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• Level: GCSE
• Subject: Maths
• Word count: 1402

To find out if there is a correlation between height and foot length using Fathom.

Extracts from this document...

Introduction

Introduction

I was given some data for 60 pupils in the school, with their height, foot length and gender. Firstly, I decided to compare this data by putting this data onto a graph and see if there is a correlation between height and foot length. I think that taller people will have bigger feet, which will be my hypotheses.

Hypotheses

My hypothesis is that taller people have bigger feet.

Aim

To find out if there is a correlation between height and foot length using Fathom.

Statement

When you square root 0.69 you know to take the positive value, not the negative value, because the line has a positive gradient.

A scatter graph to show the correlation between height and foot length

The graph measures r, the strength of the linear relationship between height and the length of foot. If all the points lie very close to the line, I expect the value of r2 to be close to 1. If r2= 1 all the products lie on the straight line.

Analysis

This circle shows a few of the anomalies on the graph. The height is very big but the foot size is not. I can see this because the points are far away from the line of best fit.

The graph shows a positive correlation, which means there is a positive gradient.

Middle

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.

Conclusion

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.

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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