# Statistics maths As height increases weight also increases.

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Introduction

INTRODUCTION The aim of this investigation is to produce a statistical investigation of students from a fictitious school, Mayfield High School. However, the data presented to us is based on a real school. I have chosen to observe the 'relationship between height and weight.' I will look into the following hypothesis: * As height increases weight also increases. * Height and weight increase with age. * Males are taller and heavier than females. OBTAINING THE SAMPLE Below is the data provided, it shows the total number of males and the total number of females in each year group. It also shows us the total number of students in each year group, as well as showing the total number of students in the school. 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 = 1183 Firstly, from the data provided I have to obtain a sample of people whose details I will work with throughout the investigation. I have decided my sample will be of 60 pupils altogether consisting of 30 males and 30 females. I will take a sample from the data as handling all the data provided will be highly time consuming, seeing as there are 1183 students in the whole school. As the number of pupils in each year group is generally high, I will investigate a small proportion from each. To get the sample I will use stratified sampling to make sure I get an equal amount of both genders and also an even proportion of people from each year group. ...read more.

Middle

93 1.96 30 30 0 0 FEMALES Weight Height Height Rank Weight rank D D2 33 1.25 1 1 0 0 55 1.41 2 26 -24 576 38 1.47 3 3 0 0 56 1.47 4 28 -24 576 47 1.48 5 12 -7 49 40 1.49 6 4 2 4 52 1.50 7 22 -15 225 48 1.51 8 17 -9 81 47 1.52 9 13 -4 16 47 1.54 10 14 -4 16 36 1.55 11 2 9 81 42 1.55 12 6 6 36 45 1.56 13 9 4 16 47 1.56 14 15 -1 1 53 1.57 15 23 -8 64 40 1.58 16 5 11 121 50 1.59 17 19 -2 4 55 1.60 18 27 -9 81 45 1.61 19 10 9 81 54 1.61 20 24 -4 16 44 1.63 21 8 13 169 48 1.67 22 18 4 16 46 1.69 23 11 12 144 54 1.69 24 25 -1 1 47 1.70 25 16 9 81 50 1.70 26 20 6 36 42 1.71 27 7 20 400 51 1.73 28 21 7 49 57 1.75 29 29 0 0 58 1.80 30 30 0 0 The rs values for both sets of data are higher than the critical value, 0.3063, for n= 30 at a 0.05 significance level. As the rs values are higher than the critical value the correlation between height and weight is confirmed. The correlation values, as well as the line of best fit on the scatter graphs, show males height and weight correlate more positively than the females. I will now look into my second hypothesis, 'height and weight increase with age.' ...read more.

Conclusion

This tells us that males generally weigh more than females. Standard deviation values support the information obtained from the box plots of males' height and weight having a wider range than females' height and weight. They show that males' height and weight are much more dispersed (spread out) than females' height and weight, as the standard deviation values obtained are higher in both cases. The values of standard deviation that I have obtained are summarized below. These values I obtained using a calculator in the 'sd' (standard deviation) mode, in which I stored the appropriate data and then pressed 'shift' '2' in order to get the standard deviation value. MALES Weight Standard Deviation = 12.3583530007 = 12. 36 (2.d.p) Height Standard Deviation = 0.11357621034 = 0.11 (2.d.p) FEMALES Weight Standard Deviation = 6.26994595051 = 6.27 (2.d.p) Height Standard Deviation = 0.11126345112 = 0.11 (2.d.p) CONCLUSION In conclusion to my first hypothesis, as height increases weight also increases, I found enough evidence to suggest this was true by carrying out bi-variate analysis, as well as using the Spearman's rank method to find the correlation coefficient of the resulting graphs. My second hypothesis, height and weight increase with age, was supported with evidence which I obtained by finding regression lines to graphs showing height or weight against year group. As for my third hypothesis, males are taller and heavier than females, this was also backed up with evidence. The evidence to back this statement I found by comparing data means, producing box plots and also by finding standard deviation values to support the box plots. Overall, all my hypothesis were supported with statistical evidence from a variety of statistical tests. However, I could improve this investigation by taking a higher sample of people from the school. ?? ?? ?? ?? Bharat Patel 10N ...read more.

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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