1. [5 pt.] For each of the following variables about students in RBS, determine whether the variable is categorical or numerical. If the variable is categorical, determine whether the variable is measured on a nominal scale or ordinal scale. If the variable is numerical, determine whether the variable is discrete or continuous and whether it is measured on an interval scale or ratio scale. (a) City where a student was born (b) Absolute distance between a student’s home and a stat. classroom (c) Current account balance of a student’s checking bank account (considering debt/loan) (d) Number of credit cards that a student has (e) Floor level on which a student spent time the most during the last semester

Is a variable that can take one value from a limited set of choices, for example “blood type (A+, AB-,etc)”, “hair color (black, red, etc)”, “country of origin”, “level of instruction (elementary, high school, college, etc)”

The categorical variable is measured in a nominal scale if there is no intrinsic order in the variable, for example if the variable is “gender”, there is no intrinsic reason to think that “male” comes before “female” or vice versa.
The categorical variable is measured in an ordinal scale if there is some intrinsic order in the values. For example if the variable is “level of instruction” we can order it from less to high (elementary, high school, college graduate, masters degree, PhD degree) or from high to low.

Numerical variable

As the name suggests is a variable that can take numerical values, for example “height”, “weight”, “number of people who smoke in Minnesota”

The numerical variable is discrete if it only takes inter values, for example “number of flights that land to JFK airport every day”
The numerical variable is continuous if it can take either integer or non integer values, for example “distance between to points in the plane”

The numerical variable is measured in an interval scale if we can determine both the order and difference between the two numbers but the ratio of the values is meaningless. For example if the variable is “year of birth” 1957 and 2001 would be two instances of the variable but 1957/2001 or 2001/1957 are meaningless.
The numerical variable is measured in a ratio scale if we can determine both the order and difference between the two numbers and the ratio of the values is meaningful. For example if you have two salaries, let's say A=$60,500 and B=$90,750, the ratio 90,750/60,500 =1.5 is meaningful because is telling us that salary B is 50% greater than A.

Once we have these concepts clear, we can determine the type of variable of the problem

(a) City where a student was born

Categorical nominal scale

(b) Absolute distance between a student’s home and a stat. classroom

Numerical ratio scale

(c) Current account balance of a student’s checking bank account (considering debt/loan)

Numerical ratio scale

(d) Number of credit cards that a student has

Numerical discrete interval scale

(e) Floor level on which a student spent time the most during the last semester

Categorical ordinal scale