Investigate the relationship between the head size and height of a person in order to prove the statement "the taller you are, the larger your head size".

The following table shows an example of the raw data and how it is lain out. It is from these tables that I hope to draw the graphs and conclusions.

Fig.1

As can be seen there are anomalies and exceptions within the data. Some of the information is incomplete and different sections are missing. The graph pictured below (Fig. 2) shows the data in the table above.

Fig. 2

It is from graphs like these that I can prove my predictions. However in order to conclusively prove the statement that ‘the taller you are, the larger your head’, I must of course take into account all of the data and compare sections of the data to others. For example, whilst the previous graph was of a Year 9 class, the following graph is of a Year 11 class.

Fig. 3

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         

                                                                                                                                                                                                                                                                                                                                                                                                                       

Add on:

As the sample is quite large, minor errors are unlikely to make any major difference to any kind of trend shown.

Just taking these two graphs it can still be seen that in the majority of cases the rule applies. As the height of students increases, so does their head size. There are two things that must be noted about both graphs. In figure 2 the results are of a much wider variance. There are more people in this sample that are quite far apart from the best fit line and have exceptions in either their height or their head size most the results in this sample are bunched up and quite close together as well. In contrast the results in figure 3 show a more expected trend with students closer to the best fit line in their measurement. The results are also much more spread out in figure 3.

This is likely to be due to the growth spurts that occur during adolescence. As both of these graphs are effectively random samples of both girls and boys of similar age the results shown give a good idea as to the overall measurements of each Year.

I will now further prove the statement that the taller you are, the larger your head. It must be noted that:

1. This factor has nothing to do with gender, and therefore in this sample the statistics for the boys will not be separated from the girls. This particular aspect of the investigation will be focused on later on.
2. And also that this trend will not be influenced by height, and as such

The graph below is an analyze of the entire school. Five students were chosen at random from each year group and their details were put on the chart. As such this graph is a particularly good analyze of the entire schools height in relation to head size.

Fig. 3

This type of trend is not unusual, as proved by the graphs above (Fig. 1 & 2) and below (Fig. 4). From this it is clear that the statement ‘the taller you are, the larger your head’ can only be applied as a general rule. Whilst the trend as a whole is upwards (as shown in the best fit line) there are several exceptions and many of the points go outside of the error range of the graph, as shown in Fig. 5.

(insert error bar graph) 

The following graph shows the general trend of head size to height in Year 7, where the students are 11 – 12 years old.

Fig. 4