### Height Vs Shoe Size

```Height Vs Shoe Size
Will how tall you are tell us what size
shoe you wear?
The Study
• Purpose of the Study: The purpose of this study was to
determine if there is a correlation between how tall a
person is and their shoe size and whether one could
predict shoe size based on a person’s height.
• Study Design: Data was gathered by going to
supermarkets and asking individuals if they would be
willing to participate. This was done on more than one
occasion and more than one store. I did not gather
information from people that were related to each
other or from minors as this could possibly skew the
data. In order for there to be variety I chose a few
different stores.
The Height of Men surveyed
Male Height
5
Frequency
4
3
2
1
0
66
67
68
69
70
71
72
Height in Inches
•
•
•
•
•
•
Mean: 71.42857
Standard Deviation: 2.890872
Five Number Summary: 66,69,72,73.5,77
Range: 11
Mode: 69, 73
Outliers: 77, 66
73
74
75
76
77
..and their Shoe Size
Male Shoe Size
6
5
Frequency
4
3
2
1
0
8
8.5
9
9.5
10
10.5
11
Shoe Size
•
•
•
•
•
•
Mean: 10.47619
Standard Deviation: 1.444612
Five Number Summary: 8, 9.5, 10, 11.5, 13
Range: 5.5
Mode: 9.5, 10
Outliers: 13
11.5
12
12.5
13
13.5
The Correlation
Male Shoe Size vs Height
14
y = 0.3812x - 16.752
R² = 0.5819
12
Shoe Size
10
8
Male Shoe size
6
Linear (Male Shoe size)
4
2
0
64
66
68
70
72
74
Height in Inches
•
•
•
Linear Correlation Coefficient: 0.762828
Critical Value for sample size 21: 0.433
Y=0.3812x-16.752
76
78
But we’re not done yet….
The Height of Women Surveyed
Female Height
9
8
7
Frequency
6
5
4
3
2
1
0
57
•
•
•
•
•
•
58
59
60
61
62
63
64
Height in Inches
Mean: 64.1875
Standard Deviation: 2.620484
Five Number Summary: 57, 63, 64, 66, 69
Range: 12
Mode: 63
Outliers: 57, 59, 61, 69
65
66
67
68
69
..and their Shoe Size
Female Shoe Size
8
7
Frequency
6
5
4
3
2
1
0
5.5
6
6.5
7
7.5
8
Shoe Size
•
•
•
•
•
•
Mean: 7.703125
Standard Deviation: 1.149049
Five Number Summary: 5.5, 7, 7.5, 8.5, 10
Range: 4.5
Mode: 7
Outliers: 5.5, 10
8.5
9
9.5
10
The Correlation
Female Shoe Size vs Height
12
10
y = 0.262x - 9.1164
R² = 0.3571
Shoe Size
8
6
Shoe Size
Linear (Shoe Size)
4
2
0
50
54
58
62
Height in Inches
•
•
•
Linear Correlation Coefficient: 0.597595
Critical Value for sample size 32: 0.361
Y=0.262x-9.1164
66
70
Analysis and Conclusion
•
•
•
Difficulties/Surprises Encountered: I realized part way into the project that men and women do not
have the same shoe size measurements. A size 9 for a woman is a size 7 for a man, so I ended up
with twice as much data as I needed and put both into this project. I also did not realize that I
would not always get data when asking for it and there were quite a few people that declined to
participate in the gathering of data. The problem with this study is that it is not necessarily
indicative of a population size beyond individuals who go to supermarkets. A person who has a wife
or husband who does the shopping would not be included in this study. It also does not reflect a
population outside of Utah.
Analysis: None of the variables had a normal distribution although male height and female shoe
size was the closest. Male height had two outliers, one on each end of the graph. Female shoe size
had three outliers with two on the right and one on the left with it being closer to a normal
distribution. Female height was skewed right and also had outliers on each end of the graph,
especially on the right side. Male shoe size had three outliers all at the size 13 mark which made it a
not normal distribution. There is a somewhat strong positive association between the heights of
males and what sizes of shoe they wear with the correlation coefficient being 0.762828 whereas
there is only a medium positive association between the heights of females versus what shoe size
they wear with a correlation coefficient of 0.597595.
Interpretation and Conclusion: Based on the information gathered there is significant evidence,
with critical value for males at 0.433, that one could get a pretty close estimate of a man’s shoe size
based on his height. The critical value for the women was 0.361, so there is also significant
evidence that one could get a pretty close estimate of a woman’s shoe size based on her height.
```