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• Level: GCSE
• Subject: Maths
• Word count: 3549

# Does Foot Size Increase With Height and Do Boys Have Larger Feet than Girls?

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Introduction

## GCSE Maths Statistics Coursework

Does Foot Size Increase With Height and Do Boys Have Larger Feet than Girls?

Throughout this coursework I will be investigating the set question, “Does foot size increase with height and do boys have larger feet than girls?”. In order to complete a substantial piece of work which conveys my investigation thoroughly I will collect data from both a Primary and Secondary source. The primary source being pupils within my Maths Set and the Secondary source being previously collected data shown on the internet.

From the data I obtain I will analyse and interpret my results, commenting on what I do at each stage.

#### Hypothesis

This is what I feel I will find by analysing my data.

• My hypothesis is that foot size has no relation to height…
• … and that boys generally have larger feet than girls.

Now I am going to plan what I am going to do in order to either prove or disprove my hypothesis and how I am going to portray the results I obtain.

Plan

• Firstly I need to collect my Primary data

In order to ensure everyone records successful, non-biased data, we all followed the guidelines below.

Height

• The pupil’s shoes and any headwear should be removed to ensure an accurate recording of the individual’s height.
• The pupils back should be against a vertical object in order to straighten their back and give a correct result. For my class’ investigation, we used a door to record height.
• Once positioned against the door the pupil’s head should be positioned so that they are looking directly in front of themselves.
• A mark should then be made where the pupil’s head reaches the highest point on the door.
• The measurement from the floor to the mark where the pupil’s head reaches should be measured accurately then recorded in centimetres.

Once Height is recorded, the next step is to record foot size.

Foot Size

• The pupil’s shoes should be removed to ensure that an accurate recording of the pupil’s foot size and not their shoe.
• The pupil should then place their foot on the floor with their heel touching a wall.
• A measurement from the wall where the pupil’s foot is touching to the big toe of the pupil’s foot should be measured then recorded, again in centimetres.
• Once I’ve obtained my Primary Data I need to collect my Secondary Data which I will take from the website www.censusatschool.ntu.ac.uk. “census at school” has the height and foot size of 518 randomly selected boys and girls. To get my data I will use systematic random sampling where I will take the data of every tenth person from the 518 provided and use it for my investigation.
• From the Primary data I will create histograms, scatter diagrams and box and whisker plots to show my findings and disprove or justify my hypothesis. Then I will create the same graphs and diagrams with my Secondary data and compare both. By doing this I can distinguish the anomalies and develop a reasonable and justified conclusion.
• After each action I make I will explain in as much detail, the reason why I have done something in order to make my investigation clear and understandable.
• Once I have completed recording data and constructing useful graphs and diagrams, I will make a conclusion from my results which will reflect what I have investigated.
• Finally I will review my work and suggest ways in which I could change things to make my investigation better. By doing this I can learn my mistakes and take them into account for future projects.

Middle

Contrasting male and female foot size I can see that the female plot has a larger range than the male plot. This suggests female foot size is more varied than male. This is also backed up by the Standard Deviation of both the plots as the female plot has the biggest variation in data. However, the male plot reaches further along the x-axis in comparison to the female plot. This tells us that the range of male values are larger than that of the females.

Additionally the median of the male plot is larger than the female plot which tell us that “the middle value” of male foot size is therefore bigger than “the middle value” of the female plot.

Histograms-Height

Histograms are bar graphs of a frequency distribution in which the widths of the bars are proportional to the classes into which the variable has been divided and the heights of the bars are proportional to the class frequencies. This makes histograms a good idea to use when showing results as they convey statistics data well.

To find the average height for males I am going to add up all the values of their heights then divide it by how many males there are, this is called the mean. The reason why I’m using the mean is because it is a more accurate way of finding an average as it uses all the data values.

Sum of values               2404.4

=                      = 171.7 to 1d.p.

Number of values          14

Again, to find the mean of the female set of data I will add up all the values then divide it by how many females there are. I will repeat this method for every histogram I will do.

Sum of values               2309

=                      = 164.9 to 1d.p.

Number of values          14

Conclusion

Additionally, my sets of data are very small and are not reliable enough to make a solid conclusion to apply to everyone. In other countries there are variations in genetics from that in England, for instance; stunts in growth because of famine and lack of food could result in data that doesn’t conform to my conclusions. So in order to overcome this problem and if I was to make a more universal conclusion, a larger set of data would have been more suitable to use taking the statistics over a broader area of the world. But considering the lack of information, resources and time needed to accomplish this, I feel I have done my best to perform a solid investigation from the information I did obtain.

Furthermore, I could widen the age range in my Primary Data this could ensure I more accurate conclusion to apply to the “boys” and “girls” parts in the set question as I only took the data from my Maths Set and we are only 15 or 16. With my Secondary Data I have no idea as to what age the data I obtained was as it only specified the titles “boys” and “girls”. This could mean any number of ages, if I was to do the investigation again I would make sure I knew the age range in which the data I obtained was as my conclusion may apply to 15-16 year olds but not to 13-14 year olds and both ages fit in to the categories “boys” and “girls”.

Further work I could do to provide relevant information could be to also collect the weight of “boys” and “girls” and see whether that could have any effect on height or foot size. I would have three variables to work with and if height or foot size did turn out to have a link to weight then my results would be very interesting and provide extra evidence to support the conclusions I have already made.

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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