Question

Classify each of the following variables as either categorical or numerical. For those that are numerical, determine whether they are discrete or continuous.

a. Number of students in a class of 35 who turn in a term paper before the due date.
b. Gender of the next baby born at a particular hospital.
c. Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop.
d. Thickness of the gelatin coating of a vitamin E capsule
e. Birth order classification (only child, firstborn, middle child, lastborn) of a math major

Answer 1

a. Numerical (discrete).

b. Categorical.

c. Numerical (continuous).

d. Numerical (continuous).

e. Categorical.

Explanation:

In Mathematics, a categorical data can be defined as a statistical data type that is used to group informations having the same attributes or characteristics. Some examples of a categorical data are age, gender, race, religion etc.

A numerical data can be defined as a data set that is expressed in numbers only or a data set consisting of numbers rather than words. A numerical data is also known as a quantitative data.

Basically, numerical data are classified into two (2) main categories and these are;

1. Discrete data: a discrete data is a data set in which the number of possible values are either finite or countable. For instance, the value of a fair die, number of sweets in a jar, number of eggs in a crate etc.

2. Continuous data: a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable. Any quantity such as height, volume, weight, density, length, pressure, temperature, speed, distance, time are generally a continuous data.

a. Number of students in a class of 35 who turn in a term paper before the due date: this is a numerical data and it is discrete in nature because the number of possible values are finite or countable.

b. Gender of the next baby born at a particular hospital: this is a categorical data because it contains a nominal variable (gender).

c. Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop: this is a numerical data and it is continuous in nature because the number of possible values are infinite or uncountable.

d. Thickness of the gelatin coating of a vitamin E capsule: this is a numerical data and it is continuous in nature because the number of possible values are infinite or uncountable.

e. Birth order classification (only child, firstborn, middle child, lastborn) of a math major: this is a categorical data because it is used to categorize an information (birth order).