Question

A numerical description of the outcome of an experiment is a random _________.
(A) Description
(B) Outcome
(C) Number
(D) Variable

Answer 1

Hint: The incomplete statement given in the question ends with “…random______” and you can choose one by one from the given choices to fill into this blank. Consider the terms “Random Description”, ”Random Outcome”, “Random Number” and “Random Variable” and eliminate the terms that do not fit with the given statement according to their meaning or definition.

Complete step-by-step answer:
Here in this problem, we are given an incomplete statement “A numerical description of the outcome of an experiment is a random_______” and four choices to complete the statement. We need to find the appropriate option among the four to complete this sentence.
A random description cannot represent a numerical description of the outcome of an experiment as it is already a description of an experiment and a random description does not describe the experiment numerically. So we can say that the option (A) does not fit with this statement.
A random outcome is just a random result that can be obtained from an action or an experiment. It cannot describe an outcome numerically and hence the option (B) is not the correct answer.
A numerical description of the outcome of an experiment may or may not be in form of a number. A random number can be any random constant value that is not always sufficient to describe an outcome of an experiment numerically. And therefore a random number is not an appropriate choice to complete the above-given statement. Thus, the option (C) cannot be a correct answer.
In probability, we define a random variable as a numerical description of the outcome of a statistical experiment. A random variable that may assume only a finite number or an infinite sequence of values is said to be discrete; one that may assume any value in some interval on the real number line is said to be continuous.
Therefore, a numerical description of the outcome of an experiment is a random variable.
Hence, the option (D) is the correct answer.

Note: In this above question we used the method of elimination of options one by one to find the appropriate answer. An alternate approach is by using the concepts of probability on the given statement. We can directly use the definition of a random variable to complete the blank space in the sentence. In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is described informally as a variable whose values depend on outcomes of a random phenomenon. The formal mathematical treatment of random variables is a topic in probability theory.