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

Span: 16 inches

Standard Deviation: 2.639178

Mean Shoe Size (US): 7.7

Standard Deviation: 1.282521

Span: 7 sizes

Correlation Coefficient: 0.714

Critical Value: 0.195

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:

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 More0

5

10

15

20

25

30

Height in Inches

Fre

quency

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:

4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 More0

5

10

15

20

25

30

Shoe Size (US)

Fre

quency

Second Quantitative Variable -Shoe Size:

Correlation Coefficient

50 55 60 65 70 75 800

2

4

6

8

10

12

f(x) = 0.347001711621319 x − 14.8733400224282R² = 0.509884048373804

Height in Inches

Shoe S

ize

(US)

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