STATSTISTICS
Decision Tree for Determining Variable Type
Examples
A. Variable: fruit
1. List a set of several possible values for the given variable.
fruit = {apple, orange, grape, melon, peach}
2. Are these values numbers and, if so, are mathematical operations (such as multiplication) meaningful?
No—the type of fruit is not numerical. Thus, this variable is qualitative .
3. Do the values have any meaningful order?
No—the values are simply categories of fruit. The variable is therefore nominal .
B. Variable: drink size
1. List a set of several possible values for the given variable.
drink size = {small, medium, large, extra large}
2. Are these values numbers and, if so, are mathematical operations (such as multiplication) meaningful?
No, they are not numbers, so the variable is qualitative .
3. Do the values have any meaningful order?
Yes. For instance, extra large is greater in size than medium. Thus, the variable is ordinal .
C. Variable: car speed
1. List a set of several possible values for a given variable.
car speed = {0, 5, 25, 60, 200}
2. Are these values numbers and, if so, are mathematical operations (such as multiplication) meaningful?
Yes, the values are numbers, and yes, math operations are meaningful. For example, if a car increases its current speed of 30 miles per hour by another 20 miles per hour, it is traveling at 50 miles per hour (30 + 20 = 50). Thus, the variable is quantitative .
3. Are there “gaps” between any two given values in which the variable has no other defined values?
No. The speed can be 20 or 21, as well as 20.5, 20.01, and so forth. Thus, the variable is continuous .
D. Variable: city residents
1. List a set of several possible values for a given variable.
city residents = {10,000, 25,000, 1,436, 6,200}
2. Are these values numbers and, if so, are mathematical operations (such as multiplication) meaningful?
Yes, the values are numbers, and yes, math operations are meaningful. Thus, the variable is quantitative .
3. Are there “gaps” between any two given values in which the variable has no other defined values?
Yes. The variable can only be a whole number—fractions are not valid. The variable is therefore discrete .
E. Variable: area code
1. List a set of several possible values for a given variable.
area code = {716, 289, 314, 750}
2. Are these values numbers and, if so, are mathematical operations (such as multiplication) meaningful?
Yes, the values are numbers, but mathematical operations are not meaningful. For example, adding 1 to an area code does not yield any systematic result. The variable is therefore qualitative .
3. Do the values have any meaningful order?
No. Although one area code might be greater than another, the order does not translate into any geographical meaning (for example). Thus, the variable is nominal .
1. List a set of several possible values for the given variable.
2. Are these values numbers and, if so, are mathematical operations (such as multiplication) meaningful?
Yes
No
Yes
3. Do the values have any meaningful order?
No
3.1 The variable is ordinal.
3.2 The variable is nominal.
2.2 The variable is qualitative (an attribute).
3.1 The variable is discrete.
Yes
No
3. Are there “gaps” between any two given values in which the variable has no other defined values?
2.1 The variable is quantitative (numerical).
3.2 The variable is continuous.