take the average of the boys (27.93) and multiply it by the total number of the boys in the year(150, not just my sample) and do the same with the girls (average 28.33, 131), then add them together and divide the total by the number of pupils in the year(281).

= ((27.92797337 X 150) + (28.33053809 X 131)) ÷ 281 = 28.11565 = 28.12(2dp)

This was more accurate because in my sample I used the same amount of boys and girls but in the whole database there were more boys than girls.

I am going to repeat the process above but with the data from year 11 instead.

((33.73745412 X 83) + (26.7814197 X 85)) ÷ 168 = 30.21803 = 30.22(2dp)

This was almost the same result as using the first method because there was only a difference of 2 in the total number of boys and girls in the year.

If there is a bigger Weight to height ratio it means a pupil whose height is 1 metre will weigh more than someone whose height is 1 metre but has a smaller weight to height ratio.

Graphs analysis:

Year 7 girls graph has a very weak positive correlation because the points are quite spread out around the line of best fit and some of the points are so extreme they do not fit.

Year 7 boys graph has an extremely weak positive correlation because the points are very spread out around the line of best fit and there are even more points that are so extreme which don't fit.

Year 11 girls graph has an even more extreme weak positive correlation because the points are at various distances around the line of best fit and there are two points which don't follow the general trend at all.

Year 11 boys graph has a weak positive correlation but out of the four the strongest correlation because the points are much more clustered around the line of best fit.

I think that the points which did not fit the general trend were because I took a non-biased random sample, so there were bound to be some exceptions to the general trend.

Evaluation:

If I was going to repeat this investigation I don't think I could have improved my results in any way with the given data. The only way I could have got more accurate results would be if I had more information on the sample I had taken at year 7 which I could follow through to year 11, then my findings would have been more successful because I would be more certain about the results because I would have been using the same pupils. To improve my sample I could have chosen the number of boys and girls I used in direct proportion to the number of girls and boys in the year, then my averages would be more likely to be accurate.

I could also have changed the way I represented my findings because my graphs weren't very conclusive, for example I could have used histograms as well as scatter graphs because I think they would be easier to interpret. I could also have used a box plot diagram to represent my data for each sex and year because they're really easy to compare one another.

Conclusion:

The graphs and my data has given evidence that my hypothesis is true because I thought that in year 7 the boys would be smaller than the girls but by year 11 they would be larger than the girls and my results show that this is true. The one thing that I hadn't realised was that the girls' average weight to height ratio would have dropped by such a significant amount but I had expected the boys average weight to height ratio to have increased by such a large amount.

Sebastian Jacobs 11S