The relationship between height and weight for students of Mayfield High School.
Extracts from this document...
Introduction
Maths Coursework
Handling Data for Mayfield High School
The Task
The following data is provided.
Year Group  Number Of Boys  Number Of Girls  Total 
7  151  131  282 
8  145  125  270 
9  118  143  261 
10  106  94  200 
11  84  86  170 
Given the above data it is my task to develop a statistical investigation based upon different lines of enquiries.
The lines of enquiries which I may choose to investigate are as follows:
 The relationship between height and weight
 The relationship between IQ and key stage 2 results.
I have decided to investigate on height and weight.
Collecting the data
We first need to begin by taking a random sample of data. I collected a random sample of data for 30 boys and 30 girls as shown below in the table.
BOYS  GIRLS  
HEIGHT / m  WEIGHT/ kg  HEIGHT/ m  WEIGHT/ kg  
1  1.67  66  1.83  60 
2  1.72  63  1.63  44 
3  1.80  60  1.73  50 
4  1.32  54  1.69  51 
5  1.62  56  1.61  54 
6  1.69  50  1.70  50 
7  1.68  50  1.75  60 
8  1.80  72  1.68  48 
9  1.85  73  1.58  54 
10  1.75  68  1.74  39 
11  1.67  60  160  48 
12  1.86  80  1.61  45 
13  1.62  92  1.63  38 
14  1.70  62  1.70  60 
15  1.52  38  1.62  54 
16  1.72  64  1.56  38 
17  1.61  42  1.65  54 
18  1.73  50  1.69  46 
19  1.70  72  1.52  48 
20  1.80  62  1.54  65 
21  1.71  57  1.67  52 
22  1.85  73  1.73  64 
23  1.67  50  1.52  38 
24  1.61  47  1.57  48 
25  1.62  51  1.60  48 
26  2.00  86  1.75  56 
27  1.50  35  1.60  45 
28  1.62  48  1.73  48 
29  1.65  50  1.55  50 
30  1.84  76  1.76  56 
A more useful representation of data
Although I have collected a rather random sample of data, it is not really very useful to me, in the sense it is simply a series of numbers without much meaning.
Middle
55 – 64
 
6
65 – 74

1
75 – 84
0
85  94
0
Graphical Representation
To help analyse the data in a simple way I have produced bar graphs for both height and weight, for both boys and girls, as shown below.
Heights of Boys and Girls
To compare the two sets of discrete data, we can compare both sets of results on a dual bar graph as shown below.
Series 1 = Boys
Series 2 = Girls
Girls mode height is higher than that of boys, this is feel is quite strange, as id expect boys to be higher. Also we don’t seem to get no girls shorter than 1.50, yet there exists a boy with a shorter height than any girl.
Weight of Boys and Girls
To compare the two sets of discrete data we can record them on a dual bar graph, as shown below.
Series 1 = boys
Series 2 = girls
From the graph above it seem that boys have a weight that is more spread out. Girls seem to be consistent, and don’t seem to weigh more that 74 kg. The boy’s weight is more spread. The mode of height is more higher for girls than that of boys. This is expected, as I feel there must be some sort of relation between height and weight, and if we found the girls to have a higher mode for height in the earlier graph, then the mode for weight for girls should also be higher than boys.
Histograms
As both sets of data collected for both height and weight are continuous, we can also record it on a histogram.
Stem and Leaf
As the data is grouped into class intervals, it makes sense to record it in stem and leaf diagrams. This will make it easier to read the median values, and calculate the other averages.
Boys Height
Stem  Leaf  Frequency 
1.30  2  1 
1.40  
1.50  2,0  2 
1.60  1,1,2,2,2,2,5,7,7,7,8,9  12 
1.70  0,0,1,2,2,3,5  7 
1.80  0,0,0,4,5,56  7 
1.90  
2.00  0  1 
Boys Weight
Stem  Leaf  Frequency 
30  5, 8  2 
40  2,7,8  3 
50  0,0,0,0,0,1,4,6,7  9 
60  0,0,2,2,3,4,6,8  8 
70  2,2,3,3,6  5 
80  0,6  2 
90  2,  1 
Girls Height
Stem  Leaf  Frequency 
1.30  
1.40  
1.50  2,2,4,5,6,7,8  7 
1.60  0,0,01,1,2,3,3,5,7,8,9,9  13 
1.70  0,0,3,3,34,5,5,6  9 
1.80  3,  1 
1.90  
2.00 
Girls Weight
Stem  Leaf  Frequency 
30  8,8,8,9  4 
40  4,5,5,6,8,8,8,8,8,8  10 
50  0,0,0,1,2,4,4,4,46,6  11 
60  0,0,0,4,5  5 
70  
80  
90  
Mean, Median, Mode and Range
To help support the simple analysis from the previous section, comparing the mean, median, mode and ranges of the data collected will help give us more evidence.
Height
Mean: This can be calculated easily from the frequency tables.
Boys: 1.69m
Girls: 1.65m
Mode: We can read the modes of the height from stem diagram
Boys: 1.62m
Girls: 1.60m
Median: There are 30 people in each sample, so the median will be half way between the 15th and 16th values.
Boys: 1.69m
Girls: 1,63m
Range: The range will show us how spread the data is.
Boys: 0.68m
Girls: 0.31m
Weight
Mean: This can be calculated easily from the frequency tables.
Boys: 60.23kg
Girls: 50.5kg
Mode: We can read the modes of the height of the bar chart
Boys: 50kg
Girls: 48kg
Median: There are 30 people in each sample, so the median will be half way between the 15th and 16th values.
Boys: 60kg
Girls: 50kg
Range: The range will show us how spread the data is.
Boys: 57kg
Girls: 27kg
Table Summary
We can summarise this data found for both height and weight in a simple table format, to help with other statistical investigation still to be carried out.
Height  Mean  Mode  Median  Range 
Boys  1.69m  1.60 – 1.70  1.69m  0.68m 
Girls  1.65m  1.60 – 1.70  1.63m  0.31m 
Weight  Mean  Mode  Median  Range 
Boys  60.23kg  5060  60kg  57kg 
Girls  50.5kg  5060  50kg  27kg 
Conclusion
Although we were able to analyse all the above points, there are still limitations in our findings:
 We could have had a better sample, and analyse of results of we were to have taken the age of each student as well.
 Also out predications are based on general trends observed in the data. In both samples there were still individuals whose results were outside the general trend.
There was more time available it would be an idea to further the investigation by finding h=out how the relationship between height and weight differs when the age of the students is taken into account as well.
We could test a hypothesis that;
“When age is taken into consideration, the correlation between height and weight will be better than when age is not taken in consideration.”
Due to limitations in time I was unable to further the investigation, but based on the hypothesis, and the results gained from the analysis already carried out I would predict that considering the age would produce a more realistic analysis of the relationship between height and weight. I think we would also lose the exceptional results which fall outside the generaltrend area, as results would now be more consistent and reliable, as there would be a more larger sample used.
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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