# My first prediction is that as the height of a child increases so will the weight because it is logical that if a person is taller there will be more mass and therefore the person will weigh more.

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Introduction

Maths Coursework

Using the data provided in the Mayfield High School data sheet I have decided to investigate the relationship between height and weight in both boys and girls from year seven through to year eleven.

The data sheet provides lots of other figures other than height and weight but I have chosen to use these values because they are both examples of continuous data that can be plotted well on a graph and can be easily compared.

Hypothesis 1

My first prediction is that as the height of a child increases so will the weight because it is logical that if a person is taller there will be more mass and therefore the person will weigh more.

To investigate this hypothesis I will plot all the data of height and weight of the whole school as a scatter graph and if the correlation is positive this will prove my hypothesis

Hypothesis 2

My next prediction is that as the year increases so will the average weight and height because the children are still developing and so as they get older they will grow taller therefore gaining weight.

To investigate this hypothesis I will find an average height and weight for each year and plot them on a scatter graph. If the graph has a positive correlation this will prove my hypothesis to be correct.

Hypothesis 3

Middle

Comparing the gradients of the graphs also backs up the hypothesis as they can clearly be seen increasing with age.

The largest increase in height and weight was between year nine and year eleven. This is clearly visible from looking at the difference in the position of the bulk of points on both graphs and the difference in gradients. This radical change in height and weight between these two years could be because between the ages of 13 to 16 is when most teenagers reach puberty and therefore develop much faster than normal gaining height and weight.

These box plots further illustrate the progressive increase in height and weight between the years. The main box shows the main body of students with the central line being the median. In both the graphs the main body clearly progresses along the graph as the years increase indicating an increase in weight/ height as I predicted.

The mean values also help to show the steady increase in height and weight as age increases.

The extremes of the box plots show the span of data and in the box plots to show height these also seems to steadily progress indicating that all the student gained in height however in the box plots to show weight the box

Conclusion

This stem and leaf diagram accurately shows that the girls weighed more than the boys in year seven. This is shown by the fact that there were more numbers after the number 5 for the girls indicating more girls weighed in the 50 kg range than boys.

This diagram shows how boys start to overtake the girls in weight in year nine because more of the numbers on the boys side are further down indicating a larger weight.

This final diagram shows the full transformation and reversal of the distribution of weight clearly showing how the boys have overtaken the girls in weight therefore proving my hypothesis to be correct.

This investigation has proved to be a success and all my hypothesis were proved correct. Using the data from such a large school made sure the data was fair and stratifying the data was successful in bringing down the sample size to a useable amount whilst keeping it fair however there were some areas of the investigation that could have been improved.

Using different schools from other areas could have an effect on the data because Mayfield high school may have been in an unusually affluent area meaning that the children are more likely to eat well or from a less affluent area where food is generally unhealthier.

Also because the data was secondary there could be some anomalous data because it was not directly recorded by me this could have had a minor effect on my investigation.

Josh Blakeley

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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