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  • Level: GCSE
  • Subject: Maths
  • Word count: 4524

Mayfield High School

Extracts from this document...

Introduction

Mayfield High School I am investigating the pupils of Mayfield High School. It is a fictitious school, although the data is based on that of a real school. The line of enquiry I have decided to follow is the relationship between height and weight of the pupils. The following table shows the numbers of pupils in the school: Year Group Boys Girls Total 7 151 131 282 8 145 125 270 9 118 143 261 10 106 94 200 11 84 86 170 604 579 1183 Using this information, I have chosen to use a sample size of 30, as it is a large enough number to get a fair representation of the population, and divides fully into 360 in the event that I would need to draw any pie charts. To begin with this line of enquiry, I shall take a random sample of 30 boys and 30 girls from the whole school register, recording their heights and weights. In order to do this I will allocate each student a number, generate random numbers using my calculator, and take the data of the corresponding student. Boys Girls Height (cm) Weight (kg) Height (cm) Weight (kg) 162 48 132 35 141 45 130 36 153 40 173 51 146 53 150 40 147 47 159 38 147 45 142 29 158 48 152 33 165 50 159 52 154 40 166 50 173 59 149 47 164 42 157 45 160 41 171 40 155 68 163 47 154 48 155 66 132 48 160 60 152 38 165 45 155 74 161 38 172 42 169 48 170 50 162 54 170 57 151 39 157 64 154 68 168 64 157 40 152 45 153 65 162 52 190 40 169 65 174 47 180 68 179 45 168 58 163 48 152 38 133 55 152 45 178 55 170 72 159 48 In doing this I have encountered a few extreme values in the data that I have had to discard because they are seemingly mistakes in filling in the forms or entering the data into the database. ...read more.

Middle

The curves have enabled me to read off easily and accurately the median, upper and lower quartiles and the interquartile range. These are shown for both height and weight in the following tables. Heights (cm) Median Lower Quartile Upper Quartile Interquartile Range Mixed 160 154 167 13 Boys 159 153 168 15 Girls 159 153 168 15 Weights (kg) Median Lower Quartile Upper Quartile Interquartile Range Mixed 47 42 57 15 Boys 49 45 59 14 Girls 45 41 54 13 For height, the data for both boys and girls is very similar. They are both equally spread, discounting outliers in the lower and upper quartiles of values, and the median values are identical. This suggests that gender has little effect on height. However, there must be slight differences between the genders, as when the mixed population is considered the median is slightly raised, even though the interquartile range is smaller. In terms of weight, all the values were lower for girls than for boys, suggesting that girls weight less generally, and have a tighter distribution than boys. For example the median weight for girls is 45kg, 4kg less than the median weight for boys, and the range is 13kg compared to 14kg. This was also demonstrated in the box and whisker diagrams drawn to present the above data. The box plots show that the girls had higher and lower heights than the boys, but apart from that the diagrams are the same. This suggests that gender does not have an affect on trends in height. They also show that for weight, the lowest and highest values for boys (38kg and 74kg) were both higher than for the girls (29kg and 68kg). Also the interquartile range for girls was 1 cm less than for boys, so the girls' data is less widely spread. The cumulative frequency curves also enable me to make predictions of percentages of students with heights or weights within a certain range. ...read more.

Conclusion

boys in Year 7, and of all the boys in the stratified sample, the evidence suggest that considering the year groups in isolation gives a stronger correlation between height and weight. This mean of vertical dispersions of Year 7 boys was 8cm. The mean of vertical dispersion for all of the boys was 12.6cm, more than 1.5 times the mean of vertical dispersions of the Year 7 boys. Final Summary These are the final conclusions I have made from this investigation after extending the line of enquiry and refining my hypotheses. * A sample of 30 students stratified over age and gender shows that the mean height is 161 cm for both boys and girls. However, the range of heights was considerably greater for boys than for girls, which suggests that there would be many boys with a height smaller than the girls. * A 10% sample of the boys in Year 7 suggest that this age and gender has a mean height of 154 cm, with a mean deviation about the mean of 5 cm, excluding exceptional values. Comparing this to the stratified sample for the whole male sample, which has a mean height of 161cm and a mean deviation of 12.6 cm, the evidence suggests that both age and gender affects the strength of the correlation and there for accuracy in the approximation of the relationship between height and weight. In taking a stratified sample, I eliminated the bias of age, where the proportion of boys to girls and the different ages was not reflected in the original sample. Keeping the sample within the ratio of numbers in each age and gender, I have reduced the possibility of one category being represented more than another and therefore affecting the results. The consequences have been a more fair representation of the school's population, which theoretically will have contributed to the increased accuracy and reliability of the results and conclusions that I have drawn. ?? ?? ?? ?? GCSE Maths Statistics Coursework Hannah Napier ...read more.

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