Now, I am going to see how this compares to three pupils in my class. The table below shows the findings. I calculated the predicted height by substituting the pupils’ foot length into the equation of the line of best fit.
I can see that Georgia and Manraj were taller than predicted when comparing their foot length and height using the above graph but Manraj was closest to the prediction. However, Jenny was shorter than predicted. As none of the predicted heights matched the actual heights, I can say that the graph does not represent the pupils in my class very well. This may be because they graph represents pupils of only boys, whereas the pupils in my class are girls, which may make the results vary. The pupils in the graph may be from another country where general foot size is larger or smaller, so that when it is compared with the pupils in my class, they are different.
Refining my Hypothesis
I wanted to see if r would increase if I calculated the product moment correlation through gender. I will make a scatter graph for girls first and then a graph for boys. I think there will be a closer link between height and foot length by separating the genders.
A Scatter Graph for Males Only
Analysis
I can see that there are not many anomalies on this graph, but the two that are circled show that there are a few boys who are taller than predicted and a few that are shorter than predicted. E.g. ‘a boy has a height of about 180cm, and foot length of about 24cm’, which means the boy is 30cm taller than predicted. I can see that there is a strong correlation between height and foot length for males only. A short boy will most likely have small feet. The value for the product moment correlation coefficient is higher than that for mixed gender, which proves my hypothesis was correct.
A Scatter Graph to show the foot lengths for females.
Analysis
There are many more anomalies in this graph than in the male one, which implies that the coefficient is lower than expected, when I had expected the coefficient to be higher for both male and female, but it is only true for male. This could be because of the growth of boys is later on than girls i.e. girls start to vary in size earlier than boys.
Introduction
I want to see how the heights of boys compare with those of girls.
Plan
I will use Fathom to draw box plots in order to analyse this statement so that I can compare the median for boys and for girls.
Hypothesis
I predict that in general, boys will be taller than girls.
A box plot to show the distribution of heights for 60 pupils
Just from looking at this graph, I can see that there is a much larger range for boys than there is for girls as the box for ‘M’ is much wider. The median line is roughly in line, showing that the median for boys and girls is nearly the same.
A table to show quartile values for height
Boys (cm)
Min value: 111
Lower quartile: 131
Median: 147
Upper Quartile: 165
Max value: 184
IQR: 34
Range: 53
Girls (cm)
Min value: 122
Lower quartile: 138
Median: 146
Upper Quartile: 160
Max value: 181
IQR: 22
Range: 43
Analysis
From the table and box plot I can see that the median for boys is 147cm, which is higher than the median for girls (146cm). This is virtually the same, but still suggests that boys, in general, are taller than girls, which proves my hypothesis was still correct. However as this is a study of pupils, they are not fully grown yet, so the median heights will be roughly the same as there are many variations. All the other values are almost the same with slight differences, showing that there is not much difference in average heights, there is just a bigger range in heights for boys.
Plan
I am going to compare foot length between boys and girls.
Hypothesis
I think that boys will have bigger feet than girls, in general.
A Box plot to Show the Foot lengths of 60 Pupils
From looking at this diagram, I can say that the range for boys is larger than the range for girls, which is the same result as height. The maximum value for males is also larger than females, which means that there will be a boy/s in the class with bigger feet than the maximum value for girls.
A Table to Show the Values for Foot Length
Boys (cm)
Min Value: 15
LQ: 20
Median: 23
UQ: 25
Max Value: 29
IQR: 5
Range: 14
Girls (cm)
Min Value: 15
LQ: 20
Median: 23
UQ: 24
Max Value: 25.5
IQR: 4
Range: 10.5
From the above results, I can see that the median foot length for boys was 23 cm which also applies to the median foot length for girls (23 cm). This does not show that the boys and girls have got the same size feet because there may be one girl who has very big feet, or one boy who has very small feet or vice versa, bringing the median down or up. However, in this data, my hypothesis that boys will have bigger feet is not accurate.
The interquartile range for girls was 4 cm, whereas it was 5 cm for the boys. This shows a larger range for the males, which may be caused by a few individuals with anomalous results. These anomalous results may be caused by some boys suddenly growing, i.e. their foot length and height will increase.
Conclusion
My investigation could have been improved by taking out any anomalies in the graphs, and looking at how this would affect the results and the value of r.
I also could have used another source e.g. the Internet, to look at other examples of data for pupils’ heights and foot lengths, and compare them with the data I had.
Overall, I think the data was fairly accurate and there were not as many anomalies as expected.