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  • Level: GCSE
  • Subject: Maths
  • Word count: 10614

The relationship between height and weight - Mayfield High School.

Extracts from this document...

Introduction

At a Mayfield High School Introduction This investigation is based upon the students of Mayfield High School, a fictitious school although the data presented is based on a real school. The total number of students in the school is 1183. Year Group Number of Boys Number of Girls Total 7 151 131 282 8 145 125 270 9 118 143 261 10 106 94 200 11 84 86 170 TOTAL 604 579 1183 The line of enquiry I will choose will be the relationship between height and weight; I will use all of the students in school and begin by taking a random sample of 30 boys and 30 girls to see all the possible relationships. From the total number of students, I will choose 60 altogether. I will then analyse the sets of data I have in order to investigate the relationship between them. I will begin by taking a random sample of 60 students, 30 boys and 30 girls and record their heights and weights. I will choose 30 boys and 30 girls so that both genders are the same and the data I have chosen is fairer. The way I shall take a random sample is to use the random number button on my calculator. All the 1183 students are numbered from 1 to 1183. I will press the SHIFT button then the RAN# button in order to give a completely random number. The number displayed is between 0 and 1 and because I need a number between 1 and 1183, I will multiply the number displayed on the computer by the total number of students which is 1183. I repeated this 30 times for girls and then 30 times again for boys. Now I have a random sample of 60 students from Mayfield High School. Random Sample This is my random sample of boys and girls of Mayfield High School. ...read more.

Middle

This tells me that there is a better relationship between height and weight for girls more than boys. Conclusion from random sampling > There is a positive correlation between height and weight. In general tall people will weigh more than smaller people. > The points on the scatter diagram for the girls are less dispersed about the line of best fit than those for boys. This suggests that the correlation is better for girls than for boys. > The points on the scatter diagrams for boys and girls are less dispersed than the points on the scatter diagram for mixed sample of boys and girls. This suggests that the correlation between height and weight is better when girls and boys are considered separately. > I can use the scatter diagrams to give reasonable estimates of height and weight. This can be done either by reading from the graph or using the equations for the line of best fit. > The cumulative frequency curves confirm that boys and girls have quite a close height and weight, with girls being slightly higher in weight and boys slightly higher in height. > The median for boys is higher in height and the median for girls is higher in weight. > From the box and whisker diagrams I can conclude that, in general boys are taller than girls, but not exclusively so. The cumulative frequency curves can be used to estimate that 23% of girls have a higher height than 172 cm, the upper quartile height of boys. > Also from the box and whisker diagrams I can conclude that in general girls weigh more than boys but not exclusively so. The cumulative frequency curves can be used to estimate that 23% of boys have a higher weight than girls above 60 kg. This could also be a result of my sampling which has more students from year 7 and 8 then 9, 10 or 11. ...read more.

Conclusion

There is not much of a difference if they are considered mixed either. > The standard deviation showed me that the mean isn't a reliable way of interpreting my data. > The product-moment correlation coefficient shows that the correlation between height and weight is stronger for girls than for boys. Final conclusion > In general the taller a person is, the more they will weigh. > There is a positive correlation between height and weight. In general tall people will weigh more than smaller people. > The points on the scatter diagram for the girls are less dispersed about the line of best fit than those for boys. This suggests that the correlation is better for girls than for boys. Also, the points on the scatter diagrams for boys and girls are less dispersed than the points on the scatter diagram for mixed sample of boys and girls. This suggests that the correlation between height and weight is better when girls and boys are considered separately. > There therefore is a positive correlation between height and weight across the school as a whole. This correlation seems to be stronger when separate genders are considered > I can use the scatter diagrams to give reasonable estimates of height and weight. This can be done either by reading from the graph or using the equations for the line of best fit. > There is a better relationship between height and weight when people in the school are taken into proportion in each year. > I could have had a greater confidence in these results if we had taken larger samples. Also, my predictions are based on general trends observed in the data. In both samples there were exceptional individuals whose results fell outside the general trend. This coursework was both interesting and enjoyable to do although it was hard work. I have learnt a few things from this coursework such as standard deviation and product-moment correlation coefficient, both of which I had previously not known about. Kushal Patel KRIS MURPHY 1 ...read more.

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