Question

The Problem

Due to financial hardship, the Nyke Shoe Company feels they only need to make one size of shoes, regardless of gender or height. They have collected data on gender, shoe size, and height and have asked you to tell them if they can change their business model to include only one size of shoes—regardless of height or gender of the wearer. In no more than 5–10 pages (including figures), explain your recommendations, using statistical evidence to support your findings. The data found are given in the following table.

Only use results in the paper. You may show your work in an appendix, if you would like.

Shoe Size	Height	Gender
5	63	Female
7.5	70	Female
9	70	Female
7	64	Male
11	72	Male
12	72	Male
14	76	Male
7	66	Female
7.5	71	Female
8	68	Female
10.5	71	Male
11	71	Male
6.5	65	Female
7	67	Female
7.5	70	Female
10	69	Male
12	69	Male
6.5	65	Female
10.5	72	Male
12	73	Male
6	60	Female
6.5	64	Female
10	72	Female
9.5	69	Male
11.5	70	Male
14	75	Male
6.5	63	Female
13.5	77	Male
7	68	Female
9.5	68	Male
13	72	Male
11	73	Male
6	62	Female
7	66	Female
7.50	70	Female

Answer 1

According to the given data on shoe size,height,and gender,if the company wants to make only one size shoe,then that must be depends on the modal value of the shoe size,i.e the value of the shoe size which repeat maximum number of times.

shoe size	frequency
5	1
6	2
6.5	4
7	5
7.5	4
8	1
9	1
9.5	2
10	2
10.5	2
11	3
11.5	1
12	3
13	1
13.5	1
14	2

TOTAL 35

Here shoe size 7 occure maximum number of time.So mode of the data is(shoe size ) 7.Therefore if the company ignore gender and height,then only product 7th size shoe.

Now we are checking whether it is correct to ignore the gender on the shoe size or no.

Shoe Size	Height	Gender
5	63	Female
6	60	Female
6	62	Female
6.5	65	Female
6.5	65	Female
6.5	64	Female
6.5	63	Female
7	66	Female
7	67	Female
7	68	Female
7	66	Female
7.5	70	Female
7.5	71	Female
7.5	70	Female
7.5	70	Female
8	68	Female
9	70	Female
10	72	Female

Here ,according to the gender (female) the mode of the shoe size is 6.5,7, and 7.5

And according to the Male record,

Shoe Size	Height	Gender
7	64	Male
9.5	69	Male
9.5	68	Male
10	69	Male
10.5	71	Male
10.5	72	Male
11	72	Male
11	71	Male
11	73	Male
11.5	70	Male
12	72	Male
12	69	Male
12	73	Male
13	72	Male
13.5	77	Male
14	76	Male
14	75	Male

the mode of the shoe size is 11,12.

So ,we can see that shoe size depends on gender.The shoe size of the female is relatively small than the Male shoe size.So we can not ignore the gender while choosing the shoe size.

Now we are checking whether show size depends on height or not.

Shoe Size	Height	Gender
6	60	Female
6	62	Female
6.5	63	Female
5	63	Female
7	64	Male
6.5	64	Female
6.5	65	Female
6.5	65	Female
7	66	Female
7	66	Female
7	67	Female
9.5	68	Male
8	68	Female
7	68	Female
12	69	Male
10	69	Male
9.5	69	Male
7.50	70	Female
11.5	70	Male
9	70	Female
7.5	70	Female
7.5	70	Female
11	71	Male
10.5	71	Male
7.5	71	Female
13	72	Male
12	72	Male
11	72	Male
10.5	72	Male
10	72	Female
12	73	Male
11	73	Male
14	75	Male
14	76	Male
13.5	77	Male

Here we can see that the shoe size more or less increase with the increase of height. And if we consider the correlation between the shoe size and height ,it is 0.875682 ,which is quite high,and shows a positive correlation.

So while deciding the shoe size we can not even ignore the height of the person.

So the company should produce the shoes according to the modal value depending on the gender ,separately,i.e produce shoe size 6.5,7, and 7.5 for female and 11,12 for males and accornding to the height ,produce size 7 for both the gender in its financial crisis time.

So according to the statistics,they should not change their business model to include only one size of shoes—regardless of height or gender of the wearer.