STAT Questions

Jennifer Nguyen, Ola Abiola, and Parul Jaiswal are degree students from the Humber Fashion Management program. They have been hired by Shoe Global Design Inc. to help creating a new generation of shoes that would be popular among young North American females and would have the potential to capture a large market share. One of the questions that the girls have to analyze is the distribution of shoe sizes of potential buyers. Humber College has about 35,000 full time students; two thirds of them are young females. Girls selected a random sample of female students who agreed to provide their measurements. A shoe size is an indication of the fitting size of a shoe for a person.

There is a number of different shoesize systems used worldwide. Usually, the main parameter is the length of a person's foot commonly defined as the distance between two parallel lines that are perpendicular to the foot and in contact with the most prominent toe and the most prominent part of the heel. In USA and Canada the following table is used.

question: 1 Construct a histogram of foot lengths using the table numbers as bin values. Construct the frequency table and ogive. Use Assignment 1 Data file. Is the distribution symmetric and bell-shaped? What is the most common shoe size of young Canadian females?

Foot length (mm) Women's shoe sizes (US/Canada)

220.1 5

224.4 5.5

228.6 6

232.8 6.5

237.1 7

241.3 7.5

245.5 8

249.8 8.5

254.0 9

258.2 9.5

262.5 10

266.7 10.5

270.9 11

275.2 11.5

279.4 12

283.6 12.5

287.9 13

292.1 13.5

296.3 14

Girls agree that the shoe model under consideration is such that if the buyer's foot length falls

between two table values, the larger number should be considered. Say, for a lady with the

measurement 260 mm, which falls between 258.2 (size 9.5) and 262.5 (size 10), most likely size 10

would be appropriate.

The main question regarding the distribution is whether it is symmetric and bell-shaped. If so, then the classical methods based on z (Normal) or t (Student) distribution can be used for statistical market analysis. If the distribution is skewed or not unimodal, the different statistical tools should be applied. To answer this question girls selected a random sample of 120 Humber female students (see Assignment 1 Data file).

question 2:

One more important issue that girls helped to analyze is shoe colour. A separate survey was conducted through the social network and the female respondents were asked to indicate their preferred summer shoe colour. The survey resulted in the following table.

Shoe Colour Percent

black 1

blue 13

brown 6

green 5

orange 8

purple 10

red 27

white 21

yellow 9

Problem 2. Construct a pie chart representing the distribution of shoe colours. Make sure you label the slices and colour them correspondingly. Use Assignment 1 Data file