In this coursework I want to find out what the average height, weight, and arm span of a Year 11 pupil is
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Introduction
Philip Davies 11B8th February 2005
The Average Year 11 Pupil
Hypothesis
In this coursework I want to find out what the average height, weight, and arm span of a Year 11 pupil is. I think that my height, and arm span will be 10% more than the average Year 11 pupil, and my weight will be 5% more than the average year 11 Pupil, I want to find out if this is correct. I will also compare the height, weight, and arm span of an average Year 11 male to an average Year 11 female, because I think that an average Year 11 male will be 10% taller, heavier, and have a 10% longer arm span than an average Year 11 female. Finally, I want to find out if an average Year 11 pupil is square, and if an average Year 11 male is squarer than an average Year 11 female. The calculations and graphs that I am going to make are;









Each pupil in Year 11 measured their own height, weight, and arm span, and all the data was collected and put in a table. So the data we are using is Primary Data because we have collected it. The sampling which I used to get my data was systematic sampling. To get better results I left out any sets of data with missing measurements. I chose every 4th set of data and recorded it in a table. I decided to choose 25 male, and 25 female sets of data, so I will have 50 sets of data. Here is the data that I have selected;
Gender  Height (cm)  Arm Span (cm)  Weight (kg) 
M  187  187  76 
M  169  165  55 
M  186.4  165  73 
M  176  170  57 
M  183.5  195  64 
M  183  182  65 
M  174.5  160  76 
M  177.5  176  59 
M  180  185  65 
M  155  162  46 
M  189  200  97 
M  178  177  78 
M  176.5  175  70 
M  165  170  47 
M  180  184  58 
M  164  164  55 
M  182.5  178  92 
M  166  168  52 
M  172  179  91 
M  172.5  168  76 
M  180  179  65 
M  178  163  65 
M  169  167  63.5 
M  185  185  64 
M  172  175  60 
F  163  151  52 
F  181  181  65 
F  157  163  53 
F  160  155  43 
F  165  160  70 
F  156.5  162  42 
F  172  172  62.5 
F  167  162  51 
F  165  159  50 
F  166.7  171  70 
F  161  159  60 
F  167  168  69.5 
F  165.5  170  70 
F  164  167  60 
F  164  170  65 
F  163  155  53 
F  162.5  147  60 
F  172  165  64.5 
F  167  170  65 
F  156  165  57 
F  157  155  59 
F  152  155  47 
F  160  166  58.5 
F  161  160  58 
F  165  165  55 
Here are my measurements;
Gender  Height (cm)  Arm Span (cm)  Weight (kg)  
M  182  185  68 
There are no sets of data in the table which stand out, so I believe the data is all genuine. The data that I have collected is Continuous data so I will have to group my data for the 3 measurements.
1.Height (All data)
I will now do all my calculations and graphs for Height. I will firstly do the calculations and graphs for all of my data, and then I will split the data into male and female and complete the calculations and graphs for them. Here is my table of grouped data for height, including all my data;
Height (cm)  Frequency 
150 ≤ h < 155  1 
155 ≤ h < 160  5 
160 ≤ h < 165  10 
165 ≤ h < 170  12 
170 ≤ h < 175  6 
175 ≤ h < 180  5 
180 ≤ h < 185  7 
185 ≤ h < 190  4 
1.Histogram
From the Histogram above I can see that there are more pupils with a smaller height than pupils with a larger height. I can also see that there is a slight negative skew in the Histogram which shows that there is a bigger distribution of smaller pupils in Year 11.
2.Mean
Mean = Sum of Height = 8491.6 = 169.832cm
No. of Pupils 50
Compared to my height of 182cm, the mean height for Year 11 pupils is 169.832cm, which would make me above average height by 12.1cm. As a percentage this would mean I am 6.6% taller than the mean height of a Year 11 pupil, so my hypothesis was almost correct.
3.Mode (Modal Group)
Mode (Modal Group) = 165 ≤ h < 170 cm
The modal group height for a Year 11 pupil is 165 ≤ h < 170 which is
17cm < h ≤ 12cm smaller than my height which means I am 9.3% ≤ h < 6.6% taller than the average Year 11 pupil.
4.Cumulative Frequency Graph
Here is the table and graph for Cumulative Frequency;
Height (cm)  Frequency  Cumulative Frequency 
150 ≤ h < 155  1  1 
155 ≤ h < 160  5  6 
160 ≤ h < 165  10  16 
165 ≤ h < 170  12  28 
170 ≤ h < 175  6  34 
175 ≤ h < 180  5  39 
180 ≤ h < 185  7  46 
185 ≤ h < 190  4  50 
From the Cumulative Frequency graph above I can see that the gradient of the curve is steeper below the median height, and that the gradient is not as steep for the taller people above the median. This shows that the heights of the smaller pupils seem to be closer together, and the heights of the taller people seem to be more spread out.
5.Median
Median = 169cm
The median height of a Year 11 pupil is 169cm, this is 13cm (7.1%) smaller than my height. This shows my prediction of 10% is almost correct.
6.Interquartile Range
Interquartile Range = Q3 – Q1 = 178cm – 163cm = 15cm
From this diagram and the Interquartile Range I can see that the middle 50% of the data covers almost exactly half of the total data range, so it has got a normal spread. I can also see that the lower 50% of the data is closer together, and the higher 50% of the data is more spread out.
7.Standard Deviation
Standard Deviation = 9.52
The Standard Deviation measures how the data are dispersed from the mean. So from this figure I can see that the data values are spread widely from the mean because the standard deviation is high, this means that there is a large dispersion.
From the calculations I have made for Height I have found out that I am between 6.6% and 9.3% taller than the average Year 11 Pupil. In my hypothesis I predicted I was 10% taller, so I was not far off.
1.Height (Male & Female)
I will now split the data into male and female because I want to find out if an average Year 11 Male has a 10% bigger height than an average Year 11 Female. I will repeat the calculations and graphs, and compare the two sets of answers I get as I go along. Here are the two tables of grouped data for Male and Female Heights;
Male Data  Female Data  
Height (cm)  Frequency  Height (cm)  Frequency  
150 ≤ h < 155  0  150 ≤ h < 155  1  
155 ≤ h < 160  1  155 ≤ h < 160  4  
160 ≤ h < 165  1  160 ≤ h < 165  9  
165 ≤ h < 170  4  165 ≤ h < 170  8  
170 ≤ h < 175  4  170 ≤ h < 175  2  
175 ≤ h < 180  5  175 ≤ h < 180  0  
180 ≤ h < 185  6  180 ≤ h < 185  1  
185 ≤ h < 190  4  185 ≤ h < 190  0 
Middle
Height (cm)
Frequency
Cumulative Frequency
150 ≤ h < 155
0
0
155 ≤ h < 160
1
1
160 ≤ h < 165
1
2
165 ≤ h < 170
4
6
170 ≤ h < 175
4
10
175 ≤ h < 180
5
15
180 ≤ h < 185
6
21
185 ≤ h < 190
4
25
Here is my table and graph for Female Cumulative Frequency for Height;
Female Data  
Height (cm)  Frequency  Cumulative Frequency 
150 ≤ h < 155  1  1 
155 ≤ h < 160  4  5 
160 ≤ h < 165  9  14 
165 ≤ h < 170  8  22 
170 ≤ h < 175  2  24 
175 ≤ h < 180  0  24 
180 ≤ h < 185  1  25 
185 ≤ h < 190  0  25 
From these graphs for Cumulative frequency I can see that the gradient of the curve for Males is steeper towards the end half of the curve, and the gradient of the curve for Females is steeper at the beginning and then the gradient is very low at the end. This shows that the concentration of smaller pupils is greater for Females, and the concentration for taller pupils is much greater for Male Year 11 pupils. I can also see from the Female Cumulative Frequency graph that there are very few tall female Year 11 pupils, and from the Male Cumulative frequency graph I can see that there are very few small male Year 11 pupils.
5.Median
Male Median Height = 177.5 cm
Female Median Height = 164 cm
From these figures I can see that the Male median Height for a Year 11 pupil is 13.5 cm or 7.6% taller that the median Height for a Year 11 Female, which is not far off my prediction of 10%.
6.Interquartile Range
Male Interquartile Range
= Q3 – Q1 = 183 cm – 170 cm = 13 cm
Female Interquartile Range
= Q3 – Q1 = 167.5 cm – 160.5 cm = 7 cm
Here are my Box and Whisker Diagrams;
From the Interquartile Range and the Box and Whisker diagrams I can see that the middle 50% of the Female height data has a much tighter distribution than the middle 50% of the male height data. From the diagrams I can see that the middle 50% of the male data covers the taller heights, and the middle 50% of the female data covers mainly smaller heights.
7.Standard Deviation
Male Standard Deviation = 8.255
Female Standard Deviation = 6.018
From these calculations I can see that the spread of the data from the mean for Females is much tighter than the spread of the data from the mean for Males.
From these calculations I have found out that an average Year 11 Male is between 7.1% and 11.1% taller than an average Year 11 Female. I will now move on to Weight.
2.Weight (All data)
I will now do all my calculations and graphs for Weight. I will firstly do them for all the data, I will then split it into male and female and repeat the calculations and graphs. Here is my table of grouped data for the weight of Year 11 pupils, including all my data;
Weight (Kg)  Frequency 
40 ≤ w < 45  2 
45 ≤ w < 50  3 
50 ≤ w < 55  6 
55 ≤ w < 60  10 
60 ≤ w < 65  9 
65 ≤ w < 70  8 
70 ≤ w < 75  5 
75 ≤ w < 80  4 
80 ≤ w < 85  0 
85 ≤ w < 90  0 
90 ≤ w < 95  2 
95 ≤ w < 100  1 
1.Histogram
From this Histogram I can see that it has a negative skew, there are three outliers that can be seen on the histogram between 90 and 100. Also, the weights of Year 11 pupils have a tight distribution without the outliers.
2.Mean
Mean = Sum of Weight = 3129.5 = 62.59 Kg
No. of Pupils 50
Compared to my weight of 68 Kg, the mean weight of a Year 11 pupil is 5.41cm smaller than my weight. As a percentage this is 8.0%, which makes my prediction of 10% almost correct.
3.Mode (Modal Group)
Mode (Modal Group) = 55Kg ≤ w < 60Kg
The modal weight for an average Year 11 pupil is 55Kg ≤ w < 60Kg which is 13Kg ≤ w < 8Kg smaller than my weight of 68%. This means my weight is 19.1% ≤ w < 11.8% above average.
4.Cumulative Frequency Graph
Here is my table and graph for the Cumulative frequency for weight;
Weight (Kg)  Frequency  Cumulative Frequency 
40 ≤ w < 45  2  2 
45 ≤ w < 50  3  5 
50 ≤ w < 55  6  11 
55 ≤ w < 60  10  21 
60 ≤ w < 65  9  30 
65 ≤ w < 70  8  38 
70 ≤ w < 75  5  43 
75 ≤ w < 80  4  47 
80 ≤ w < 85  0  47 
85 ≤ w < 90  0  47 
90 ≤ w < 95  2  49 
95 ≤ w < 100  1  50 
From this graph I can see that the gradient of the curve is steep up to 80Kg, and then it hardly goes up at all. The flat line in the curve shows that no pupils from my data have a height of between 80Kg and 90Kg.
5.Median
Median = 62 Kg
The median weight of a Year 11 pupil is 6 Kg or 8.8% smaller than my weight of 68 Kg.
6.Interquartile Range
Interquartile Range = Q3 – Q1 = 69.5Kg – 56Kg = 13.5Kg
From the Box and Whisker diagram and the Interquartile range I can see that the middle 50% of the data covers 25% of the total data, which shows that the data in the middle 50% is tightly distributed.
7.Standard Deviation
Standard Deviation = 11.671
From this figure I can see that the data has a high dispersion, and is spread quite far from the mean.
From all the calculations and graphs I have made for weight I have found out that I am between 8.0% and 19.1% heavier than the average Year 11 Pupil. In my hypothesis I predicted I would be 10% heavier, so my prediction was correct.
2.Weight (Male & Female)
I will now split the data into male and female because I want to find out if an average Year 11 Male is 10% heavier than an average Year 11 Female, I will do my calculations and graphs for both and compare the figures and results I get as I go along. Here are the two tables of grouped data for Male and Female Weights;
Male Data  Female Data  
Weight (Kg)  Frequency  Weight (Kg)  Frequency  
40 ≤ w < 45  0  40 ≤ w < 45  2  
45 ≤ w < 50  2  45 ≤ w < 50  1  
50 ≤ w < 55  1  50 ≤ w < 55  5  
55 ≤ w < 60  5  55 ≤ w < 60  5  
60 ≤ w < 65  4  60 ≤ w < 65  5  
65 ≤ w < 70  4  65 ≤ w < 70  4  
70 ≤ w < 75  2  70 ≤ w < 75  3  
75 ≤ w < 80  4  75 ≤ w < 80  0  
80 ≤ w < 85  0  80 ≤ w < 85  0  
85 ≤ w < 90  0  85 ≤ w < 90  0  
90 ≤ w < 95  2  90 ≤ w < 95  0  
95 ≤ w < 100  1  95 ≤ w < 100  0 
1.Histogram
From these two Histograms I can see that the data for females seems to show a tighter distribution than the data for males. I can also see from these graphs that the outliers with a high weight all seem to be males. Overall, the gender with mainly small weights seems to be females, and the Year 11 males seem to have heavier weights.
2.Mean
Mean Male Weight = Sum of Weight = 1669.5 = 66.76 Kg
No. of Pupils 25
Mean Female Weight = Sum of Weight = 1460 = 58.4 Kg
No. of Pupils 25
From these results I can see that the mean weight for a Year 11 male is 8.36 Kg more than the mean weight for a Year 11 Female, which is 12.52% heavier on average.
3.Mode (Modal Group)
Male Modal Weight = 55 ≤ w < 60 Kg
Female Modal Weight = 50 ≤ w < 65 Kg
From these figures I can see that the mode for females covers a larger range of weight than the mode weight for males, this is because the frequency for females is the same for three columns in my Histogram.
4.Cumulative Frequency Graph
Here is the table and graph for Male Cumulative Frequency for Weight;
Male Data  
Weight (Kg)  Frequency  Cumulative Frequency 
40 ≤ w < 45  0  0 
45 ≤ w < 50  2  2 
50 ≤ w < 55  1  3 
55 ≤ w < 60  5  8 
60 ≤ w < 65  4  12 
65 ≤ w < 70  4  16 
70 ≤ w < 75  2  18 
75 ≤ w < 80  4  22 
80 ≤ w < 85  0  22 
85 ≤ w < 90  0  22 
90 ≤ w < 95  2  24 
95 ≤ w < 100  1  25 
Here is the table and graph for Female Cumulative Frequency for Weight;
Female Data  
Weight (Kg)  Frequency  Cumulative Frequency 
40 ≤ w < 45  2  2 
45 ≤ w < 50  1  3 
50 ≤ w < 55  5  8 
55 ≤ w < 60  5  13 
60 ≤ w < 65  5  18 
65 ≤ w < 70  4  22 
70 ≤ w < 75  3  25 
75 ≤ w < 80  0  25 
80 ≤ w < 85  0  25 
85 ≤ w < 90  0  25 
90 ≤ w < 95  0  25 
95 ≤ w < 100  0  25 
Conclusion
If I was to do this coursework again I would take all of the measurements myself and measure them in the same way to make it fair. I would also take a larger set of data which would hopefully give more accurate results.
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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