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height and foot size

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GCSE Coursework: Statistics Investigation by Stephanie Liu

Hypothesis 1

I predict that the taller the pupil is, the bigger their foot size will be.


I’ve been given 60 pieces of data from pupils, about their height and foot size.

I will be using a piece of software called Fathom where I will place this information into a scatter graph, to see whether or not my hypothesis is correct. Fathom will produce a line of best fit on my graph and tell me what my r-value is. The r-value shows the product moment correlation coefficient. I am expecting a positive correlation. To prove that my hypothesis is correct, I am looking for a product moment correlation coefficient from something between 0 to 1 and the closer the line of best fit is to 1; the more evidence there is to back up my hypothesis.

The product moment correlation coefficient is a measurement of the degree of scatter. It is usually denoted by “r” sometimes referred to as the “r-value” and “r” can be any value between -1 and +1. It can be used to tell us how strong the correlation between two variables is. A positive value indicates a positive correlation and the higher the value, the stronger the correlation. Similarly, a negative value indicates a negative correlation and the lower the value the stronger the correlation.

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This scatter graph only shows the heights and foot sizes of the boys. As I previously expected, there is a strong positive correlation as for this graph the r-value is 0.860 (square root of 0.74). Evidently, this r-value is a better correlation than the original one, meaning that the equation is more accurate to work out the height or foot size of a male. This might be because they may have stopped growing and therefore their feet and height are in a better proportion. Within this scatter graph there are a few anomalies. For example, there is a boy whose foot measures only 24cm and has a height of approximately 180cm, which is almost 30cm taller than that which the line of best fit predicts. As before, looking at the data for males only, I can see that there is a very high positive correlation, which means that long footed males will tend to be tall. The value for the coefficient is higher than for mixed gender, which concurs with my hypothesis.

Now I am going to repeat the same process to find a better equation to work the height and foot size for female pupils, although this suggests that the relationship for females should be weaker. I will plot a scatter graph for females only and see if this is true.

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I was given 60 pieces data on pupils’ heights and foot sizes from a school then I investigated the relationship between the foot size and height put placing all the provided data in a scatter graph. Next to make my equations more accurate, I separated the genders and investigated foot size and I found out that there was a better equation for males but I couldn’t get one for females. From my results, generally males had a wider range and was taller and had a bigger foot length than females although I cannot be sure and will need to do further testing.

If I were to re-do this investigation I would like to investigate the age of the pupils from who I have received the data. I think this would have made my investigation better because it would give me some clues to why I got the trends that I got. It could also affect my hypothesises. I would extend the number of pupils I used in this investigation so that I got a wider range of data and may give us more accurate views of the relationships for example something like 600 pieces of data would be significant to draw up conclusions whereas now, as far as my hypothesises are concerned, they are inconclusive and I can’t make a judgement about whether their correct or not. In addition, I would like to remove any anomalies and see how this affects the value of r. This may mean that my r-value goes up.

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