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For my coursework I will be doing an investigation of the heights and weights at Mayfield High School.

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Introduction

Mathematics Coursework For my coursework I will be doing an investigation of the heights and weights at Mayfield High School. This is fictuous Data and I will be taking a stratified Sample of 60 Pupils that will be representative of the whole school. I will be using 60 because it is an easy number to graph and to make into cumulative frequency graphs. Also it is a better number to average and it will not be too hard to do things with. I will be trying to see if the height of boys increases more than the heights of girls. I will do this by working out all of the averages and I will also make some histograms and cumulative frequency graphs. To take a stratified sample of the boys and the girls I started by working out how many of each strata to take. This is the original numbers of Pupils in the 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 To get a stratified sample of this group I will take the number in the year and divide it by the total number of pupils then multiply that by the total sample size which is 60 Boys Girls Total 7 151/1183 X 60 131/1183 X 60 282 8 145/1183 X 60 125/1183 X 60 270 ...read more.

Middle

is as Follows: Heights Boys Girls Total Boys Total Girls Total Total Total 130<H<140 140<H<150 150<H<160 160<H<170 170<H<180 And For Weights: Weights Boys Girls Total Boys Total Girls Total Total Total See Histograms From these histograms you can draw the conclusion that the boys and the girls are in a standard distribution about the middle of the data and you can see that in both the modal group is 150<H<160. Because of this you know that most of the boys and the girls fall into this category. From the two histograms you can see that the mean averages are already strained as it shows that there are taller boys in the year than girls but there are also some shorter boys in the year. There are more girls in the middle group and they are more compressed into a shorter range than the boys are. See Frequency Polygon From this frequency polygon you can see that the girls are much more even in their distribution than the boys and you can also see that they are taller in the centre group. Because the boy's line is very jagged it shows that there is a greater variation of the number of boys in each group and that there are some boys that are taller than the girls Stem and leaf Diagram for Boys Heights Stem Leaf Frequency 130 2,5,8 3 140 0 150 0,0,2,2,2,2,3,4,5,8,8 11 160 ...read more.

Conclusion

These are put into the table below. Heights Median Lower Quartile Upper Quartile Inter Quartile Range Mixed 157.5 152 166.5 4.5 Boys 158 152.5 167.5 5 Girls 157 152 165.5 5.5 From this information we can draw the conclusion that the boys are taller than the girls. As there is a higher IQR on the girls than on the boys there are almost certainly some girls that are taller than the tallest boy and some really short boys. There is a higher median for the boys than the girls and this shows that there are taller boys than there are taller girls. See Box and Whisker Diagrams From the box and whisker diagrams you can see that there is almost no difference in the IQRs and the way that the values are distributed. From all of the data that I have produced you can see that there is almost no difference in the average heights of boys and girls. However I have used all of the data from the whole school. If I were to only use Y7 and Y11 data and compare that then my results maybe very different. Also I know that the girls sample is not very representative by the fact that there is no correlation in the scatter diagram. Matthew Abraham Maths Coursework 01/05/2007 ...read more.

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