Size of a Shoe: More Body Proportions

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Abstract

The purpose of this experiment was to determine if the relationship between the height of an individual and the size of their shoes is linear.

Introduction

The foot is a biological structure that enables animals to move. It is logical to believe that the taller an individual is, the bigger their feet should be. The length of the foot should balance the height of the individual to enable them to move easily. Limb growth in humans is genetically balanced. The length of a human foot from the heel to the tip of the big toe is exactly the same length as the forearm from the inside of the elbow and the bend of the wrist.

Procedure

  1. Using a meter stick, measure the height of 34 students.
  2. Ask the same 34 students for their shoe sizes.
  3. Converted the measurement for their shoe sizes using the American Shoe Sizing System.
  4. Graphed Height Vs. Shoe Sizes for both males and females.

Analysis

Females
Shoe Size (US) Height (m)
7.0 1.5748
5.0 1.5494
5.0 1.5748
7.0 1.6764
9.0 1.6256
7.0 1.6256
10.0 1.7526
8.0 1.7270
6.0 1.5748
8.0 1.6256
8.0 1.7526
11.0 1.7270
7.0 1.7018
Males
Shoe Size (US) Height (m)
8.5 1.6500
10.0 1.7270
12.0 1.8796
10.0 1.7270
9.5 1.7018
9.5 1.7018
10.5 1.8280
10.0 1.7526
10.0 1.7270
9.0.0 1.7018
10.0 1.6764
10.0 1.7270
11.0 1.8280
13.0 1.8280
8.0 1.7270
9.0 1.7018
11.0 1.7526
13.0 1.8280
11.5 1.8796
12.0 1.7526

Conclusion

According to the graph, there is a 59% correlation between the height of a person and their shoe sizes. This correlation is relatively weak but it does show a relationship between height and shoe sizes.

Sources of Error

Lily Li, Stephanie Kim, May Wan, Vashti Prasad -- 2007

Students Choice pages in The Physics Factbook™ for 2007


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