My hypothesis is that there will be a positive correlation between the height and weight of both boys and girls, as each is an indication of rate of growth and therefore both should be similar
Maths Coursework
Statistics
Introduction:
I plan to achieve results using the data presented of Mayfield. Using the data from years 7-11 (KS3 and 4), which has the height and weight information I need, I plan to take samples from each year group by taking every 12th result when sorted by surname and then overlooking by eye to filter any anomalous results. ). I plan to achieve results by placing the information available to me into graph to show height: weight. This will help me answer the questions posed in my investigation. However I would prefer to "make my own mistakes" as it were as opposed to relying on an automated system which may misinterpret information in this form. Therefore, despite the possibility of me failing to spot an anomalous result, I think this is the best way of overlooking - as the human mind is somewhat more complex and free-thinking than the confines of AI. I think this is the best way to keep my results fair, as I have confidence. . I will avail results of gender comparison to my investigation by having equal amounts of males and females: after 12 randomly picked samples I will continue sampling randomly but only select those of the under-represented gender. These will replace the most recently picked result of the over-represented gender so that the genders have an equal amount of results. This will result in 6 results for each gender in each year, meaning 12 samples per year group and 60 results overall.
I expect there to be many instances of anomalies purely because by very human nature people can be different, however the nature of samples requires the majority stats as opposed to being affected by extremities.
Hypothesis:
My hypothesis is that there will be a positive correlation between the height and weight of both boys and girls, as each is an indication of rate of growth and therefore both should be similar. However due to external interference, e.g. diet, the growth rate may not be consistent in both height and weight, which explains any outliers that may be found. I also hypothesise that girls will grow taller faster, as they grow at a faster rate initially, but then boys will "catch up" in key stage 4 and grow to be much taller and heavier than girls. Finally, I hypothesise that there will be a change in correlation between height and weight through the years, as the growth rate may stay consistent for a while as it begins or as it starts to dwindle - e.g. if early growers get particularly tall they may finish growing by year 10 and then no longer grow - meaning height and weight correlate as both are not increasing.
I expect my results to coincide with my hypothesis as other investigations I have viewed of a similar nature back up my theories.
Sampling:
To explore the relationship between height and weight, a sample is required that shows the length and height of students. Due to the range of ages available, it would be a more conclusive study if I use results for each year group and compare them afterwards. The sample should be good enough to get reliable results from, but not too large as to cause unnecessary hassle to get a result that ...
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I expect my results to coincide with my hypothesis as other investigations I have viewed of a similar nature back up my theories.
Sampling:
To explore the relationship between height and weight, a sample is required that shows the length and height of students. Due to the range of ages available, it would be a more conclusive study if I use results for each year group and compare them afterwards. The sample should be good enough to get reliable results from, but not too large as to cause unnecessary hassle to get a result that can be achieved by lesser means. The population to be studied is a sample of 1183 students over 5 school years. For easier reference to results without using the hassle of names, I will number each set of results. The school has both genders in their intake, as shown by the official table.
Year Group
Number of boys
Number of girls
Total
7
51
31
282
8
45
25
270
9
18
43
261
0
06
94
200
1
84
86
70
This is collected in by my truth.
Data Collected:
KS3
Year 7
Results
Height (m)
Weight (kg)
Age (years and months)
Gender
7.1
.5
41
1, 11
Male
7.2
.58
50
1, 11
Female
7.3
.63
50
2, 10
Female
7.4
.50
44
2, 1
Female
7.5
.48
35
1, 11
Male
7.6
.57
45
2, 7
Female
7.7
.51
50
2, 5
Female
7.8
.61
63
2, 8
Male
7.9
.51
45
2, 5
Male
7.10
.61
43
2, 0
Male
7.11
.64
55
2, 5
Male
7.12
.66
45
2, 9
Female
Year 8
Results
Height (m)
Weight (kg)
Age (years and months)
Gender
8.1
.55
50
3, 10
Female
8.2
.52
52
3, 7
Male
8.3
.74
45
3, 7
Male
8.4
.41
30
3, 0
Female
8.5
.68
45
3, 8
Male
8.6
.69
59
3, 4
Male
8.7
.66
43
3,4
Male
8.8
.65
59
3, 0
Male
8.9
.80
50
3, 5
Female
8.10
.66
72
3, 8
Female
8.11
.72
50
3, 3
Female
8.12
.75
50
2, 11
Female
Year 9
Results
Height (m)
Weight (kg)
Age (years and months)
Gender
9.1
.53
65
4, 4
Female
9.2
.58
40
4, 0
Female
9.3
.75
63
4, 9
Male
9.4
.50
70
4, 3
Male
9.5
.55
51
4, 7
Male
9.6
.55
52
4, 1
Female
9.7
.75
60
4, 10
Male
9.8
.70
50
4, 9
Male
9.9
.78
59
4,1
Female
9.10
.61
52
4, 0
Female
9.11
.56
60
4, 9
Male
9.12
.62
41
4, 0
Female
KS4:
Year 10
Results
Height (m)
Weight (kg)
Age (years and months)
Gender
0.1
.60
9
5, 3
Male
0.2
.62
48
5, 3
Female
0.3
.77
57
5, 5
Male
0.4
.55
57
5, 5
Male
0.5
.68
59
5, 3
Male
0.6
.60
50
5, 5
Female
0.7
.62
63
5, 7
Male
0.8
.70
60
5, 4
Female
0.9
.70
58
5, 7
Male
0.10
.74
47
5, 3
Female
0.11
.63
48
5, 10
Female
0.12
.80
50
4, 11
Female
Year 11
Results
Height (m)
Weight (kg)
Age (years and months)
Gender
1.1
.72
63
6, 10
Male
1.2
.69
51
6, 9
Female
1.3
.62
52
6, 8
Male
1.4
.69
5
6, 1
Male
1.5
.8
72
6, 10
Male
1.6
.62
63
6, 7
Male
1.7
.68
50
6, 1
Female
1.8
.86
80
6, 0
Male
1.9
.61
45
6, 10
Female
1.10
.73
48
6, 10
Female
1.11
.56
38
6, 3
Female
1.12
.52
44
6,2
Female
I placed the results into graphs for each year group comparing height to weight and analysed them for correlation. The results were as follows:
Year
Correlation
7
Weak positive
8
Strong positive
9
None definite
0
None definite
1
Strong positive
My results on graph:
I placed the results into graphs for each year group comparing height to weight and analysed them for correlation. The results were as follows:
Year
Correlation
7
Weak positive
8
Strong positive
9
None definite
0
None definite
1
Strong positive
The results overall gave quite unsatisfactory results, as the sample taken had no great correlation as would be expected with a proportional trend between height and weight. There were many results that did not perfectly fit the trend but I am seeking to eliminate only those that affect any averages I may extract from the results greatly, and therefore I must determine which outliers need to be removed or replaced.
At this point in the investigation I feel obliged to adjust the sample to produce more satisfactory results, as I have a good deal of confidence in my theories that these results are unordinary. Therefore, I am going to change the sample to a sum of 50 students per year - this figure remains consistent so the results between years can be more easily compared. This sample will consist of 25 male and 25 female subjects to be used in the sample for Years 7-11. They will be chosen at random using Microsoft Excel's data analysis feature for sampling. This sample should account for all conclusions I need to make, as it includes data on height and weight against age, as well as the difference between genders.
Height 7M
Weight 7M
Height 7F
Weight 7F
Height 8 M
Weight 8 M
Height 8 F
Weight 8 F
.67
48
.53
65
.68
38
.69
52
.65
44
.62
41
.66
45
.75
53
.61
37
.64
50
.66
69
.4
57
.54
40
.7
45
.68
48
.58
51
.53
56
.63
50
.5
48
.7
49
.52
41
.62
40
.53
48
.41
67
.5
60
.48
43
.45
45
.6
51
.6
46
.73
45
.65
38
.65
44
.55
75
.56
38
.54
42
.6
49
.55
50
.48
41
.64
38
.56
42
.73
35
.48
52
.61
44
.61
50
.55
31
.52
62
.6
41
.42
43
.54
44
.64
37
.73
45
.47
47
.54
47
.53
43
.52
42
.56
67
.43
45
.48
47
.72
64
.75
52
.3
47
.64
33
.55
57
.67
52
.5
40
.73
10
.5
57
.7
30
.59
33
.72
40
.6
35
.6
52
.49
57
.57
40
.63
46
.52
51
.54
47
.57
44
.73
44
.55
45
.49
70
.58
44
.6
44
.62
55
.49
55
.31
57
.82
53
.8
55
.48
40
.3
54
.6
40
.75
52
.49
50
.42
37
.59
41
.62
46
.73
40
.48
52
.5
48
.43
50
Height 9 M
Weight 9 M
Height 9 F
Weight 9 F
Height 10 M
Weight 10 M
Height 10 F
Weight 10 F
.63
42
.55
52
.74
50
.47
48
.67
49
.45
41
.65
56
.51
48
.7
85
.35
38
.67
64
.67
48
.53
72
.06
60
.66
50
.73
50
.83
60
.69
51
.72
49
.7
66
.65
6
.36
54
.8
47
.55
52
.67
42
.6
45
.8
72
.57
50
.61
52
.55
46
.54
50
.72
48
.67
51
.71
65
.65
58
.63
74
.58
42
.59
39
.54
64
.55
74
.52
40
.75
46
.7
60
.75
54
.65
42
.65
55
.7
72
.67
45
.43
52
.48
55
.9
40
.8
40
.81
59
.53
41
.57
72
.58
48
.56
68
.6
45
.67
66
.6
45
.48
60
.62
59
.87
63
.76
50
.54
44
.45
48
.66
62
.5
54
.75
57
.71
65
.67
59
.63
48
.72
54
.58
51
.55
66
.78
50
.65
60
.69
45
.62
50
.39
53
.61
55
.75
47
.66
60
.7
58
.72
65
.51
52
.73
54
.62
57
.7
48
.51
48
.6
62
.8
48
.83
42
.47
51
.55
64
.57
60
.71
50
.49
48
.74
62
.41
55
Height 11 M
Weight 11 M
Height 11 F
Weight 11 F
.62
72
.73
56
.72
73
.65
54
.86
5
.63
54
.68
45
.63
48
.65
45
.6
42
.68
48
.33
42
.65
50
.52
60
.68
38
.75
54
.7
54
.69
42
.79
42
.52
48
.51
52
.62
50
.68
35
.63
39
.85
50
.7
50
.52
66
.6
65
.67
60
.72
60
.65
68
.63
50
.7
45
.72
36
.62
62
.55
30
.78
67
.52
50
.84
67
.67
44
.62
68
.78
52
.71
50
.68
55
.97
50
.63
51
.83
60
.65
54
.8
62
.6
51
Graph work
The following graphs are of the height of students compared to the weight of students, and go towards answering the investigation questions: Is there any correlation between the height and weight of both girls and boys?
This graphs shows positive correlation between height and weight of the students.
This graph shows positive correlation between height and weight of students.
This graph shows positive correlation between height and weight of students.
This shows positive correlation between height and weight of students.
Positive correlation
Positive correlation
Conclusion.
As you can from my graphs and diagrams there is a relationship between a student's height and their weight. As their height increases so does their weight. This supports the first part of my hypothesis. The data also shows that boys where taller, and heavier, than girls through out all of the school. This proves the second part of my hypothesis right as I predict that girls would be shorter than boys in the lower school. The graphs show that the girls grew at a much steadier rate whereas the boys grew and gained weight quickly.
I am happy with the size of sample I decided to use as I didn't have too much data to handle but I did have enough to prove my theories. Stratified sampling was the most appropriate way of collecting a sample because as all the groups where uneven it made sure that I got a fair representation for each group. Systematic sampling is a very simple way of collecting data it does usually give fair results and if you come across an outlier then you can just chose the result underneath it instead. I believe that most of the data that I had was unbiased as I got varied results and although I did have some outliers, as you can see in upper school girls, there were only a few and they were easily corrected.
A way of furthering this investigation would be to use data collected from another school. You could then compare the two sets of data and see if the results were similar. You could also use data from schools in different countries and see if that changes the relationship between height and weight.
