Height Vs Shoe Size

Will how tall you are tell us what sizeshoe 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

• Mean: 71.42857• Standard Deviation: 2.890872• Five Number Summary: 66,69,72,73.5,77• Range: 11• Mode: 69, 73• Outliers: 77, 66

66 67 68 69 70 71 72 73 74 75 76 770

1

2

3

4

5

Male Height

Height in Inches

Freq

uenc

y

..and their 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

8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.50

1

2

3

4

5

6

Male Shoe Size

Shoe Size

Freq

uenc

y

The Correlation

• Linear Correlation Coefficient: 0.762828• Critical Value for sample size 21: 0.433• Y=0.3812x-16.752

64 66 68 70 72 74 76 780

2

4

6

8

10

12

14

f(x) = 0.381196581196581 x − 16.7521367521368R² = 0.581906475346293

Male Shoe Size vs Height

Male Shoe sizeLinear (Male Shoe size)

Height in Inches

Shoe

Size

But we’re not done yet….What about the women?

The Height of Women Surveyed

• Mean: 64.1875• Standard Deviation: 2.620484• Five Number Summary: 57, 63, 64, 66, 69• Range: 12• Mode: 63• Outliers: 57, 59, 61, 69

57 58 59 60 61 62 63 64 65 66 67 68 690

1

2

3

4

5

6

7

8

9

Female Height

Height in Inches

Freq

uenc

y

..and their 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

5.5 6 6.5 7 7.5 8 8.5 9 9.5 100

1

2

3

4

5

6

7

8

Female Shoe Size

Shoe Size

Freq

uenc

y

The Correlation

• Linear Correlation Coefficient: 0.597595• Critical Value for sample size 32: 0.361• Y=0.262x-9.1164

50 52 54 56 58 60 62 64 66 68 700

2

4

6

8

10

12

f(x) = 0.262037580739871 x − 9.11641221374046R² = 0.357119359893621

Female Shoe Size vs Height

Shoe SizeLinear (Shoe Size)

Height in Inches

Shoe

Size

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.