# Height and Weight corralarion in boys and girls

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Introduction

Kauser Ismailjee 10H Maths Coursework

Maths Statistics Coursework

Introduction

For my statistics coursework I have chosen to study the hypothesis ‘The taller you are the heavier you weigh’. I expect to see that as the height of a student increases so does the weight, this means that a student weighing at 60 kg should be taller than a student weighing 40 kg; within this I will compare the differences between height and weight between boys and girls. I will be using real data from KS3 and KS4 students at Mayfield high school and comparing it to data from the internet. Firstly I will be conducting a pilot study of 30 KS4 pupils of which 15 will be girls and 15 will be boys, this will help me to see whether my hypothesis is correct and to determine whether there is any correlation at all. If my hypothesis does prove to be correct I will then go on to do a stratified sample of 60 students from Mayfield high, I will stratify them according to gender and year group. I will then put the data into separate graphs to show the difference between the correlation of height and weight between boys and girls. I will also work out the spearman’s rank correlation coefficient to help determine the strength of the correlation and compare my results. I will then compare the results of my scatter graph from published results from the internet of the height and weight of boys and girls. Finally I will use box plots comparing the height

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Stratified sample of Height and Weight

From the graph you can see that there is a fairly strong positive correlation between the height and weight of the stratified sample of the boys and girls combined, the line of best fit shows this clearly. To see the strength of the correlation I decided to use Spearman’s Rank Correlation Coefficient which is 0.47, this means it is fairly strong correlation. The way I did this was to first sort the data from highest to lowest and rank it from 1 to 60; 1 being the lowest and 60 being the highest. I then looked to see if there were any tied values in the data and when there were I added the ranks up of the tied values and divided it by the amount of tied data there was, so if there was 3 people that had the same weight of 60 kg and the ranks were 15, 16 and 17, I would add the ranks up to make 48 and dived it by 3 so the rank of the three peoples weight would be 16. I did this for both the height and the weight. After I had ranked the data I had to find the difference between each of the ranks between the height and the weight and then square it so if I had any negative values squaring it would make it positive. I then added all the squared values and multiplied it by 6. After that I had to divide the number by the amount of values there were altogether and minus 1 from the answer and then multiple the answer by the amount of values there are again. Lastly I had to minus 1 by the divided.

Conclusion

Conclusion

Overall I believe that I have proved my hypothesis ‘The taller you are the heavier you weigh’ true as all of the research I have done has shown that there is a definite positive correlation between the height and weight of students. All my graphs show that there is correlation including the research that was done from the internet show strong positive correlation. I found from both my stratified sample and the results from the internet that boys were overall more strongly correlated in height and weight compared to girls, I find these results very surprising as I had predicted the boys to have a weaker correlation than the girls due to the growth spurt they go through due to puberty but apparently I did not find this in my results this can be due to the simple fact that I may need to do more research and include a larger number of pupils in my sample. Although boys may be closely correlated the results were more spread out compared to the girls and they had a much larger range compared to the girls. Overall I am satisfied with my results and think I have successfully proved that the taller you are the heavier you weigh.

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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