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Correlation between the heights and weights of boys and girls in the school

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Introduction

Sarah Hancock 10L

Statistics Coursework

I am going to investigate data provided by Mayfield High School.  I am going to look at forty bits of data and the difference in correlation between the heights and weights of boys and girls in the school.  I am going to look at them separately and together because I can then compare them to each other.

Method for choosing my data

I am choosing my data by going to every other 10 names, for years 7, 8 and 9.  Then every 5 names for years 10 and 11.  I am going to record my data by putting it into tables one for girls and one for boys.  My data is going to be collected by:

Name

Height

Weight

Year

image00.png

     Alphabetical

     Order

Then putting my data onto a scatter graph.  A graph for all years, a graph for girls and a graph for boys.

...read more.

Middle

1.67

1.60

1.77

1.67

1.86

1.77

1.68

1.68

1.77

1.70

1.55

1.61

1.62

1.97

1.63

70

54

48

49

38

56

53

50

38

44

52

59

57

60

80

80

56

58

57

60

57

47

50

84

56

Name

Gender

Height

Weight

Ali, Aisha

Anderson, Kylie

Bellfield, Janet

Bolton, Megan

Brown, Caroline

Burney, Amna

Campbell, Nichole

Casey, Danielle

Cook, Melissa

Ali, Amera

Black, Mia

Bradbury, Natalie

Brown, Louise

Daniels, Charelle

Mitchelle, Katy

Female

Female

Female

Female

Female

Female

Female

Female

Female

Female

Female

Female

Female

Female

Female

1.52

1.42

1.58

1.72

1.59

1.35

1.57

1.46

1.62

1.62

1.75

1.69

1.73

1.76

1.58

45

41

40

43

48

51

62

45

49

56

57

51

58

52

36

Finding the equations on my graphs

To find the equation for the line of best fit I know it will be in the form ‘y = mx + c’ m = gradient, c = y intercept.

All years

...read more.

Conclusion

x = 1.7

y = 58

So I need to replace x and y to find c:

58 = 7 x 1.7 + Cimage02.png

58 = 11.9 + C      -11.9

46.1 = C

So the equation is:

y = 7x + 46.1

To test this I need to test it on the graph and using the equation:

The Graph

x = 1.6

y = 52

The Equation

y = 7 x 1.6 + 46.1

y = 11.2 + 46.1

y = 57.3

So this isn’t exact but it is very close.

Conclusion

On average the graph shows that the taller boys are heavier than the taller girls, and on average I would say my graphs show the boys to be heavier.  My graphs show that the correlation is positive and it is good.

Small boys are lighter in weight than small girls.  Medium boys are heavier in weight than medium girls, ditto with tall boys and tall girls.  So my original prediction is correct, the majority of boys are heavier than girls.

...read more.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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