The two types of quantitative variables are
A. ordinal and ratio.
B. interval and ordinal.
C. nominative and ordinal.
D. interval and ratio.
E. nominative and interval.
The correct answer and explanation is :
The correct answer is D. interval and ratio.
Explanation:
Quantitative variables are those that are measured on a numerical scale and represent quantities. These variables can take on values that are meaningful and allow for mathematical operations such as addition, subtraction, multiplication, and division. Quantitative variables can be classified into two main types: interval and ratio.
1. Interval Variables:
Interval variables are those where the difference between two values is meaningful, but there is no true zero point. This means that while you can measure the difference between values, you cannot say that one value is “twice as much” as another. A common example of interval data is temperature (measured in Celsius or Fahrenheit). The difference between 10°C and 20°C is the same as the difference between 30°C and 40°C. However, 0°C does not represent the absence of temperature—it is simply a point on the scale, so we cannot claim that 20°C is twice as hot as 10°C.
2. Ratio Variables:
Ratio variables have all the properties of interval variables, but they also include a true zero point, which allows for meaningful comparisons involving multiplication and division. In ratio variables, you can make statements such as “twice as much” or “half as much” because the zero point indicates the absence of the quantity being measured. Examples of ratio variables include height, weight, age, and income. For instance, a person who is 200 pounds weighs twice as much as someone who weighs 100 pounds, and a person who is 0 years old has no age.
Why not the other options?
- A. Ordinal and ratio: Ordinal variables refer to categories with a meaningful order but not equal intervals, which is different from quantitative data.
- B. Interval and ordinal: Ordinal variables are categorical with an order, not quantitative.
- C. Nominative and ordinal: Nominative (or nominal) variables are categorical and not quantitative.
- E. Nominative and interval: Nominal variables are categories without any numerical meaning, unlike interval variables.
Thus, the most appropriate classification for quantitative variables is interval and ratio (D).