Transcript Is Shoe Size Generally Proportional to Height?

Is Shoe Size Generally
Proportional to Height?
Katilyn Pangborn
Hilary Christensen
Jessica Howsden
Jeffrey Ellsworth
Tammy Kiholm
Purpose of Study
This study was formulated to examine if there is
a correlation, whether positive or negative,
between our study samples. For this study the
question was asked “In adult women, is height
related to shoe size (US)?’ for centuries it has
been a common belief that “shoe size is
generally proportional to height”. Our purpose is
to test that theory.
Study Design
In order to obtain data for our research, each
member of our 7-member group will take a stratified
sample of 20 adult women from separate locations
(i.e. school campus, mall, restaurant, gym) and then
place all of the data together. We will then separate
groups by classes of height, class width being one
inch, and record the shoe sizes (US) that occur in
each one-inch class. We will then use that
information to conclude whether height has any
correlation to shoe size.
Study Analysis
140 women were asked their shoe size (US) and height (in)
280 pieces of data were collected
Mean Height: 65 inches
Correlation Coefficient: 0.714
Span: 16 inches
Critical Value: 0.195
Standard Deviation: 2.639178
Mean Shoe Size (US): 7.7
Standard Deviation: 1.282521
Span: 7 sizes
First Quantitative Variable – Height:
Mean: 65.114
Standard Deviation: 2.639
Five Number Summary: 58, 63, 65, 67, 74
Range: 16
Mode: 64
Outliers: 58, 74
First Quantitative Variable – Height:
30
25
Frequency
20
15
10
5
0
58
59
60
61
62
63
64
65
66
67
Height in Inches
68
69
70
71
72
73
74
More
First Quantitative Variable – Height:
Second Quantitative Variable Shoe Size:
Mean: 7.721
Standard Deviation: 1.283
Five Number Summary: 4, 7, 7.5, 8, 11
Range: 7
Mode: 7.5
Outliers: 4, 4.5, 5, 10, 10.5, 11
Second Quantitative Variable Shoe Size:
30
25
Frequency
20
15
10
5
0
4
4.5
5
5.5
6
6.5
7
7.5
8
Shoe Size (US)
8.5
9
9.5
10
10.5
11
More
Second Quantitative Variable Shoe Size:
Correlation Coefficient
12
y = 0.347x - 14.873
R² = 0.5099
10
Shoe Size (US)
8
6
4
2
0
50
55
60
65
Height in Inches
70
75
80
Correlation Coefficient
The linear correlation between the two lines is R= 0.714
The regression line is y=mx+b, where shoe size is “y” and the
equation is: (0.347)height + (-14.873)
Conclusion
 There is a positive correlation between shoe size and height, as
height increases shoe size tends to as well.
 There were few outliers found through our research.
 Next time we would use a larger, more random data collection
procedure.
 Challenges:
 Accuracy
 Randomness
 Relatively small sample size - unable to verify if it is actually
attributable to a population