Data Handling  GCSE Coursework
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Introduction
Maths Coursework – Data Handling
Hypothesis and Planning
My hypothesis is that there will be a relationship between pupils’ heights and weights. I predict that generally pupils who are taller will weigh more. In order to do this I am going to choose them from Year 11 because I think that this people are more likely to be more fully grown than any of the younger years and may be more in proportion.
In order to carry out my investigation, I should first select the data I will use. I’m going to do this randomly to make it fairer. I can use my calculator to help me choose using the random sample button. When I press shift, RAN#, it will give me a random number between 0 and 1. I need a random number between 1 and 84 for the boys, and between 1 and 86 for the girls, so I should multiply this number by 84 or 86 and round to the nearest whole to get my random sample number. I can then look for this number piece of data on my table.
Once I have collected the data I am going to put it into tally charts. Using a tally chart means it is easier to work out the totals for cumulative frequency graphs and is also easier to make a histogram from. A stem and leaf diagram will also make it easier to find the median of the data.
Middle

3
140 < h < 150

2
150 < h < 160

2
160 < h < 170

12
170 < h < 180

8
180 < h < 190

4
190 < h < 200

1
200 < h < 210

3
I’m going to do the same for weight as well:
Boys  
Weight, w, (kg)  Tally  Frequency 
40 < w < 45    1 
45 < w < 50    1 
50 < w < 55    4 
55 < w < 60  0  
60 < w < 65    3 
65 < w < 70    2 
75 < w < 80    1 
80 < w < 85    1 
85 < w < 90    1 
90 < w < 95    1 
Girls  
Weight, w, (kg)  Tally  Frequency 
40 < w < 45    2 
45 < w < 50    2 
50 < w < 55    8 
55 < w < 60    1 
60 < w < 65    3 
65 < w < 70  0  
75 < w < 80  0  
80 < w < 85    1 
85 < w < 90  0  
90 < w < 95  0 
CombinedBoys& Girls  
Weight, w, (kg)  Tally  Frequency 
40 < w < 45    3 
45 < w < 50    3 
50 < w < 55    12 
55 < w < 60    1 
60 < w < 65    6 
65 < w < 70    2 
75 < w < 80    1 
80 < w < 85    2 
85 < w < 90    1 
90 < w < 95    1 
I am now going to do histograms for these tally charts. I think it is good to do a histogram because it makes it easy for me to compare results and see which is the highest. I can compare height and weight on several separate graphs.
Histograms displaying my data in several different ways:
From these graphs I can first see that the higher numbers and lower numbers tend to be more rare. There are very few people who are above 180cm.Most people seem to be around the middle of my graphs. I’m going to work out the average height and average weight later using a stem and leaf diagram. I can also see that generally boys tend to be slightly heavier than girls, because there are more heavy boys in the 70kg – 90kg than in the girls. The modal class interval for height is 160 < h < 170, and the modal class interval for weight is 50 < w < 55.
So far I think I can say that generally those who are taller tend to be heavier, because the graphs seem very similar in shape (small at lower end, high in middle, small at higher end).
I’m going to make a frequency polygon so I can compare girls and boy’s weights and heights on one graph. This will help me try to prove my hypothesis.
You can see from the height frequency polygon that the two different genders follow the same pattern as the histograms. The middle values are much higher than the low values and high values. This again shows that my hypothesis may be true. They are also very similar – girls seem to be a little shorter in some places than the boys.
I’m going to do a stem and leaf diagram. Stem and Leaf diagrams make it very easy to find out the mean, mode, range and median of my results because they are set out easily.
Boys Height  
Stem  Leaf  Frequency 
130  2  1 
140  0  
150  1  1 
160  5, 5, 7, 9  4 
170  1, 2, 3  3 
180  0, 1, 3, 4  4 
190  7  1 
200  3  1 
Conclusion
167
180
132
151
165
173
181
169
183
171
197
172
165
203
184
Weight
66
60
45
40
54
65
75
54
84
64
50
86
76
50
63
GirlsResults
Height  183  167  160  162  155  133  163  172  168  183  173  133  172  148  203 
Weight  60  52  54  56  46  44  54  61  54  64  50  47  50  54  85 
The line of best fit is useful for helping me work out averages. For example, I can work out that someone who is 150 cms tall might weigh 50kg. Of course this is only an estimate.
I’m going to make a cumulative frequency graph. Cumulative frequency graphs are good for display continuous data. The cumulative frequency is the running total of the frequency up to the end of the class interval. To find the cumulative frequency I first need to make a running total by adding the numbers.
CombinedBoys& Girls  
Weight, w, (kg)  Frequency  Cumulative Frequency 
40 < w < 45  3  3 
45 < w < 50  3  6 
50 < w < 55  12  18 
55 < w < 60  1  19 
60 < w < 65  6  25 
65 < w < 70  2  27 
75 < w < 80  1  28 
80 < w < 85  2  30 
85 < w < 90  1  31 
90 < w < 95  1  32 
Combined Girls & Boys  
Height, h, (cm)  Frequency  Cumulative Frequency 
130 < h < 140  3  3 
140 < h < 150  2  5 
150 < h < 160  2  7 
160 < h < 170  12  19 
170 < h < 180  8  27 
180 < h < 190  4  31 
190 < h < 200  1  32 
200 < h < 210  3  35 
From this I can work out which points I need to plot on my cumulative frequency graphs.
Weight: 45, 3 50, 6 55, 18 60, 19 65, 25 70, 27 80, 28 85, 30 90, 31 95, 32
Height: 140, 3 150, 5 160, 7 170, 19 180, 27 190, 31 200, 32 210, 35
Now I have finished all my graphs I think I can say that generally the taller someone is the more they weight. This is not always true as some people weight a lot but are quite short. However I think that my scatter graph especially shows a positive correlation, which tells me that my hypothesis was correct. My hypothesis was also that the Year 11’s would be more fully grown and I believe this is correct too.
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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