# Mayfield High. I am going to investigate the relationship between the height and weight of the pupils. I will be investigating how height and weight affect each other. For example, if an increased height means an increased weight.

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Introduction

## Coursework: Mayfield High

Mayfield High: Maths coursework

I am going to investigate the relationship between the height and weight of the pupils. I will be investigating how height and weight affect each other. For example, if an increased height means an increased weight.

Before I begin, I predict that the correlations for all of my graphs will be positive. The reason for this prediction is because I know that as your height increases so does your weight.

After deleting what I found, I deleted all columns except for ‘Year group’, ‘Gender’, ‘Height’ and ‘Weight’ on both the ‘KS3’ and ‘KS4’ sheets on the excel, since they were not needed to work out the relationship between height and weight. Then, using the above table, I calculated 40% of each of the numbers inside it, for example, Year 7 girls: 131 x 0.4 = 52. The reason that I chose to use a sample of just 40% is because using all of it would clutter my graphs too much. I did, however, want of all my samples to be above 30, as this would provide enough information to create the graphs. From this I counted the resulted number of people of each gender and year group and coloured them red, deleting the rest, as they were not needed. The reason for this is because I am using a stratified random sample; this is because it collects a certain percentage of each section that gives a good estimate to represent everyone’s views. A stratified random sample helps to avoid bias.

Middle

There are no outliers worth deleting.

Correlation:

=CORREL(S6:S251,T6:T251)

=0.635105

The value 0.635105 tells me the correlation of this graph is also positive, and quite strong. It forms more of a straight line than the graph for the ‘Height & Weight of all girls’ does.

The boys’ correlation, since it is quite strong, represents a stronger relationship between the heights and weight of the boys. This makes it easier to work out the weight of a boy if it was unknown by looking at his height.

However, as the girls’ correlation wasn’t very strong, it is harder to work out the weight of a girl, if it was unknown, by looking at their height.

Therefore a stronger correlation makes data easier to work out.

Earlier, I predicted my results would be of a positive correlation, and I was correct; both of the graphs lean in a positive direction, and the numbers I obtained from excel show positive correlations.

Since my hypothesis was correct, I will go ahead and make a new one. This time I predict that as the year increases, the correlation will become stronger, displaying higher values. I am making this prediction because I think that right in the middle of adolescence (year 11), I think there will be more balanced heights and weights.

I will now measure the co-efficient of each of the years to help me find out if my hypothesis is correct.

Year 7: 0.532377

Year 8: 0.453785

Year 9: 0.379894

Year 10: 0.279076

Year 11: 0.780212

Conclusion

An example of a positive skew is the box plot for year 9 boys. This implies that the curve for this diagram (if sketch out onto a cumulative frequency diagram) would be steeper at first, but would start to reach the right of the graph towards the last part of the data.

An example of a negative skew is the box plot for year 10 girls. The interquartile range here is quite small but the whiskers are quite long, so the curve would look strongly vertical in the middle.

Conclusion

After investigating the relationship between height and weight using scatter diagrams, and then finding out how height is affected by age, the information I received back from the project reinforced what I already knew. I was aware that year 11s are taller than year 7s, and this proved that with numbers. It also taught me general things that happen to the bodies of the children as they grow, as stated above.

However, I could further my investigation by creating box plots for weight, and exploring how this is affected by age too. I could have also created cumulative frequency curves that reflect the shapes of the box plots, so that I have information of how height is affected by age in two different kinds of graph.

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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