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  • Level: GCSE
  • Subject: Maths
  • Essay length: 4124 words

Statistics Is there a correlation between 100m times and shot-put distances compared to BMI (Body Mass Index)?

Extracts from this essay...

Introduction

GCSE Statistics Coursework Introduction Project Title: Is there a correlation between 100m times and shot-put distances compared to BMI (Body Mass Index)? I plan to investigate the following: 1. Whether BMI ranking affects performance in 100m and shot put. I predict that people with a higher BMI, will perform better than people with low BMI in shot put, however I also predict that people with a low BMI will be perform better in 100m than shot put compared to people with a high BMI. 2. Is there a similar correlation between females and males in 100m and shot put performance? If so any trends I predict that boys will have an overall better performance at both events compared to females. Background Research Definition of BMI: BMI or Body Mass Index is a mathematical formula to access relative body weight. It is a ratio of height and weight, which determines approximately how much body fat a person has on their body. This can be used as a guide to weight levels and can establish whether a person is obese or not as it correlates highly with body fat. It is calculated as weight in kilograms, divided by the square of the height in meters or kg/m2 for short. I will use me as an example of how BMI is calculated; 65/1.72 = 22.49 The sections of weight categories are as follows : Underweight = <18.5 Normal weight = 18.5-24.9 Overweight = 25-29.9 Obesity = BMI of 30 or greater Data Collection In order to answer any of the above questions, I must first look at samples of select data from year 10 students. I will conduct the above in the following way: 1 I will take my sample from year 10 students, with 50% boys and 50% girls. I will be taking from only year 10 students as age will not be taken into account.

Middle

The data is clustered around certain areas and are in a flat line so to speak, which indicates that BMI has no real evident effect on performance. There is, however, a clear outlier in the female 100m times, again could be down to numerous factors - errors in recording, laziness etc. In order to see if there were any similarities between BMI and shot-put and 100m times, and between genders, it is clear that I would need to produce a box and whiskers graph. Male Female These two box and whisker graphs show 100m times and shot-put distances against BMI for both male and female gender types. For male BMI, we see that the median is slightly skewed to the left, and that the range is very wide on the right, making it fairly unsymmetrical. This is down to an outlier, most likely from an error in calculating BMI. However, for male shot-put, we can see an almost perfect symmetrical result, if only for the median which is once again skewed to the left slightly. The 100m results are similar to the BMI in terms of ranges and position of median, as the median is skewed to left, and the whiskers or ranges of the 100m are longer on the right, making it unsymmetrical. The long whiskers of the 100m data could be down to errors again or laziness. However for females, the BMI is much more symmetrical compared to males, and the median is much more central, with the whiskers quite close to the box indicating a close spread of data. The same can be said for shot-put distances, however the range is much more narrower than that of males, yet the median is skewed to the left as it is in males, which could indicate positive correlation between the two. However for 100m times, the data is very wide spread, with the right whisker extending much further out then what should be.

Conclusion

1.85 20.71585099 8.9 13.91 high 77.7 1.79 24.25017946 8.1 13.29 high 59.5 1.74 19.65253006 7.1 13.64 low 65 1.84 19.1989603 7.76 15.45 low 95 1.77 30.32334259 7.37 20.15 high 106.4 1.83 31.7716265 6.95 26 high 80.9 1.73 27.03063918 6.88 17.23 high 78 1.82 23.54788069 8.5 13.6 high 45 1.63 16.93703188 6.8 13.6 low 37 1.5 16.44444444 5.6 13.8 low 57 1.64 21.19274242 10.4 11.9 High 57 1.67 20.43816558 6.25 15.38 High 64 1.78 20.19946976 9.3 11.3 Low 40 1.56 16.4365549 5.15 13.84 Low 55 1.69 19.25702882 9.2 12.54 Low 68 1.8 20.98765432 7.59 14.46 High 64 1.69 22.40817899 6.7 13.45 High Average 21.36176291 7.67375 14.59583333 Lower quart 18.92136707 6.84 13.195 Upper quart 23.52024569 8.725 14.83 Median 20.31881767 7.48 13.82 Standard deviation 4.010422062 1.360608971 2.951622318 Standard deviation Above mean 25.37218497 9.034358971 17.54745565 Standard deviation Below mean 17.35134085 6.313141029 11.64421102 Female Kilograms Height BMI Shot-put 100m time High/low BMI 51.8 1.57 21.01505132 4.4 26.53 High 55.9 1.61 21.56552602 6.2 18.24 High 33.2 1.51 14.56076488 4.27 21.48 Low 58.6 1.68 20.76247166 3 19.07 High 38.2 1.62 14.55570797 5.05 13.1 Low 36.4 1.58 14.58099664 5.35 18.45 Low 43.2 1.55 17.98126951 5 16.54 Low 60.9 1.74 20.11494253 5.2 20.15 High 48 1.61 18.5178041 5.2 17.54 Low 57 1.61 21.98989237 5.3 17.51 High 60 1.72 20.2812331 4.4 17.55 High 65 1.65 23.87511478 5.1 17.83 High 65 1.69 22.75830678 7.5 13.87 High 65 1.72 21.97133586 6.71 18.24 High 50 1.63 18.81892431 2.2 47.83 Low 50 1.6 19.53125 4.1 18.21 Low 68 1.68 24.09297052 4.1 20 High 49 1.68 17.36111111 4.3 18.54 Low 52 1.58 20.82999519 3.3 20.2 High 67 1.68 23.73866213 4.1 16.03 High 50 1.6 19.53125 4.4 15.52 Low 53 1.7 18.33910035 4.2 15.03 Low 49 1.6 19.140625 3.5 14.77 Low 52 1.71 17.78324955 4.4 14.55 Low Average 19.73739815 4.636666667 19.0325 Lower quartile 18.76032385 4.1 15.775 Upper quartile 19.248861 5.2 19.535 Median 19.82309626 4.4 18.02 Standard deviation 2.71156419 1.122937616 6.6126295 Standard deviation Above mean 22.44896234 5.759604282 25.645129 Standard deviation Below mean 17.02583396 3.513729051 12.419871 ?? ?? ?? ?? Robert Hanson

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