- That boys are taller than girls
- That the taller a person is, the heavier they are.
- That boys are heavier than girls
The first set of graphs I did were Histograms to show the most common heights throughout the entire sample of girls and boys. As a rule, the boys one showed that the taller one was, the more common one was. The only exception to this was the interval 145-155cm. This was not what I had expected. I had expected the most common heights to be in the middle. This could be explained by my having a non-representative sample. The girls one did conform to my expectation however, showing that the most common height was in the interval of 155-165cm, and after this, the Frequency Density fell away. The mean height was in the most dense class interval among women, whereas the boys’ wasn’t. The most dense class was in fact between approximately seven and twelve centimetres taller.
Therefore the second set of graphs I did were Scatter charts, to see if there was a correlation between height and weight. I expected these to show a strong positive correlation, and both the graphs for boys, and the graph for girls did this. However, the correlation when I put both girls and boys together was weaker than when they were done individually. This was shown by only having a correlation coefficient of 0.467, compared to the boys’ coefficient of 0.572. However, the girls’ had the weakest correlation with a coefficient of 0.288. This weak correlation could be explained by some exceptional values in my data, for example the girl who was 151cm tall, but weighed 65kg. Also, often as girls get older, they become concerned about their figure and diet, so this could affect the correlation as well. The lines of best fit in my diagrams predict that a boy who was 170 cm tall would have a weight of around 59 kg, and a girl who was the same height would weigh around 54 kg.
The third set of graphs I did was the Pie Charts. These were to provide a visual representation of the standard deviation. The closer the two segments were to a ration of 1:1, the more reliable I could consider my average to be. The boys’ chart perfectly fitted this ratio, and the girls’ was only slightly off. Therefore I concluded from this that my average was acceptable. To find out which pupils were over of under the mean, I used the IF function on my spreadsheet. This speeded up the process considerably, and eliminated the possibility of human error.
All three measures showed the boys to be on average shorter and heavier than the girls. The sample for boys was more spread out though, with a standard deviation of 0.141034m for height and 10.697879kg for weight, compared to the girls 0.10092 and 7.41509917 respectively. The evidence shows that the most common height of boys is between 170 and 175 cm. This is shown by it having the highest class frequency density. The girls’ most common height is between 165 and 175, with a class frequency density of 1.2. This is shown on the frequency polygon. This frequency polygon also shows that in general the girls are taller than boys.
However, these conclusions are based on a total sample of only 50 pupils. I could extend the sample or select a new sample to confirm my results.
As a result of my previous graphs, I believe that when height increases, the weight will also increase.
In order to find the lower and upper quartiles for the height of girls, boys and the entire sample, I decided to draw a cumulative frequency graph. This is because you can get a more accurate calculation of the median from a cumulative frequency graph than from a stem and leaf diagram. This is because the cumulative frequency graph is a continuous approximation of the distribution of values. I plotted all three on the same set of axis rather than separate ones, as they are easier to compare when plotted on one set.
Cumulative frequency curves can also be used to predict percentages of students who have a height within a given range. For example, if I wanted to estimate how many boys in the school were between 165 and 175 cm tall, I would read off how many boys had heights of up to 165, and how many had heights up to 175cm, the subtract the former from the latter. In this case it would be 21 – 13, which would mean approximately 8 boys had heights between 165 and 175cm.
From this I can estimate that 8/26, or 31% of the boys in the school fall into the above range. A randomly selected boy from the school being within the height range would have a probability of 0.3.
The box plots show that the girls’ inter-quartile range is some 9cm less than the boys’. This suggests that the boys’ heights were more spread out than the girls’.
The cumulative frequency graph shows that whilst in general boys are taller than girls, the evidence suggests that some 8/24, or 33% of girls are taller than the median height of boys.
From looking at my graphs, I can conclude that there is a positive correlation between height and weight. In general taller people are heavier than shorter people.
The points on the scatter diagram for the boys are less dispersed about the line of best fit than those for the girls. This suggests that the correlation works better for boys than for girls, and that girls, often through dieting and other forms of weight control, do not conform as strongly.
The scatter graphs can be used to give reasonable estimates of weight and height. This can be done either by reading them from the graph, or using equations of lines of best fit. Cumulative frequency curves confirm that boys are in general taller than girls, and this is also shown by the fact that the boys’ median height on the curve slightly higher. This is also supported by the box plots, which show that in general boys are taller than girls, but not absolutely so. The cumulative frequency curve does show that as mentioned earlier, some 33% of girls are above the male median.
The analysis was subject to some limitations however. The results could be considered more representative if a larger sample of pupils had been taken and some consideration had been given to the ages of students in the sample.
Also, my predictions are based on general trends observed in the data. Within the sample, there were exceptional individuals whose results fell outside the general trend, for example the Year 9 girl who weighed 65kg despite only being 151cm tall.
If the time were available, I would extend my investigation to consider the relationship between shoe size and weight, not only between genders, but between ages as well. From the work done in this project, I could predict that once age is considered, the correlation between height and weight will be much stronger than when it is not.
Overall therefore, although I feel that the conclusions drawn from the data I have do support my hypotheses, the data are only conclusively proves my hypothesis “that as boys get taller they get heavier.” My research does also show that there is a strong correlation between height and weight.
