Is the eye color of people on commercial aircraft flights a discrete random variable, a continuous random variable, or not a random variable?
A. It is a continuous random variable.
B. It is a discrete random variable.
C. It is not a random variable.
The Correct Answer and Explanation is:
Correct Answer: B. It is a discrete random variable.
Explanation:
To determine the type of variable, we first need to understand what a random variable is. A random variable is a function that assigns numerical values to the outcomes of a random phenomenon. Random variables can be discrete or continuous:
- Discrete random variables take on countable values, such as the number of children in a family, or the outcome of rolling a die (1 to 6).
- Continuous random variables take on an uncountably infinite number of values within a given range, such as height, weight, or temperature, where measurements can take on any value within an interval.
Now let’s analyze the example: eye color of people on commercial aircraft flights.
Eye color refers to categorical values such as brown, blue, green, hazel, gray, etc. Since these are distinct and countable categories, eye color is a qualitative (categorical) variable. However, when used in a statistical context, we often assign numerical codes to these categories (e.g., 1 for brown, 2 for blue, and so on) to allow analysis. Once numerical values are assigned to these categories, we can treat them as a discrete random variable if the outcome (eye color) is subject to chance.
For example, suppose we randomly select a passenger from a commercial flight and record their eye color. The outcome depends on the specific individual selected — a process involving randomness. The number of possible eye colors is finite and countable, so the variable takes on a discrete set of values.
It is not a continuous random variable, because eye color is not measured on a continuum. It is also not “not a random variable”, because if the selection of individuals is random, then eye color becomes a random outcome.
Conclusion:
The eye color of people on commercial aircraft flights is a discrete random variable because it takes on countable, categorical values determined through a random process.
