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AS statistics coursework - correlation coefficient between height and weight in year 11 boys and girls

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Introduction

Antony Georgiou

Statistics Coursework

Aim

   The aim of this investigation is to discover if there is a link between two variables and see whether they are dependant or independent on each other. In order to carry this out with reliable results I will need to collect suitable data which I can use statistical methods to calculate and analyse correlation coefficients and regression lines, taking into account any anomalies that may affect the correlation coefficients and regression.

   In this investigation I am going to look into whether or not there is a connection between the height and weight of year 11 boys and girls (I chose height and weight as my variables as I feel that they will have a strong correlation and should be dependant on each other i.e. the taller the person is the more they should weigh. I also chose the background variable of gender to see if this influences the result). The population from which I shall gather my sample is the boys and girls in year 11 from Wilnecote High school. I will gather data on 35 boys and 35 girls chosen randomly to give me a set of data that represents the whole year group.

   To pick people from the year at random I will get a list of every boy and every girl from year 11 on separate sheets and assign a number to each name (1-135 for boys and 1-124 for girls). To randomly choose which students will be used I will use the random function on my calculator (as there were 135 boys on the calculator you press 135, Ran, and then the equals button 35 times taking note of each number)

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Middle

1.65

59

2.72

3481

97.35

1.60

66

2.56

4356

105.6

1.60

55

2.56

3025

88

1.52

48

2.31

2304

72.96

1.57

54

2.46

2916

84.78

1.52

47

2.31

2209

71.44

Totals

Sxx

0.19

x2

Syy

2433.54

93.12

y2

Sxy

7.41

94594.00

xy

r

0.34

2933.86

x total

57.03

y total

1796.00

Height : Weight Males yr 11

Height in m (x)

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Conclusion

I was correct in thinking that the boys would have a steeper gradient but that doesn’t necessarily mean my reason is correct it could be many different reasons that I have overlooked such as sport they do etc.

  1. I think that height and weight will be very dependant on each other.

I was correct in thinking that height and weight would be dependant on each other.

Modifications That Would Make The Investigation More Reliable

  • Look at different year groups and compare results
  • it could have been more accurate if I took a larger sample (the larger the more accurate).
  • Gather secondary information from the internet looking at national data for height and weight rather than localised
  • Look at different schools year 11 pupils for a wider range of sources to produce a more reliable result
  • Use more precise measuring instruments which could measure to 3 or possibly 4 decimal figures
  • I could have used a stratified sample which would take into account that there are more boys than girls in year 11
  • Take many small samples and collect the averages together this will give you more accurate readings and will also allow you to negate anomalies
  • Look into the subjects background and see how environmental differences such as wealth has a trend in the data

All of the above would make improvements to the accuracy of my results however I feel that the easiest to do with the most impact on reliability would be to increase the sample i.e. use the whole year group. Also with equal ease you could take a stratified sample which would reverse the error which would be caused by the difference in amount of students boys : girls.

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