Question

\((\mathrm{C} 1, \mathrm{C} 2)\) In a survey of 100 people who had recently purchased motorcycles, data on the following variables were recorded: Gender of purchaser Brand of motorcycle purchased Number of previous motorcycles owned by purchaser Telephone area code of purchaser Weight of motorcycle as equipped at purchase a. Which of these variables are categorical? b. Which of these variables are discrete numerical? c. Which type of graphical display would be an appropriate choice for summarizing the gender data, a bar chart or a dotplot? d. Which type of graphical display would be an appropriate choice for summarizing the weight data, a bar chart or a dotplot?

Short answer

a. The categorical variables are the gender and brand of motorcycle. b. The discrete numerical variables are the number of previous motorcycles owned by the purchaser and the telephone area code. c. A bar chart would be the more appropriate choice for summarizing the gender data, as it's a categorical variable. d. A dot plot would be the more appropriate choice for summarizing the weight data, as it's an infinite numerical variable.

Step-by-step solution

Differentiate Categorical and Discrete Numerical Data

A categorical data is a type of data that can be grouped by categories and does not have a mathematical meaning. The gender of purchaser and brand of motorcycle purchased are categorical variables, as we assign the data into several categories. On the other hand, a discrete numerical variable is a variable for which the possible values constitute a subset of the integers. The number of previous motorcycles owned by purchaser and the telephone area code of purchaser are numerical variables because they can be counted and take on numerical values.

Choosing Graphical Display for Gender Data

For categorical data such, as the gender of the purchaser, it is appropriate to use a bar chart. This is because a bar chart allows for easy comparison of categories.

Choosing Graphical Display for Weight Data

Weight of the motorcycle can be considered continuous numerical data since it can take on any value within a certain range. In this case, a dot plot can be an appropriate selection as it allows to visually see dispersion and central tendency of this type of data.