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  • Level: GCSE
  • Subject: Maths
  • Word count: 8468

Although I have noticed a trend between height and weight it is not completely clear, this may be because the data is rather biased.

Extracts from this document...

Introduction

Although I have noticed a trend between height and weight it is not completely clear, this may be because the data is rather biased. For my first part of the investigation I used data of 30, although I did use separate girls and boys data, it is not completely reliable as it was a mixture year groups. Looking at the data now, I can see that there is not many year tens or elevens, the older people who I feel will be heavier and tall than the year groups who appear frequently in the sample, year sevens and eights, the younger ones. This shows the original samples to be a biased sample. To eliminate this bias I have taken a 10% sample for each year group and also the different sexes within the year groups, giving me ten different sets of data. I predict to see that there will be a much clear trend between height and weight between girls and boys, it will be much clearer to see that boys are taller than girls and boys also weigh more than girls. To do this I will draw cumulative frequency tables for the girl's heights and weights, and then the same for the boys for the year seven data. Then I will transfer the data on to cumulative frequency graphs and compare the data. I will repeat this for all of the year groups. Year 7 Height Girls Height (cm) Tally Total Cumulative Frequency < 130 / 1 1 < 140 // 2 3 < 150 //// 4 7 < 160 //// 5 12 < 170 // 2 14 < 180 / 1 15 Boys Height (cm) Tally Total Cumulative Frequency < 150 /// 3 3 < 155 //// 4 7 < 160 / 1 8 < 165 //// // 7 15 The cumulative graph I have drawn from the data shows both the boys and girls data. ...read more.

Middle

Weight Girls Weight Tally Total Cumulative Frequency < 50 // 2 2 < 55 //// 5 7 <60 // 2 9 Boys Weight Tally Total Cumulative Frequency < 40 / 1 1 < 50 / 1 2 < 60 //// 4 6 < 70 //// 5 11 The cumulative frequency graph I have drawn shows the curve for the girls to be very steep and almost straight, this shows that the girls weigh about the same weights. The curve for the boys is curved at first, this shows a steady increase in the number of people at that weight; it then gets steeper. I will now find the mean, mode and range, and then using the graph I will find the median and quartiles. Mean Girls: 54kg Boys: 58kg To find the mode I will draw a stem and leaf diagram, as this will set out the data in an easier to use layout. Girls 4 8 5 0 1 2 5 5 5 8 6 0 Boys 4 0 5 0 2 6 8 6 0 2 4 4 4 7 0 Mode Girls: 55kg Boys: 64kg Range Girls: 60-48=12kg Boys: 70-40=30kg Median (Q2) Girls: 52kg Boys: 60kg Lower Quartile (Q1) Girls: 50kg Boys: 52kg Upper Quartile (Q3) Girls: 54kg Boys: 65kg Inter Quartile Range Girls: 54-50=4kg Boys: 65-52=13kg By using the cumulative frequency graph I have drawn I can pick a girl at random and by using the curve of best fit I can see that the probability of her weighing between 50kg and 60kg is 0.8. After taking the mean, mode and median I can see that all of the three measures of average in the sample were higher for boys than the girls. The sample for the boys was spread out more than the girls, with a range of 12kg, compared to 3kg for the girls. The evidence from the sample suggests that 7 out of 9, or 78% of the girls weigh between 50kg and 60kg. ...read more.

Conclusion

165 8.88 5.5 Girls 161 7.44 9.33 Final Summery A sample of 30 students stratified over age and gender shows a mean height of 169.93cm for the boys and 149.13cm for the girls. However the range of heights for the boys was considerably greater than that for the girls. This suggests that there will be many boys who are shorted than 149cm, the girls mean height. A 10% sample of boys in year 7 suggests that this year group of boys has a mean height of 153cm with a mean deviation about that mean of 5.2cm. My evidence suggests that the girls in this year group have a mean height of 149cm with a mean deviation about this mean of 9.73cm. The deviations for these two only differ by 4.53cm, so I can fairly conclude that the boys in year 7 are in general taller than the girls. This conclusion is supported by the evidence gathered from 10% samples in other year groups. The 10% sample means that the sample sizes for years 9, 10 and 11 were particularly small, especially when compared to the 10% samples for years 7 and 8. There is a positive correlation between height and weight both across the school as a whole and within each year group. The correlation appears to be stronger when individual year groups and separate genders are considers, as opposed to when a stratified sample is used to represent the school as a whole. Over the full range of heights, there is evidence to suggest that a line of best fit is not the most suitable model to describe the relationship between height and weight. Further sampling and analysis could determine whether a curve of best fit would more accurately describe the relationship. However I can fairly conclude that there is a connection between height and weight; the taller the person is, the more they weigh. I have also found out that age and gender are connected to how height and weight are linked. ...read more.

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