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• Level: GCSE
• Subject: Maths
• Word count: 2098

# The correlation between height and weight.

Extracts from this document...

Introduction

Harriet Walden.

Maths investigation: Mayfield High School.

Mayfield is a fictitious high school but the data presented is based on a real school.

The data is secondary and I am reliant on Edexcel for its validity. There are a total of 31941 datum points, because of such a huge database I am going to select only some points to develop a statistical investigation.

I have chosen to investigate the correlation between height and weight.

I will sort the data into what is relevant to my specific investigation and what is not. I will hide the irrelevant data, which is everything except the year group, gender, height and weight.

I expect the lower years to be shorter and lighter on average than those in the higher years. After grouping the data into year groups I will assign each pupil a number. I will take 30 stratified samples from the whole school. I have chosen to use stratified sampling because each year group is represented proportionally to their occurrence within the whole school. This means that I the results I obtain should show accurately the general trend in height and correlation throughout each year group. Without the sampling being stratified I could end up 30 samples all from the higher end of the school with none of the lower school represented.

I will use the formula:

Middle

The line of best fit confirms that there is a positive correlation, however there are a few outliners and I have ignored these when I drew my line of best fit so I could have a more accurate diagram. I did use include all the data in my calculation for the mean.

To achieve a more precise diagram I need to separate the random sample into two categories: male and female.

I took 30 stratified samples for females, and then for males.

Below is the table that shows how I worked out the 30 samples using a similar formula to previously mentioned, except I had to discount any boys so the formula became:  number of girls in year               x number of the samples

Total number of girls in school

 YEAR NO. OF FEMALES SAMPLE SIZE ROUND FIGURE RANDOM NO.FROM CALC. 7 131 131 / 579 x 30 = 6.78 7.00 103.00 23.00 19.00 60.00 77.00 71.00 79.00 8 125 125 / 579 X 30 = 6.48 7.00 129.00 213.00 254.00 222.00 138.00 178.00 143.00 9 143 143 / 579 X 30 = 7.41 7.00 299.00 398.00 389.00 330.00 263.00 280.00 366.00 10 94 94 / 579 X 30 = 4.87 5.00 441.00 426.00 474.00 449.00 421.00 11 86 86 / 579 X 30 = 4.46 4.00 529.00 570.00 558.00 541.00

From this table I drew another table to show the 30 female pupils whose numbers were produced by the calculator.

From the results on the table I plotted another scatter graph to show the correlation between height and weight in females. This scatter graph shows a more precise representation of heights and weights, as it is gender specific. The reason for this is that females are generally shorter and lighter than males. This will be shown later.

Conclusion

These points are labelled on my cumulative frequency graph as follows:

Lower Frequency Q1

Median Q2

Upper quartile Q3

By taking the quartiles and median that I found from my cumulative frequency curve I could plot a box and whisker diagram. From this you can clearly see that the both the lower and upper quartile, and the median on the males diagram is higher than that of the females showing that males are taller on average. The range of the females is larger than the boys although both upper ends of the range are 180cm. This shows that some girls are as tall as boys are, but this may be due to results being to the extremes as the quartile range is lower than the boys.

From this investigation I have concluded that there is a positive correlation between height and weight, in both males and females. By developing my results and plotting scatter graphs and working out the gradient of the line of best fit I could show that boys were generally heavier and taller than girls. This matched my initial predictions and was confirmed when I plotted a cumulative frequency curve and box and whisker diagram. The box and whisker plot showed the medians and ranges, which helped compare the genders more effectively. This confirmed that males were generally taller and heavier than females.

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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