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  • Level: GCSE
  • Subject: Maths
  • Word count: 6405

we can see if there is any correlation between a person's height and weight because if no correlation is present: Mayfield High School

Extracts from this document...

Introduction

Data handling coursework: Mayfield High School

Mayfield School is a secondary school of 1183 pupils aged 11-16 years of age. For my data handling coursework, I am going to investigate a line of enquiry from the pupils' data. Some of the options include; relationship between IQ and Key Stage 3 results, comparing hair colour and eye colour, but I have chosen to investigate the relationship between height and weight. One of the main reasons being that this line of enquiry means that my data will be continuous (numerical), thus allowing me to produce a more detailed analysis rather than eye or hair colour, where I would be quite limited as to what I can do because the data is discrete. I think that this will be a more varied investigation unlike the relationship between eye colour and hair colour, as it is pretty random which colour eyes and hair you have and does not have anything in common.

All the information given to us is too much to use, and therefore I have selected only a small amount of data for each student, which will be relevant to the height and weight of each student.

My variables only looking at height and weight so I have deleted all the other variables besides: name, age, gender, height, weight together with method of getting to school, how far away they live from school and favourite sport since I could use all the information to extend my enquiry and could be significant when looking at height and weight.

Pre-test

We do a pre-test so we can see if there is any correlation between a person’s height and weight because if no correlation is present, there is not any point in continuing with the investigation.

...read more.

Middle

-1     0       1

My correlation was here (0.5), this is a positive correlation and is in                                                                          the middle of 0 and 1 therefore there is a positive and medium correlation between height and weight.

x

1.30

1.69

1.42

2.02

1.42

2.02

1.42

2.02

1.44

2.07

1.45

2.10

1.45

2.10

1.45

2.10

1.50

2.25

1.51

2.28

1.52

2.31

1.52

2.31

1.52

2.31

1.54

2.37

1.55

2.4025

1.55

2.4025

1.55

2.4025

1.55

2.4025

1.55

2.4025

1.55

2.4025

1.56

2.4336

1.57

2.46

1.57

2.46

1.57

2.46

1.57

2.46

1.58

2.50

1.58

2.50

1.59

2.53

1.60

2.56

1.60

2.56

1.61

2.59

1.62

2.62

1.63

2.66

1.64

2.69

1.65

2.72

1.65

2.72

1.68

2.82

1.68

2.82

1.68

2.82

1.69

2.86

1.69

2.86

1.69

2.86

1.70

2.89

1.70

2.89

1.71

2.92

1.71

2.92

1.71

2.92

1.71

2.92

1.73

2.99

1.74

3.03

1.75

3.06

1.76

3.0976

1.77

3.13

1.78

3.1684

1.79

3.20

1.80

3.24

1.80

3.24

1.83

3.35

1.85

3.42

1.86

3.4596

Working out the standard deviation of the 60 students heights in years 7-11.

x = 97.16   x² = 158.22

x = Height (m) therefore x² = Height (m)²

∑= sum of  

              _____________

S.D. =  √∑x²   -    ∑x²

                n            n²

              _____________

        =  √ 158.22  -  97.16²

                  60            60²

              __________________

        =  √ 158.22  -  9440.0656

                  60            

                                    3600

             _________________

         =  √  2.636987 - 2.62223936

             ________

         =√0.014748

0.1214413 = Standard Deviation

0.014748 = Variance (The variance is just the standard deviation before you square route it)

Standard deviation is calculating weather your mean is accurate and good for a correlation. The nearer the standard deviation is to 0 the more good and reliable the mean is. Standard deviation works out how much either side of the mean can be accepted to be as the mean. For example say the mean was 5 and the standard deviation was 0.5 the mean can then be seen to be anything from 4.5 – 5.5. In my case my total mean of the samples is 1.63; meaning anything between 1.5085587 and 1.7514413 will numbers that will be covered.

Not only by working out the standard deviations you can see how good your mean is, you can also see if you have come across any anomalies.

Mean = 1.63 S.D= 0.1214413

1 S.D:

1.63 +  0.1214413 = 1.7514413

1.63 -   0.1214413 = 1.5085587

1.5085587 – 1.7514413

The number of students in the range (1.5085587 – 1.7514413) divided by the total amount of students (60) x by 100 = 72% of the students heights covered.

2 S.D:

1.63 + 2(0.1214413) = 1.8729        you do two lots of the standard deviation

1.63 -  2(0.1214413) = 1.3871        because you are working out 2 standard                        

                 deviations

1.8729 - 1.3871

The number of students in the range (1.8729 - 1.3871) divided by the total amount of students (60) x by 100 = 98 % of the students heights covered.

Working out the standard deviation of the 60 students weights in years 7-11.

x

26

676

33

1089

35

1225

36

1296

38

1444

40

1600

40

1600

42

1764

42

1764

42

1764

43

1849

45

2025

45

2025

45

2025

45

2025

46

2116

46

2116

47

2209

47

2209

47

2209

48

2304

48

2304

48

2304

48

2304

48

2304

48

2304

49

2401

49

2401

49

2401

50

2500

52

2704

52

2704

52

2704

54

2916

54

2916

55

3025

55

3025

55

3025

56

3136

56

3136

56

3136

56

3136

57

3249

58

3364

58

3364

58

3364

59

3481

59

3481

60

3600

60

3600

60

3600

60

3600

61

3721

62

3844

62

3844

64

4096

65

4225

67

4489

70

4900

75

5625

x = 3083  x² = 163567

x = Weight (kg) therefore x² = Weight (kg)²

∑= sum of  

              _____________

S.D. =  √∑x²   -    ∑x²

                n            n²

              _____________

        =  √ 163567 -  3083²

                  60            60²

              _______________

        =  √ 163567  -  9504889

                  60              3600

             ____________________

       =  √2726.116667 – 2640.246944

             _________

         =85.869723

9.266591768 = Standard Deviation

85.

...read more.

Conclusion

The mode in each year also increases; Year 7 – 45 kg, Year 8 – 49 kg and so on. (You can clearer see by looking at the table). Again, until year 10 where it goes up to the highest mode 60 kg it then decreases in year 11 where it drops as low as 48 and 56 kg. This also adds to the fact that only to an extent about the older you are in school years the more you will weigh.

The median is also increasing in every year that goes up; it ranges from in year 7 – 45 kg year 10 – 57.5 kg. Furthermore, in this case the medium for year 10 is higher than the year 11’s median of 56kg. This is also another factor which helps to prove that my hypothesis was wrong to an extent.

Year 7

Year 8

Year 9

Year 10

Year 11

Years Totalled

Upper Quartile(kg)

59

64

70

75

67

75

Lower Quartile(kg)

38.5

48

47

54.5

54

45.75

Inter Quartile Range (kg)

20.5

16

23

20.5

13

29.25

image07.png

From the graph above there is a clear indication that overall the older you are in school years, the taller you are.

Again in the graph below there is an obvious view that the taller you are year of school most likely the taller you are going to be. This shows that my hypothesis is correct because I predicted that the older you are in school years the taller you will be.

image08.png

image09.png

From the graph above there isn’t really any indications of the relationship between years 7-11, whereas the graph below show that the height goes up as the year group goes up till year 11 where there is a decrease in weight.  This shows that my hypothesis is wrong to extent because I predicted that the older you are in school years the more you will weigh, and quite clearly this is wrong to an extent.

image10.png

...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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